Chapter 27: Multiplying Unit Fractions by Whole Numbers
Learn Grade 4 mathematics with very-beginner explanations, original worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Multiplying Unit Fractions by Whole Numbers in original, simple language with step-by-step reasoning, worked examples, practice exercises, common mistakes, and review questions.
27.1 Repeated addition of one half
A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.
Beginner Explanation
First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.
10 Worked Examples with Answers
Worked Example 1
Problem: A model has 6 equal parts and 1 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 1/6
Worked Example 2
Problem: A model has 6 equal parts and 4 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 4/6
Worked Example 3
Problem: A model has 6 equal parts and 3 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 3/6
Worked Example 4
Problem: A model has 8 equal parts and 8 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 8/8
Worked Example 5
Problem: A model has 4 equal parts and 1 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 1/4
Worked Example 6
Problem: A model has 5 equal parts and 2 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 2/5
Worked Example 7
Problem: A model has 3 equal parts and 3 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 3/3
Worked Example 8
Problem: A model has 3 equal parts and 2 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 2/3
Worked Example 9
Problem: A model has 8 equal parts and 3 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 3/8
Worked Example 10
Problem: A model has 5 equal parts and 3 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 3/5
Practice Exercise
Create and solve one new example of Repeated addition of one half. Show the steps and explain how you checked it.
Common Mistake
Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.
27.2 Repeated addition of one third
A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.
Beginner Explanation
First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.
10 Worked Examples with Answers
Worked Example 1
Problem: A model has 6 equal parts and 4 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 4/6
Worked Example 2
Problem: A model has 4 equal parts and 3 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 3/4
Worked Example 3
Problem: A model has 8 equal parts and 1 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 1/8
Worked Example 4
Problem: A model has 6 equal parts and 5 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 5/6
Worked Example 5
Problem: A model has 10 equal parts and 1 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 1/10
Worked Example 6
Problem: A model has 5 equal parts and 1 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 1/5
Worked Example 7
Problem: A model has 6 equal parts and 4 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 4/6
Worked Example 8
Problem: A model has 4 equal parts and 1 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 1/4
Worked Example 9
Problem: A model has 6 equal parts and 5 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 5/6
Worked Example 10
Problem: A model has 6 equal parts and 1 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 1/6
Practice Exercise
Create and solve one new example of Repeated addition of one third. Show the steps and explain how you checked it.
Common Mistake
Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.
27.3 Repeated addition of one fourth
A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.
Beginner Explanation
First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.
10 Worked Examples with Answers
Worked Example 1
Problem: A model has 5 equal parts and 5 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 5/5
Worked Example 2
Problem: A model has 3 equal parts and 2 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 2/3
Worked Example 3
Problem: A model has 8 equal parts and 3 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 3/8
Worked Example 4
Problem: A model has 4 equal parts and 4 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 4/4
Worked Example 5
Problem: A model has 5 equal parts and 5 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 5/5
Worked Example 6
Problem: A model has 10 equal parts and 5 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 5/10
Worked Example 7
Problem: A model has 4 equal parts and 3 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 3/4
Worked Example 8
Problem: A model has 6 equal parts and 1 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 1/6
Worked Example 9
Problem: A model has 3 equal parts and 1 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 1/3
Worked Example 10
Problem: A model has 5 equal parts and 3 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 3/5
Practice Exercise
Create and solve one new example of Repeated addition of one fourth. Show the steps and explain how you checked it.
Common Mistake
Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.
27.4 Repeated addition of one fifth
A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.
Beginner Explanation
First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.
10 Worked Examples with Answers
Worked Example 1
Problem: A model has 10 equal parts and 8 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 8/10
Worked Example 2
Problem: A model has 3 equal parts and 1 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 1/3
Worked Example 3
Problem: A model has 6 equal parts and 4 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 4/6
Worked Example 4
Problem: A model has 6 equal parts and 4 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 4/6
Worked Example 5
Problem: A model has 10 equal parts and 1 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 1/10
Worked Example 6
Problem: A model has 3 equal parts and 2 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 2/3
Worked Example 7
Problem: A model has 5 equal parts and 3 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 3/5
Worked Example 8
Problem: A model has 2 equal parts and 1 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 1/2
Worked Example 9
Problem: A model has 2 equal parts and 1 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 1/2
Worked Example 10
Problem: A model has 10 equal parts and 8 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 8/10
Practice Exercise
Create and solve one new example of Repeated addition of one fifth. Show the steps and explain how you checked it.
Common Mistake
Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.
27.5 Repeated addition of one sixth
A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.
Beginner Explanation
First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.
10 Worked Examples with Answers
Worked Example 1
Problem: A model has 5 equal parts and 4 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 4/5
Worked Example 2
Problem: A model has 5 equal parts and 4 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 4/5
Worked Example 3
Problem: A model has 10 equal parts and 3 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 3/10
Worked Example 4
Problem: A model has 8 equal parts and 6 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 6/8
Worked Example 5
Problem: A model has 2 equal parts and 1 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 1/2
Worked Example 6
Problem: A model has 2 equal parts and 2 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 2/2
Worked Example 7
Problem: A model has 4 equal parts and 1 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 1/4
Worked Example 8
Problem: A model has 6 equal parts and 1 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 1/6
Worked Example 9
Problem: A model has 8 equal parts and 8 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 8/8
Worked Example 10
Problem: A model has 6 equal parts and 4 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 4/6
Practice Exercise
Create and solve one new example of Repeated addition of one sixth. Show the steps and explain how you checked it.
