Multiplying a Whole Number by a Fraction — Part 1
4A · Chapter 8 · Lesson 5 · MATH-4A-C08-L05
Learning goal. Interpret a whole quantity multiplied by a proper fraction as a part-of operation.
Before you begin
Recall: 4A Ch6/7: equal partitions, mixed numbers and fraction operations; Fraction of a Set. Try these three warm-up problems. If they are difficult, revisit the prerequisite lesson before advancing.
Find 5/6 of a set of 18 objects.
Show answer & reasoning
Divide into 6 equal groups of 3, then choose 5 groups for 15 objects.
Find 2/6 of a set of 30 objects.
Show answer & reasoning
Divide into 6 equal groups of 5, then choose 2 groups for 10 objects.
Find 3/4 of a set of 28 objects.
Show answer & reasoning
Divide into 4 equal groups of 7, then choose 3 groups for 21 objects.
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 positive whole number by a proper fraction less than one finds a part of that whole. Thus 24×3/4 is 18, which is smaller than 24. This is a useful check because multiplying by a fraction does not always make a positive quantity larger.
Model it: part-of-whole bar. 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
Find 7/10 of a set of 60 objects.
Divide into 10 equal groups of 6, then choose 7 groups for 42 objects.
Check your understanding 1
Find 3/6 of a set of 18 objects.
Show answer & reasoning
Divide into 6 equal groups of 3, then choose 3 groups for 9 objects.
Worked example 2
Find 1/2 of a set of 10 objects.
Divide into 2 equal groups of 5, then choose 1 groups for 5 objects.
Check your understanding 2
Find 2/5 of a set of 20 objects.
Show answer & reasoning
Divide into 5 equal groups of 4, then choose 2 groups for 8 objects.
Worked example 3
Find 1/2 of a set of 12 objects.
Divide into 2 equal groups of 6, then choose 1 groups for 6 objects.
Check your understanding 3
Find 2/5 of a set of 35 objects.
Show answer & reasoning
Divide into 5 equal groups of 7, then choose 2 groups for 14 objects.
Guided practice
Find 1/2 of a set of 16 objects.
Show answer & reasoning
Divide into 2 equal groups of 8, then choose 1 groups for 8 objects.
Find 1/3 of a set of 9 objects.
Show answer & reasoning
Divide into 3 equal groups of 3, then choose 1 groups for 3 objects.
Find 2/10 of a set of 70 objects.
Show answer & reasoning
Divide into 10 equal groups of 7, then choose 2 groups for 14 objects.
Find 2/5 of a set of 30 objects.
Show answer & reasoning
Divide into 5 equal groups of 6, then choose 2 groups for 12 objects.
Find 2/4 of a set of 32 objects.
Show answer & reasoning
Divide into 4 equal groups of 8, then choose 2 groups for 16 objects.
Independent practice
Find 2/10 of a set of 20 objects.
Show answer & reasoning
Divide into 10 equal groups of 2, then choose 2 groups for 4 objects.
Find 1/2 of a set of 18 objects.
Show answer & reasoning
Divide into 2 equal groups of 9, then choose 1 groups for 9 objects.
Find 1/2 of a set of 6 objects.
Show answer & reasoning
Divide into 2 equal groups of 3, then choose 1 groups for 3 objects.
Find 7/8 of a set of 48 objects.
Show answer & reasoning
Divide into 8 equal groups of 6, then choose 7 groups for 42 objects.
Find 9/10 of a set of 80 objects.
Show answer & reasoning
Divide into 10 equal groups of 8, then choose 9 groups for 72 objects.
Find 9/10 of a set of 20 objects.
Show answer & reasoning
Divide into 10 equal groups of 2, then choose 9 groups for 18 objects.
Find 1/3 of a set of 21 objects.
Show answer & reasoning
Divide into 3 equal groups of 7, then choose 1 groups for 7 objects.
Find 6/10 of a set of 20 objects.
Show answer & reasoning
Divide into 10 equal groups of 2, then choose 6 groups for 12 objects.
Challenge and transfer
Explain the relationships and justify your method. Multiple correct approaches may be accepted if the reasoning is valid.
A learner says 24 × 3/4 must be bigger than 24 because this is multiplication. Correct the claim.
Show answer & reasoning
Multiplying by a positive proper fraction takes part of the whole: three groups of six are eighteen.
Find 1/2 of a set of 4 objects.
Show answer & reasoning
Divide into 2 equal groups of 2, then choose 1 groups for 2 objects.
Exit check
Find 1/10 of a set of 80 objects.
Show answer & reasoning
Divide into 10 equal groups of 8, then choose 1 groups for 8 objects.
Find 3/4 of a set of 8 objects.
Show answer & reasoning
Divide into 4 equal groups of 2, then choose 3 groups for 6 objects.
Find 5/8 of a set of 48 objects.
Show answer & reasoning
Divide into 8 equal groups of 6, then choose 5 groups for 30 objects.