Home / Lessons / Percentage, Rate & Ratio

Rate, ratio and direct proportion

2026-10-06Percentage, Rate & Ratio Ms Lam

Express ratios in simplest form, share quantities, and solve direct proportion problems with clear units.

Key formulas

a:b = (a \div k):(b \div k)

\text{Share in} a:b \rightarrow parts = a+b

y/x = constant (\text{direct proportion})

Ratio language

A ratio a:b compares two quantities of the same type. Simplify by dividing both parts by their highest common factor. Keep units consistent before forming a ratio — convert minutes to hours or cm to m first if needed.

Sharing in a ratio

To share an amount in the ratio a:b, find the total number of parts a + b, find the value of one part, then multiply. Check that the shares add back to the original amount.

Rate and direct proportion

A rate compares different types of quantity, such as km/h or $/kg. If y is directly proportional to x, then y = kx for some constant k. Find k from one pair, then use it for other values.

Exam habit

Write units beside every rate. For proportion, state y = kx before substituting.

Worked example

Share in a ratio

Problem. Share $960 in the ratio 5:7.

Solution. Parts = 12. One part = 960/12 = 80. Shares = 400 and 560. Check: 400 + 560 = 960.

Review quiz

1 / 4

Simplify 36:48

Practice questions

Simplify the ratio 36:48.
Share $420 in the ratio 3:4.
If y is directly proportional to x and y = 15 when x = 6, find y when x = 10.

Study notes

Is 2:3 the same as 2/3?

2:3 compares parts; 2/3 is a single fraction. Related ideas, different notation.

What is inverse proportion?

When the product xy stays constant — covered later; here we focus on direct proportion.