A ratio tells you how many equal "shares" each person or part gets. The method is always the same three steps:

1. Add the parts of the ratio to find the total number of shares.
2. Divide the total quantity by that number to find the value of one share.
3. Multiply the value of one share by each part of the ratio to find each person's amount.

Example: Share £21,000 between Emma and Jake in the ratio $4:3$.

1. Total shares: $4+3=7$.
2. Value of one share: $£21{,}000 \div 7 = £3{,}000$.
3. Emma: $4 \times £3{,}000 = £12{,}000$. Jake: $3 \times £3{,}000 = £9{,}000$.

Always check your shares add back up to the original total — it's a free way to catch an arithmetic slip.

Use the given share to find the value of one part first, then scale up to find the total or anyone else's share.

Example: Sam and Priya share money in the ratio $5:3$. Sam gets $£40$. Find the total amount.

1. Sam's $5$ parts $= £40$, so one part $= £40 \div 5 = £8$.
2. Total parts $= 5+3=8$, so the total amount $= 8 \times £8 = £64$.

If two ratios share a term (e.g. green:orange sweets is $2:3$, and orange:yellow is $1:5$), scale both ratios so the shared term (orange) matches, using its LCM.

Orange is $3$ in the first ratio and $1$ in the second — LCM is $3$. Scale the second ratio by $3$: orange:yellow becomes $3:15$. Now both ratios agree on orange ($3$), so green:orange:yellow $= 2:3:15$.

The method is identical — just add all three parts for the total number of shares.

Example: £360 is shared between Alex, Ben, and Cara in the ratio $2:3:4$.

1. Total shares: $2+3+4=9$.
2. Value of one share: $£360\div9=£40$.
3. Alex: $2\times£40=£80$. Ben: $3\times£40=£120$. Cara: $4\times£40=£160$.
4. Check: $£80+£120+£160=£360$ ✓.

A shop has an offer: "pay for 2 pens, get 1 free." Pens cost $34$ cents each. Priya wants $25$ pens. How much does she pay?

1. For every $3$ pens received, only $2$ are paid for — that's the ratio $2:3$ (paid:received).
2. $25$ pens $\div 3 = 8$ remainder $1$: that's $8$ complete groups of 3 (24 pens, $8\times2=16$ paid for) plus $1$ extra pen (which must be paid for, since it's not part of a free-pen group).
3. Total pens paid for: $16+1=17$.
4. Total cost: $17 \times 34\text{c} = 578\text{c} = £5.78$.