Fraction of a Set
4A · Chapter 8 · Lesson 4 · MATH-4A-C08-L04
Learning goal. Partition object collections into equal groups and select the stated fractional count.
Before you begin
Recall: 4A Ch6/7: equal partitions, mixed numbers and fraction operations; Multiplying a Fraction by a Whole Number — Part 2. Try these three warm-up problems. If they are difficult, revisit the prerequisite lesson before advancing.
Calculate 3/4 × 2. Give the simplified result.
Show answer & reasoning
2 copies of 3/4 make 6/4 = 1 1/2.
Calculate 3/8 × 3. Give the simplified result.
Show answer & reasoning
3 copies of 3/8 make 9/8 = 1 1/8.
Calculate 4/8 × 4. Give the simplified result.
Show answer & reasoning
4 copies of 4/8 make 16/8 = 2.
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 of a set means selecting an equal portion of discrete objects. Three fifths of 20 buttons means create five equal groups of four, then choose three groups for twelve buttons. If the set can't be equally divided into whole objects, interpret the question and units carefully instead of inventing broken buttons.
Model it: equal groups of counters with a selected portion. 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 4/5 of a set of 45 objects.
Divide into 5 equal groups of 9, then choose 4 groups for 36 objects.
Check your understanding 1
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.
Worked example 2
Find 1/10 of a set of 80 objects.
Divide into 10 equal groups of 8, then choose 1 groups for 8 objects.
Check your understanding 2
Find 3/8 of a set of 32 objects.
Show answer & reasoning
Divide into 8 equal groups of 4, then choose 3 groups for 12 objects.
Worked example 3
Find 2/4 of a set of 16 objects.
Divide into 4 equal groups of 4, then choose 2 groups for 8 objects.
Check your understanding 3
Find 1/4 of a set of 24 objects.
Show answer & reasoning
Divide into 4 equal groups of 6, then choose 1 groups for 6 objects.
Guided practice
Find 3/10 of a set of 20 objects.
Show answer & reasoning
Divide into 10 equal groups of 2, then choose 3 groups for 6 objects.
Find 4/8 of a set of 48 objects.
Show answer & reasoning
Divide into 8 equal groups of 6, then choose 4 groups for 24 objects.
Find 1/10 of a set of 40 objects.
Show answer & reasoning
Divide into 10 equal groups of 4, then choose 1 groups for 4 objects.
Find 5/8 of a set of 72 objects.
Show answer & reasoning
Divide into 8 equal groups of 9, then choose 5 groups for 45 objects.
Find 1/2 of a set of 12 objects.
Show answer & reasoning
Divide into 2 equal groups of 6, then choose 1 groups for 6 objects.
Independent practice
Find 3/4 of a set of 24 objects.
Show answer & reasoning
Divide into 4 equal groups of 6, then choose 3 groups for 18 objects.
Find 4/6 of a set of 12 objects.
Show answer & reasoning
Divide into 6 equal groups of 2, then choose 4 groups for 8 objects.
Find 1/2 of a set of 10 objects.
Show answer & reasoning
Divide into 2 equal groups of 5, then choose 1 groups for 5 objects.
Find 1/2 of a set of 14 objects.
Show answer & reasoning
Divide into 2 equal groups of 7, then choose 1 groups for 7 objects.
Find 1/8 of a set of 16 objects.
Show answer & reasoning
Divide into 8 equal groups of 2, then choose 1 groups for 2 objects.
Find 7/8 of a set of 24 objects.
Show answer & reasoning
Divide into 8 equal groups of 3, then choose 7 groups for 21 objects.
Find 2/5 of a set of 40 objects.
Show answer & reasoning
Divide into 5 equal groups of 8, then choose 2 groups for 16 objects.
Find 4/6 of a set of 30 objects.
Show answer & reasoning
Divide into 6 equal groups of 5, then choose 4 groups for 20 objects.
Challenge and transfer
Explain the relationships and justify your method. Multiple correct approaches may be accepted if the reasoning is valid.
How many buttons are in three-fifths of a set of 20 buttons? Explain the equal groups.
Show answer & reasoning
Twenty makes five groups of four; three groups contain twelve buttons.
Find 2/3 of a set of 15 objects.
Show answer & reasoning
Divide into 3 equal groups of 5, then choose 2 groups for 10 objects.
Exit check
Find 1/4 of a set of 32 objects.
Show answer & reasoning
Divide into 4 equal groups of 8, then choose 1 groups for 8 objects.
Find 3/4 of a set of 12 objects.
Show answer & reasoning
Divide into 4 equal groups of 3, then choose 3 groups for 9 objects.
Find 1/4 of a set of 8 objects.
Show answer & reasoning
Divide into 4 equal groups of 2, then choose 1 groups for 2 objects.