Treat a ratio like a fraction: divide every part by their highest common factor. If the ratio contains decimals or fractions, first multiply every part by the same number to clear them.

1. Add up the parts of the ratio.
2. Divide the total amount by this sum to find the value of one part.
3. Multiply by each ratio number to get each share.

Example: divide \360$between Priya, Sam and Tom in the ratio$3:4:5$.

1. Add the parts: $3+4+5=12$.
2. One part: \dfrac{\360}{12} = \$30$.
3. Shares: Priya = 3 \times \30 = \$90$, Sam = 4 \times \30 = \$120$, Tom = 5 \times \30 = \$150$.
4. Check: $90+120+150 = 360$ ✓

Match the difference in parts to the difference in amount, then scale up to find one part.

Example: two amounts are in the ratio $3:7$. The larger is \48$ more than the smaller. Find the smaller amount.

1. Difference in parts: $7-3=4$ parts.
2. This difference corresponds to \48$, so$1$part$= \dfrac{\48}{4} = \12$.
3. Smaller amount ($3$ parts): 3 \times \12 = \$36$.

A map scale like $1:25\,000$ means every $1$ unit on the map represents $25\,000$ of the same unit in real life. To find a real distance, multiply the map distance by the second number in the ratio (making sure both are in the same unit first).

Example: a map has a scale of $1:25\,000$. Two towns are $6\text{ cm}$ apart on the map. Find the real distance between them, in kilometres.

1. Real distance in cm: $6 \times 25\,000 = 150\,000\text{ cm}$.
2. Convert to metres: $150\,000 \div 100 = 1500\text{ m}$.
3. Convert to kilometres: $1500 \div 1000 = 1.5\text{ km}$.

• Dividing the total by only one ratio number instead of the sum of every part.
• Treating a stated difference as if it were the total to be shared. A difference corresponds to a difference in parts, not the total number of parts.
• Leaving a ratio with decimals or fractions instead of scaling up to whole numbers in simplest form.