Divide every term in the ratio by their highest common factor: $20:30:40 = 2:3:4$.

1. Add the ratio terms to find the total number of parts.
2. Divide the quantity by the total to find the value of one part.
3. Multiply back up to find each share.

Worked Example (ratio division)

Divide \260$in the ratio$3:5:2$.

1. Total parts $= 3+5+2 = 10$. Value of one part = \260 \div 10 = \$26$.
2. Shares: 3\times26=\78$,$5\times26=\$130$, 2\times26=\52$. Check:$78+130+52=260$. ✓

Convert every option to the same unit price (cost per single item, or per fixed unit of measure like $100\text{ g}$), then compare like with like.

Worked Example (best value)

A $750\text{ g}$ jar of coffee costs \9.00$and a$$1.2\text{ kg}$$jar costs$\$13.20$. Which is better value?

1. Convert to cost per $100\text{ g}$.
2. Jar 1: \9.00 \div 7.5 = \$1.20$ per $100\text{ g}$.
3. Jar 2: \13.20 \div 12 = \$1.10$ per $100\text{ g}$.
4. The $1.2\text{ kg}$ jar is better value, since it costs less per $100\text{ g}$.

Work backwards: figure out what fraction of the total that one share represents, then use it to find the value of one part just as before.

Worked Example

Two amounts are in the ratio $5:7$. The larger amount is \210$. Find the total of the two amounts.

1. The larger amount corresponds to $7$ parts, so one part = 210 \div 7 = \30$.
2. Total parts $= 5+7=12$.
3. Total = 12 \times 30 = \360$.

Direct proportion means the ratio between two linked quantities stays fixed — so multiplying one quantity by a scale factor multiplies the other by the same factor.

Worked Example

A recipe for $6$ people needs $450\text{ g}$ of flour. How much flour is needed for $10$ people?

1. Find the scale factor from the given quantity to the required one: $10 \div 6 = \dfrac{5}{3}$.
2. Multiply the flour amount by the same factor: $450 \times \dfrac{5}{3} = 750\text{ g}$.

Sharing in a ratio splits one fixed total into parts. Direct proportion instead links two separate, growing quantities (like people and flour) so that scaling one automatically scales the other by the same factor — there's no fixed total being divided up at all.