Multiplying a Fraction by a Whole Number — Part 1
4A · Chapter 8 · Lesson 2 · MATH-4A-C08-L02
Learning goal. Relate repeated addition of equal fractional parts to multiplication.
Before you begin
Recall: 4A Ch6/7: equal partitions, mixed numbers and fraction operations; Multiplying a Unit Fraction by a Whole Number. Try these three warm-up problems. If they are difficult, revisit the prerequisite lesson before advancing.
What is 1/5 of 30 counters?
Show answer & reasoning
Partition 30 into 5 equal groups: 30 ÷ 5 = 6.
What is 1/6 of 18 counters?
Show answer & reasoning
Partition 18 into 6 equal groups: 18 ÷ 6 = 3.
What is 1/2 of 18 counters?
Show answer & reasoning
Partition 18 into 2 equal groups: 18 ÷ 2 = 9.
Key vocabulary
- unit fraction
- fraction with numerator one
- fraction of a set
- part of a discrete collection
- reference whole
- quantity to which a fraction applies
- remaining amount
- quantity after some part is removed
Understand the concept
Multiplying a fraction by a whole number can mean repeated addition of that fraction. Three copies of 2/5 form 6/5, which is 1 1/5. The denominator names part size, and the numerator counts parts. Use fraction strips before relying on a memorized multiplication rule.
Model it: repeated fraction strips. Explain what every part of the model represents, then write a matching equation.
Fully worked examples
Read the problem first and predict the answer. Then study how each quantity is represented and calculated.
Worked example 1
Calculate 4/6 × 2. Give the simplified result.
2 copies of 4/6 make 8/6 = 1 1/3.
Check your understanding 1
Calculate 3/6 × 7. Give the simplified result.
Show answer & reasoning
7 copies of 3/6 make 21/6 = 3 1/2.
Worked example 2
Calculate 1/2 × 6. Give the simplified result.
6 copies of 1/2 make 6/2 = 3.
Check your understanding 2
Calculate 2/5 × 3. Give the simplified result.
Show answer & reasoning
3 copies of 2/5 make 6/5 = 1 1/5.
Worked example 3
Calculate 1/4 × 5. Give the simplified result.
5 copies of 1/4 make 5/4 = 1 1/4.
Check your understanding 3
Calculate 1/4 × 6. Give the simplified result.
Show answer & reasoning
6 copies of 1/4 make 6/4 = 1 1/2.
Guided practice
Calculate 1/5 × 4. Give the simplified result.
Show answer & reasoning
4 copies of 1/5 make 4/5 = 4/5.
Calculate 3/5 × 4. Give the simplified result.
Show answer & reasoning
4 copies of 3/5 make 12/5 = 2 2/5.
Calculate 2/3 × 6. Give the simplified result.
Show answer & reasoning
6 copies of 2/3 make 12/3 = 4.
Calculate 1/2 × 2. Give the simplified result.
Show answer & reasoning
2 copies of 1/2 make 2/2 = 1.
Calculate 1/10 × 5. Give the simplified result.
Show answer & reasoning
5 copies of 1/10 make 5/10 = 1/2.
Independent practice
Calculate 1/4 × 3. Give the simplified result.
Show answer & reasoning
3 copies of 1/4 make 3/4 = 3/4.
Calculate 1/2 × 5. Give the simplified result.
Show answer & reasoning
5 copies of 1/2 make 5/2 = 2 1/2.
Calculate 6/8 × 4. Give the simplified result.
Show answer & reasoning
4 copies of 6/8 make 24/8 = 3.
Calculate 3/6 × 3. Give the simplified result.
Show answer & reasoning
3 copies of 3/6 make 9/6 = 1 1/2.
Calculate 3/6 × 8. Give the simplified result.
Show answer & reasoning
8 copies of 3/6 make 24/6 = 4.
Calculate 5/8 × 6. Give the simplified result.
Show answer & reasoning
6 copies of 5/8 make 30/8 = 3 3/4.
Calculate 2/10 × 6. Give the simplified result.
Show answer & reasoning
6 copies of 2/10 make 12/10 = 1 1/5.
Calculate 3/6 × 6. Give the simplified result.
Show answer & reasoning
6 copies of 3/6 make 18/6 = 3.
Challenge and transfer
Explain the relationships and justify your method. Multiple correct approaches may be accepted if the reasoning is valid.
A student says (2/5) × 3 equals 2/15 because the denominator should multiply by three. Correct and explain.
Show answer & reasoning
Three copies of two fifths give six fifths, or one and one fifth.
Calculate 3/8 × 8. Give the simplified result.
Show answer & reasoning
8 copies of 3/8 make 24/8 = 3.
Exit check
Calculate 1/6 × 8. Give the simplified result.
Show answer & reasoning
8 copies of 1/6 make 8/6 = 1 1/3.
Calculate 1/3 × 9. Give the simplified result.
Show answer & reasoning
9 copies of 1/3 make 9/3 = 3.
Calculate 1/2 × 3. Give the simplified result.
Show answer & reasoning
3 copies of 1/2 make 3/2 = 1 1/2.