Fractions

Multiply or divide both by the same number

提示Keep the fraction worth what it is — change the top and bottom in step, up or down.

为什么Doing the same thing to top and bottom is really multiplying by a disguised 1, such as 2/2, so the fraction's value cannot change.

3/4

提示Look for the biggest number that goes into both 6 and 8, then cancel it.

为什么6 and 8 share a common factor of 2. Dividing both by 2 gives 3/4 — the same amount, in lowest terms.

15

提示Split the amount into four equal parts, then take three of them.

为什么One quarter of 20 is 5, so three quarters is 3 × 5 = 15. Find one part first, then scale up.

2/3

提示Rewrite both over a shared denominator so the pieces are the same size to count.

为什么Over a common denominator of 15, 2/3 = 10/15 and 3/5 = 9/15, so 2/3 is the larger.

0.5

提示Think of it as one whole shared between two — or half of a pound.

为什么A fraction is a division: 1 ÷ 2 = 0.5. Knowing the common ones (1/2, 1/4, 3/4, 1/10) by heart speeds up percentage work later.

5/6

提示Turn both into sixths first, then add the tops.

为什么Over a denominator of 6, 1/2 = 3/6 and 1/3 = 2/6. Add the numerators: 3 + 2 = 5, giving 5/6.

The denominator

提示Once the pieces are equal in size, you only count how many — the size label is unchanged.

为什么The denominator names the size of each piece. Adding thirds to thirds still gives thirds — you add how many pieces (the numerators), not the size.

8/15

提示Multiply straight across — tops together, bottoms together.

为什么Multiply the numerators (2 × 4 = 8) and the denominators (3 × 5 = 15) to get 8/15. No common denominator is needed for multiplying.

It gets smaller

提示You are taking only a part of the number, not the whole of it.

为什么Multiplying 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.

12

提示Ask how many halves fit inside six whole ones.

为什么Dividing asks 'how many fit?'. Twelve halves fit into 6, which is why dividing by 1/2 is the same as multiplying by 2.

multiply

提示The reciprocal turns the division into its opposite operation.

为什么Flipping a fraction gives its reciprocal; dividing by 3/4 is the same as multiplying by 4/3 — the same result from an easier sum.

11/4

提示Count how many quarters are in two whole ones, then add the extra three.

为什么Two wholes are 8 quarters; adding the 3 quarters gives 11 quarters, written 11/4. Multiply the whole by the denominator, then add the numerator.