Equivalent Fractions and Simplifying
Equivalent fractions are different fractions that show the same amount, and by Year 5 they become a tool for comparing, ordering and simplifying. In Year 5 (ACARA v9), students use equivalence to compare and order fractions with related denominators — where one denominator is a multiple of another, like halves, quarters and eighths — and to simplify fractions to their smallest form. The key idea: to compare fractions fairly, you rewrite them with the same denominator so the pieces are the same size, then the one with more pieces is larger. Simplifying works the other way — dividing top and bottom by the same number to write a fraction as simply as possible.
Worked examples
Which is bigger: 3/4 or 5/8?
Rewrite 3/4 with denominator 8: 3/4 = 6/8. Now compare 6/8 and 5/8 — same-sized pieces. 6/8 has more.
Answer: 3/4 is bigger
Order from smallest to largest: 1/2, 3/8, 3/4.
Rewrite all as eighths: 1/2 = 4/8, 3/4 = 6/8, and 3/8 stays. Order the eighths: 3/8, 4/8, 6/8.
Answer: 3/8, 1/2, 3/4
Simplify 6/8 to its smallest form.
Divide top and bottom by the same number. Both divide by 2: 6/8 = 3/4. Nothing divides 3 and 4 further.
Answer: 3/4
Real-world: one jug is 2/3 full, another is 5/6 full. Which has more?
Rewrite 2/3 with denominator 6: 2/3 = 4/6. Compare 4/6 and 5/6. 5/6 has more.
Answer: The second jug (5/6) has more
Tips
- •To compare, make the denominators match first. Rewrite the fractions with a common denominator so the pieces are the same size — then just compare the top numbers.
- •Simplify by dividing, not guessing. Find a number that divides both top and bottom (a common factor) and divide by it; repeat until nothing divides both.
- •Common mistake to watch for: children sometimes compare fractions by the top number alone, thinking 3/8 is bigger than 1/2 because 3 is more than 1. The size of the pieces matters — 1/2 is 4/8, which beats 3/8.
- •Use a fraction wall. Lining up halves, quarters and eighths on a wall shows at a glance which fraction is bigger and which fractions are equal.