Common Mistake
Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.
27.6 Repeated addition of one eighth
A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.
Beginner Explanation
First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.
10 Worked Examples with Answers
Worked Example 1
Problem: A model has 10 equal parts and 5 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 5/10
Worked Example 2
Problem: A model has 6 equal parts and 2 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 2/6
Worked Example 3
Problem: A model has 4 equal parts and 2 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 2/4
Worked Example 4
Problem: A model has 4 equal parts and 1 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 1/4
Worked Example 5
Problem: A model has 8 equal parts and 2 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 2/8
Worked Example 6
Problem: A model has 3 equal parts and 3 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 3/3
Worked Example 7
Problem: A model has 5 equal parts and 5 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 5/5
Worked Example 8
Problem: A model has 5 equal parts and 3 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 3/5
Worked Example 9
Problem: A model has 2 equal parts and 1 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 1/2
Worked Example 10
Problem: A model has 4 equal parts and 4 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 4/4
Practice Exercise
Create and solve one new example of Repeated addition of one eighth. Show the steps and explain how you checked it.
Common Mistake
Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.
27.7 Repeated addition of one tenth
A decimal with one digit after the decimal point represents tenths. Tenths can also be written as fractions with denominator 10. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.
Beginner Explanation
First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.
10 Worked Examples with Answers
Worked Example 1
Problem: Write 7/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.7
Worked Example 2
Problem: Write 5/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.5
Worked Example 3
Problem: Write 4/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.4
Worked Example 4
Problem: Write 3/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.3
Worked Example 5
Problem: Write 2/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.2
Worked Example 6
Problem: Write 8/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.8
Worked Example 7
Problem: Write 1/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.1
Worked Example 8
Problem: Write 4/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.4
Worked Example 9
Problem: Write 7/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.7
Worked Example 10
Problem: Write 1/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.1
Practice Exercise
Create and solve one new example of Repeated addition of one tenth. Show the steps and explain how you checked it.
Common Mistake
Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.
27.8 Writing repeated addition as multiplication
Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.
Beginner Explanation
First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.
10 Worked Examples with Answers
Worked Example 1
Problem: Calculate 12 × 6.
- Break 12 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 72
Worked Example 2
Problem: Calculate 2 × 7.
- Break 2 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 14
Worked Example 3
Problem: Calculate 8 × 7.
- Break 8 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 56
Worked Example 4
Problem: Calculate 8 × 6.
- Break 8 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 48
Worked Example 5
Problem: Calculate 7 × 5.
- Break 7 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 35
Worked Example 6
Problem: Calculate 2 × 8.
- Break 2 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 16
Worked Example 7
Problem: Calculate 10 × 7.
- Break 10 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 70
Worked Example 8
Problem: Calculate 2 × 5.
- Break 2 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 10
Worked Example 9
Problem: Calculate 2 × 3.
- Break 2 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 6
Worked Example 10
Problem: Calculate 3 × 4.
- Break 3 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 12
Practice Exercise
Create and solve one new example of Writing repeated addition as multiplication. Show the steps and explain how you checked it.
Common Mistake
Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.
27.9 Using models for unit-fraction multiplication
A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.
Beginner Explanation
First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.
10 Worked Examples with Answers
Worked Example 1
Problem: Calculate 11 × 7.
- Break 11 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 77
Worked Example 2
Problem: Calculate 3 × 5.
- Break 3 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 15
Worked Example 3
Problem: Calculate 12 × 7.
- Break 12 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 84
Worked Example 4
Problem: Calculate 3 × 3.
- Break 3 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 9
Worked Example 5
Problem: Calculate 6 × 7.
- Break 6 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 42
Worked Example 6
Problem: Calculate 7 × 6.
- Break 7 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 42
Worked Example 7
Problem: Calculate 5 × 8.
- Break 5 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 40
Worked Example 8
Problem: Calculate 9 × 5.
- Break 9 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 45
Worked Example 9
Problem: Calculate 7 × 6.
- Break 7 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 42
Worked Example 10
Problem: Calculate 5 × 6.
- Break 5 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 30
Practice Exercise
Create and solve one new example of Using models for unit-fraction multiplication. Show the steps and explain how you checked it.
Common Mistake
Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.
27.10 Counting and multiplication connections
Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.
Beginner Explanation
First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.
10 Worked Examples with Answers
Worked Example 1
Problem: Calculate 4 × 2.
- Break 4 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 8
Worked Example 2
Problem: Calculate 6 × 8.
- Break 6 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 48
Worked Example 3
Problem: Calculate 12 × 5.
- Break 12 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 60
Worked Example 4
Problem: Calculate 4 × 6.
