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Mathematics · Year 5 · Chapter 1

Same fraction, different name

Practice

1/2 as sixths: 3/6
1/2 as tenths: 5/10
1/4 as eighths: 2/8
2/3 as sixths: 4/6
3/4 as eighths: 6/8
Simplify 4/8: 1/2
Simplify 3/9: 1/3
Simplify 6/10: 3/5
Bigger: 1/4 or 1/8?: 1/4
Bigger: 1/3 or 1/2?: 1/2

Easy questions

1/2 = ?/8: 8 / 2 = 4, so 1 x 4 = 4 -> 4/8
1/3 = ?/9: 9 / 3 = 3, so 1 x 3 = 3 -> 3/9
Simplify 2/6: divide both by 2 -> 1/3
Simplify 5/10: divide both by 5 -> 1/2
Which is bigger: 1/5 or 1/10?: 1/5 — fewer pieces means bigger pieces

Medium questions

2/3 = ?/12: 12 / 3 = 4, so 2 x 4 = 8 -> 8/12
3/4 = ?/20: 20 / 4 = 5, so 3 x 5 = 15 -> 15/20
Simplify 8/12: common factor 4: 8 / 4 = 2, 12 / 4 = 3 -> 2/3
Simplify 9/12: common factor 3: 9 / 3 = 3, 12 / 3 = 4 -> 3/4
Is 3/4 the same as 6/8?: 6/8 divided by 2 = 3/4 -> yes, equivalent

Hard questions

Which is bigger: 2/3 or 3/4?: make twelfths: 2/3 = 8/12, 3/4 = 9/12 -> 3/4 is bigger
Which is bigger: 3/5 or 5/8?: make fortieths: 3/5 = 24/40, 5/8 = 25/40 -> 5/8 is bigger
Order smallest first: 1/2, 2/5, 3/4: make twentieths: 1/2 = 10/20, 2/5 = 8/20, 3/4 = 15/20 -> 2/5, 1/2, 3/4
A cake is cut into 12. You eat 8 pieces. Simplest form?: 8/12, divide both by 4 -> 2/3
Sam says 1/6 > 1/4 because 6 > 4. Correct?: No — sixths are smaller than quarters, so 1/6 < 1/4

Lesson

More pieces, smaller pieces

The number on the bottom of a fraction — the denominator — tells you how many equal pieces the whole is cut into. It is not an amount on its own. Cut one pizza into 4 and each slice is a quarter; cut the same pizza into 8 and each slice is an eighth. There are more slices, but every slice is smaller. So 1/8 is smaller than 1/4, even though 8 is a bigger number than 4. That is the trap most people fall into: a bigger bottom number means smaller pieces, not more pizza. When you compare unit fractions like 1/3, 1/5 and 1/10, the one with the smallest bottom number is the biggest piece.

1/4 vs 1/8: cut into 4 gives big slices, cut into 8 gives small ones. 1/4 is bigger.
1/3 vs 1/6: thirds are bigger than sixths, so 1/3 > 1/6.
Biggest first: 1/2, 1/5, 1/10 — the smallest bottom number wins.
Trap check: 1/100 is tiny, not huge. A hundred pieces means each one is minute.

Lesson

Making equivalent fractions

Two fractions are equivalent when they are the same amount wearing different names: 1/2, 2/4 and 5/10 all fill exactly half the pizza. To build one, multiply the top and the bottom by the same number — you are only cutting every piece into more pieces, which never changes how much you have. For example 1/2 = (1 x 3)/(2 x 3) = 3/6. To go the other way and simplify, divide the top and bottom by a number that goes into both (a common factor): 6/8 = (6 / 2)/(8 / 2) = 3/4. The golden rule is: whatever you do to the top, do to the bottom. Change only one of them and you have changed the amount.

1/2 = ?/6: 6 / 2 = 3, so 1 x 3 = 3, giving 3/6.
2/3 = ?/12: 12 / 3 = 4, so 2 x 4 = 8, giving 8/12.
Simplify 6/8: divide both by 2, giving 3/4.
Simplify 10/20: divide both by 10, giving 1/2.

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