Chapter 3: Fractions and Fraction Reasoning
Fractions and Fraction Reasoning
Use equivalent fractions to compare, simplify and calculate without losing the size of the parts.
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Workbook pages
Fun Maths Book 3 pages 20-34
Simplify fractions, use equivalent fractions, calculate with fractions and find fractions of amounts.
Think first
Good mathematicians decide what the question is asking before they calculate.
- 1Are the parts the same size?
- 2Do we need a common denominator?
- 3Can the fraction be simplified?
- 4Does the answer make sense as less than one, equal to one, or more than one?
Visual teaching
See the method
Fraction bars split into common denominators, shaded parts combine, and a reciprocal flip is shown with labelled numerator and denominator.
3/4 = 15/20
2/5 = 8/20
23/20 = 1 3/20
Same value, new name
Equivalent fractions let you compare and calculate with same-sized parts.
Worked examples
Simplify 18/24.
Step 1: First, what are we trying to do?
We want an equivalent fraction with smaller numbers.
Why: Simplifying changes the name of the fraction, not its value.
Step 2: What common factor can divide both numbers?
18 and 24 can both be divided by 6.
Why: We must divide the numerator and denominator by the same number.
Be careful: Dividing only the top number changes the value.
Step 3: Now divide both parts.
18 ÷ 6 = 3 and 24 ÷ 6 = 4.
Why: The fraction becomes 3/4.
Common mistake: Dividing the numerator and forgetting the denominator.
Find 3/4 + 2/5.
Step 1: Can we add the numerators straight away?
No. Fourths and fifths are different-sized parts.
Why: For addition, the denominators must show the same-sized pieces.
Step 2: What common denominator can we use?
20 works because 4 x 5 = 20.
Why: Twentieths can represent both fourths and fifths.
Step 3: Rename both fractions and add.
3/4 = 15/20 and 2/5 = 8/20. Then 15/20 + 8/20 = 23/20.
Why: Now the parts are the same size, so we add the numerators.
Step 4: Should we leave the answer as an improper fraction?
23/20 = 1 3/20.
Why: The answer is a little more than one whole.
Common mistake: Adding denominators and writing 5/9.
Find 3/5 of 40.
Step 1: What does the denominator tell us?
The denominator 5 tells us to split 40 into 5 equal parts.
Why: One fifth is one of five equal groups.
Step 2: Find one part first.
40 ÷ 5 = 8, so one fifth is 8.
Why: Finding one part makes the rest easier.
Step 3: Now find three parts.
3 fifths is 3 x 8 = 24.
Why: The numerator tells us how many equal parts we need.
Common mistake: Multiplying 40 by 5 instead of dividing into fifths first.
Guided practice
Find 5/6 - 1/4.
Independent practice
Your turn
Simplify 18/24.
Find 1/2 + 1/3.
Find 3/5 of 40.
Mini checkpoint
Check your thinking
Find 2/3 + 1/6.
Find 3/4 of 32.
Which mistake should you avoid when adding 1/2 + 1/3?
Key idea
Fractions work when the size of the parts is clear. For addition and subtraction, make the parts the same size first. Use equivalent fractions to rename values, simplify by dividing both parts, and check whether your final fraction is a sensible size.
Parent signal
If the child adds denominators, return to the visual model of same-sized pieces.