- Break 4 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 24
Worked Example 5
Problem: Calculate 3 × 3.
- Break 3 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 9
Worked Example 6
Problem: Calculate 12 × 6.
- Break 12 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 72
Worked Example 7
Problem: Calculate 3 × 3.
- Break 3 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 9
Worked Example 8
Problem: Calculate 12 × 3.
- Break 12 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 36
Worked Example 9
Problem: Calculate 12 × 3.
- Break 12 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 36
Worked Example 10
Problem: Calculate 11 × 2.
- Break 11 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 22
Practice Exercise
Create and solve one new example of Counting and multiplication connections. Show the steps and explain how you checked it.
Common Mistake
Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.
27.11 Whole numbers times unit fractions
A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.
Beginner Explanation
First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.
10 Worked Examples with Answers
Worked Example 1
Problem: A model has 10 equal parts and 3 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 3/10
Worked Example 2
Problem: A model has 3 equal parts and 3 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 3/3
Worked Example 3
Problem: A model has 3 equal parts and 3 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 3/3
Worked Example 4
Problem: A model has 10 equal parts and 7 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 7/10
Worked Example 5
Problem: A model has 4 equal parts and 4 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 4/4
Worked Example 6
Problem: A model has 3 equal parts and 1 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 1/3
Worked Example 7
Problem: A model has 3 equal parts and 1 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 1/3
Worked Example 8
Problem: A model has 6 equal parts and 6 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 6/6
Worked Example 9
Problem: A model has 4 equal parts and 4 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 4/4
Worked Example 10
Problem: A model has 5 equal parts and 4 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 4/5
Practice Exercise
Create and solve one new example of Whole numbers times unit fractions. Show the steps and explain how you checked it.
Common Mistake
Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.
27.12 Real-life fraction-group problems
A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.
Beginner Explanation
First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.
10 Worked Examples with Answers
Worked Example 1
Problem: A model has 4 equal parts and 1 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 1/4
Worked Example 2
Problem: A model has 8 equal parts and 7 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 7/8
Worked Example 3
Problem: A model has 3 equal parts and 3 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 3/3
Worked Example 4
Problem: A model has 8 equal parts and 5 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 5/8
Worked Example 5
Problem: A model has 2 equal parts and 1 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 1/2
Worked Example 6
Problem: A model has 10 equal parts and 7 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 7/10
Worked Example 7
Problem: A model has 10 equal parts and 4 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 4/10
Worked Example 8
Problem: A model has 5 equal parts and 3 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 3/5
Worked Example 9
Problem: A model has 4 equal parts and 4 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 4/4
Worked Example 10
Problem: A model has 5 equal parts and 1 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 1/5
Practice Exercise
Create and solve one new example of Real-life fraction-group problems. Show the steps and explain how you checked it.
Common Mistake
Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.
30 Review Questions and Answers
Q1. What is important to understand about Repeated addition of one half?
Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.
Q2. What is important to understand about Repeated addition of one third?
Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.
Q3. What is important to understand about Repeated addition of one fourth?
Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.
Q4. What is important to understand about Repeated addition of one fifth?
Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.
Q5. What is important to understand about Repeated addition of one sixth?
Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.
Q6. What is important to understand about Repeated addition of one eighth?
Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.
Q7. What is important to understand about Repeated addition of one tenth?
Answer: A decimal with one digit after the decimal point represents tenths. Tenths can also be written as fractions with denominator 10.
Q8. What is important to understand about Writing repeated addition as multiplication?
Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.
Q9. What is important to understand about Using models for unit-fraction multiplication?
Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.
Q10. What is important to understand about Counting and multiplication connections?
Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.
Q11. What is important to understand about Whole numbers times unit fractions?
Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.
Q12. What is important to understand about Real-life fraction-group problems?
Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.
Q13. How would you explain Repeated addition of one half?
Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.
Q14. How would you explain Repeated addition of one third?
Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.
Q15. How would you explain Repeated addition of one fourth?
Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.
Q16. How would you explain Repeated addition of one fifth?
Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.
Q17. How would you explain Repeated addition of one sixth?
Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.
Q18. How would you explain Repeated addition of one eighth?
Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.
Q19. How would you explain Repeated addition of one tenth?
Answer: A decimal with one digit after the decimal point represents tenths. Tenths can also be written as fractions with denominator 10.
Q20. How would you explain Writing repeated addition as multiplication?
Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.
Q21. How would you explain Using models for unit-fraction multiplication?
Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.
Q22. How would you explain Counting and multiplication connections?
Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.
Q23. How would you explain Whole numbers times unit fractions?
Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.
Q24. How would you explain Real-life fraction-group problems?
Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.
Q25. What should a beginner check when working with Repeated addition of one half?
Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.
Q26. What should a beginner check when working with Repeated addition of one third?
Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.
Q27. What should a beginner check when working with Repeated addition of one fourth?
Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.
Q28. What should a beginner check when working with Repeated addition of one fifth?
Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.
Q29. What should a beginner check when working with Repeated addition of one sixth?
Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.
Q30. What should a beginner check when working with Repeated addition of one eighth?
Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.