Every card in Fractions
The whole deck, in order — so you can read it through before your child ever sees it.
- The fractions 12/n and 30/45 are equivalent. What is the value of n?
18
HintReduce the known pair to its lowest terms first, then scale that up until its top matches 12.
Why30/45 cancels to 2/3, and 12 is 6 × 2, so the bottom must be 6 × 3 = 18. Cross-multiplying is the quick check: 12 × 45 = 540 and 30 × 18 = 540, so the two fractions really are equal.
- What is 36/48 written in its simplest form?
3/4
HintFind the highest common factor of both numbers and cancel it in one go, or cancel in stages.
Why36 and 48 share a highest common factor of 12, so dividing both by 12 gives 3/4. Cancelling in stages (÷2, ÷2, ÷3) reaches the same place — keep going until top and bottom share no factor except 1.
- Three quarters of a number is 48. What is the number?
64
HintThree equal parts make 48, so find one part first, then build up to four of them.
WhyIf three quarters is 48, one quarter is 48 ÷ 3 = 16, and the whole is four quarters: 4 × 16 = 64. Working backwards from a fraction of an amount is a step up from finding one, and it is the same reasoning used later for reverse percentages.
- Over a common denominator of 15, 2/3 becomes ____ and 3/5 becomes ____, so ____ is the larger fraction.
10/15 and 9/15, so 2/3 is the larger
HintRewrite both over a shared denominator so the pieces are the same size to count.
WhyFifteen is the smallest number both 3 and 5 divide into, so fifteenths are the shared piece — once the pieces match, only the counts need comparing.
- What is 3/8 written as a decimal?
0.375
HintFind one eighth first by halving a quarter, then take three of them.
WhyA fraction is a division, so 3 ÷ 8 = 0.375. Quicker: 1/4 = 0.25, so 1/8 = 0.125 and 3/8 = 3 × 0.125 = 0.375. Knowing the eighths as well as halves, quarters and tenths by heart speeds up percentage work later.
- To add 1/2 and 1/3, write both as ____: 1/2 = ____ and 1/3 = ____, so the sum is ____.
sixths; 3/6 and 2/6, so the sum is 5/6
HintThe pieces must be the same size before the tops can be counted together.
WhySix is the smallest number both 2 and 3 divide into — the reason halves and thirds can only be added once both are renamed in sixths.
- When adding two fractions whose pieces are already the same size, what stays the same as the numerators are added?
The denominator
HintOnce the pieces are equal in size, you only count how many — the size label is unchanged.
WhyThe denominator names the size of each piece. Adding thirds to thirds still gives thirds — you add how many pieces (the numerators), not the size.
- To work out 2/3 × 4/5, multiply the tops to get ____ and the bottoms to get ____.
8 and 15, giving 8/15
HintStraight across on each row — no shared denominator is needed for this one.
WhyUnlike adding, multiplying needs no common denominator: you are taking 2/3 of 4/5, so the counts multiply and the piece sizes multiply at the same time.
- When you multiply a positive number by a fraction less than 1, what happens to its size?
It gets smaller
HintYou are taking only a part of the number, not the whole of it.
WhyMultiplying by 1/2 means finding half of the number, so the answer is smaller. Multiplying only grows a number when you multiply by more than 1.
- Half of a number, divided by 2/3, gives 9. What is the number?
12
HintWork backwards one step at a time: undo the division first, then undo the halving.
WhyDividing by 2/3 means multiplying by 3/2, so half the number × 3/2 = 9. That makes half the number 9 × 2/3 = 6, and the number itself 12. Checking forwards: half of 12 is 6, and 6 ÷ 2/3 = 6 × 3/2 = 9.
- To divide by a fraction, flip it and ____.
multiply
HintThe reciprocal turns the division into its opposite operation.
WhyFlipping a fraction gives its reciprocal; dividing by 3/4 is the same as multiplying by 4/3 — the same result from an easier sum.
- To write 2 3/4 as an improper fraction, count the two wholes as ____ quarters, then add the extra 3 quarters to reach ____ quarters in all.
8 and 11 — so 2 3/4 = 11/4
HintEvery whole one hides four quarters — count those first, and the spare quarters join on at the end.
WhyThe quick rule — multiply the whole number by the denominator, then add the numerator — is exactly this quarter-counting written as a recipe.
1★ KS3-MATH-NUM-0001
2★ KS3-MATH-NUM-0002
3★ KS3-MATH-NUM-0003
4★ KS3-MATH-NUM-0004
5★ KS3-MATH-NUM-0005
6★ KS3-MATH-NUM-0006
7★ KS3-MATH-NUM-0007
8★ KS3-MATH-NUM-0008
9★ KS3-MATH-NUM-0009
10★ KS3-MATH-NUM-0010
11★ KS3-MATH-NUM-0011
12★ KS3-MATH-NUM-0012
Keep what you learn
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