Multiplying a Fraction by a Whole Number — Part 2
4A · Chapter 8 · Lesson 3 · MATH-4A-C08-L03
Learning goal. Simplify products and use partition first, then scale, when efficient.
Before you begin
Recall: 4A Ch6/7: equal partitions, mixed numbers and fraction operations; Multiplying a Fraction by a Whole Number — Part 1. Try these three warm-up problems. If they are difficult, revisit the prerequisite lesson before advancing.
Calculate 2/4 × 8. Give the simplified result.
Show answer & reasoning
8 copies of 2/4 make 16/4 = 4.
Calculate 1/3 × 9. Give the simplified result.
Show answer & reasoning
9 copies of 1/3 make 9/3 = 3.
Calculate 6/10 × 6. Give the simplified result.
Show answer & reasoning
6 copies of 6/10 make 36/10 = 3 3/5.
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
A fraction times a whole number can often be simplified efficiently by dividing before multiplying. For (3/4)×20, split 20 into four groups of five, then take three groups to get 15. This is the same result as (3×20)/4. Explain why changing calculation order preserves the value.
Model it: whole bar divided into four shares. 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 1/2 × 5. Give the simplified result.
5 copies of 1/2 make 5/2 = 2 1/2.
Check your understanding 1
Calculate 4/10 × 2. Give the simplified result.
Show answer & reasoning
2 copies of 4/10 make 8/10 = 4/5.
Worked example 2
Calculate 5/10 × 8. Give the simplified result.
8 copies of 5/10 make 40/10 = 4.
Check your understanding 2
Calculate 1/4 × 2. Give the simplified result.
Show answer & reasoning
2 copies of 1/4 make 2/4 = 1/2.
Worked example 3
Calculate 1/5 × 3. Give the simplified result.
3 copies of 1/5 make 3/5 = 3/5.
Check your understanding 3
Calculate 2/4 × 6. Give the simplified result.
Show answer & reasoning
6 copies of 2/4 make 12/4 = 3.
Guided practice
Calculate 1/3 × 3. Give the simplified result.
Show answer & reasoning
3 copies of 1/3 make 3/3 = 1.
Calculate 7/8 × 3. Give the simplified result.
Show answer & reasoning
3 copies of 7/8 make 21/8 = 2 5/8.
Calculate 2/4 × 7. Give the simplified result.
Show answer & reasoning
7 copies of 2/4 make 14/4 = 3 1/2.
Calculate 1/6 × 3. Give the simplified result.
Show answer & reasoning
3 copies of 1/6 make 3/6 = 1/2.
Calculate 1/4 × 4. Give the simplified result.
Show answer & reasoning
4 copies of 1/4 make 4/4 = 1.
Independent practice
Calculate 2/6 × 7. Give the simplified result.
Show answer & reasoning
7 copies of 2/6 make 14/6 = 2 1/3.
Calculate 1/2 × 4. Give the simplified result.
Show answer & reasoning
4 copies of 1/2 make 4/2 = 2.
Calculate 4/8 × 2. Give the simplified result.
Show answer & reasoning
2 copies of 4/8 make 8/8 = 1.
Calculate 2/10 × 3. Give the simplified result.
Show answer & reasoning
3 copies of 2/10 make 6/10 = 3/5.
Calculate 2/4 × 2. Give the simplified result.
Show answer & reasoning
2 copies of 2/4 make 4/4 = 1.
Calculate 1/10 × 7. Give the simplified result.
Show answer & reasoning
7 copies of 1/10 make 7/10 = 7/10.
Calculate 8/10 × 6. Give the simplified result.
Show answer & reasoning
6 copies of 8/10 make 48/10 = 4 4/5.
Calculate 1/2 × 7. Give the simplified result.
Show answer & reasoning
7 copies of 1/2 make 7/2 = 3 1/2.
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 2/3 × 7. Give the simplified result.
Show answer & reasoning
7 copies of 2/3 make 14/3 = 4 2/3.
Exit check
Calculate 7/8 × 9. Give the simplified result.
Show answer & reasoning
9 copies of 7/8 make 63/8 = 7 7/8.
Calculate 3/4 × 3. Give the simplified result.
Show answer & reasoning
3 copies of 3/4 make 9/4 = 2 1/4.
Calculate 2/3 × 4. Give the simplified result.
Show answer & reasoning
4 copies of 2/3 make 8/3 = 2 2/3.