11+ Ratio Sharing: Questions and Worked Answers

In a sharing ratio, compare the shares before finding the whole

Read 2:3 as “two parts to three parts”. The first share is 2/5 of the combined total, because 2 + 3 = 5. It is not 2/3 of the total. However, the first share is 2/3 of the second share. Knowing which quantities are being compared prevents confusion.

The order matters. If the question says apples to pears is 2:3, apples take two parts and pears take three. Reverse the labels and you reverse the answer. Before calculating, copy the names in the same order as the ratio.

Sharing a known total

Add the ratio numbers to find how many equal parts make the total. Divide the total amount by this number of parts. Then multiply the value of one part by each ratio number to calculate the separate shares.

For a visual method, draw a row of equal boxes: two boxes for the first person and three for the second. Label the whole row with the total. Every box must have the same value even though the people receive different numbers of boxes.

Check the result twice. The shares should add back to the original total, and they should simplify to the stated ratio. Correct addition alone is not enough: two equal shares would add correctly but would not match a 2:3 ratio.

When one share is given instead

Do not divide every number you see by the total number of parts. First decide what the given amount represents. If the second person has three parts and receives £24, one part is £24 ÷ 3. You can then calculate the first share or the combined total.

The same idea works for three people. In a 2:3:4 ratio there are nine parts altogether, but a known middle share represents three parts. Underlining “altogether” or the name attached to a number helps you choose the correct calculation.

Stretch: when the difference is given

A difference compares how much more one person receives. In a 5:2 ratio, the larger share exceeds the smaller by three parts. If the difference is £18, those three parts are worth £18, so each part is £6.

The total would be seven parts, or £42. Dividing the £18 difference by seven would treat it as the total and answer a different problem. A labelled bar drawing can make the extra three parts easier to see.

Choosing the right first step

Ask: “Does the known amount represent all the parts, one person’s parts, or the difference in parts?” Match the amount to that number of parts, then divide. Once you know one part, multiply to build the quantity the question requests.

Try the six questions without timing yourself first. After checking, revisit the ones where you chose the wrong number of parts. Explain why the correct divisor represents the amount given; memorising a sequence of operations without that explanation is less useful.