Ratios and Proportions Made Simple

A ratio compares quantities, such as 2 parts sand to 3 parts cement (2 : 3). Simplify it like a fraction by dividing every part by the greatest common factor. A proportion says two ratios are equal; solve it by cross-multiplying.

Simplifying ratios

$12 : 18$: the GCF is 6, so it simplifies to $2 : 3$.

With decimals, multiply first: $1.5 : 2.5 = 15 : 25 = 3 : 5$.

Sharing in a ratio

Share 500 in the ratio $2 : 3$:

1. Total parts: $2 + 3 = 5$.
2. One part: $500 \div 5 = 100$.
3. Shares: $2 \times 100 = 200$ and $3 \times 100 = 300$.

Check: $200 + 300 = 500$ ✓.

Solving proportions

$\frac{3}{4} = \frac{15}{x}$. Cross-multiply:

Everyday examples

Recipe: 2 cups of flour serve 5 people. For 8 people: $\frac{2}{5} = \frac{x}{8}$, so $x = 3.2$ cups.

Map scale: at $1 : 50\,000$, 4 cm on the map is $4 \times 50\,000 = 200\,000$ cm $= 2$ km.

Ratio vs fraction

In $2 : 3$, the first part is $\frac{2}{5}$ of the whole, not $\frac{2}{3}$. A ratio compares parts with each other; a fraction compares a part with the whole.

Common mistakes

• Dividing the amount by one part of the ratio instead of the total.
• Mixing the order of the quantities.
• Forgetting to convert units before writing a ratio (cm and m).

Practice questions

1. Simplify $45 : 60$.
2. Share 90 in the ratio $2 : 3 : 4$.
3. Solve $\frac{5}{x} = \frac{2}{7}$.

Answers: 1) $3 : 4$ 2) 20, 30, 40 3) $x = 17.5$

The ratio calculator simplifies and shares, and the proportion calculator solves for the missing value. Fractions are covered in how to simplify fractions.

Frequently asked questions

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