CBSE Class 7 Maths — Ratio and Proportion

Chapter Overview & Weightage

Ratio and Proportion is one of the most practical chapters in Class 7 Maths. It connects to everyday situations — sharing money, mixing solutions, scaling recipes. Expect 4–8 marks in school exams.

Question Type	Marks	Common Topics
Direct calculation	1–2	Find ratio in simplest form
Word problems	3	Sharing in given ratio, unitary method
Proportion	2	Check if four numbers are in proportion

This chapter is the foundation for Percentages (Class 7), Profit & Loss (Class 8), and Direct/Inverse Proportion (Class 8). Get the basics right now.

Key Concepts You Must Know

1. Ratio

A ratio compares two quantities of the same unit. If A = 20 and B = 30:

\text{Ratio of A to B} = \frac{A}{B} = \frac{20}{30} = \frac{2}{3}

Written as $2:3$ (read “2 is to 3”).

Important: Both quantities must have the same unit before taking ratio. Ratio of 50 cm to 2 m = ratio of 50 cm to 200 cm = $50:200 = 1:4$ .

Equivalent ratios: $2:3 = 4:6 = 6:9$ (multiply or divide both terms by the same number).

2. Proportion

Four numbers $a, b, c, d$ are in proportion if $a:b = c:d$ .

This means: $\frac{a}{b} = \frac{c}{d}$ , or equivalently (cross-multiply): $a \times d = b \times c$ .

$a$ and $d$ are called extremes. $b$ and $c$ are called means.

Property: Product of extremes = Product of means. ( $a \times d = b \times c$ )

3. Unitary Method

Find the value of one unit first, then scale to find any quantity.

Example: If 8 notebooks cost ₹96, find cost of 5 notebooks.

Cost of 1 notebook = 96 ÷ 8 = ₹12

Cost of 5 notebooks = 12 × 5 = ₹60

Important Formulas

Ratio in simplest form: Divide both terms by their HCF.

Proportion condition: $a:b::c:d \iff a \times d = b \times c$

Mean proportional of $a$ and $b$ : $x = \sqrt{ab}$

Third proportional of $a$ and $b$ : $x = b^2/a$

Solved Examples

Example 1 — Simple Ratio (1 mark)

Find the ratio of 75 cm to 3 m in simplest form.

Solution: Convert to same unit: 3 m = 300 cm.

Ratio = $\frac{75}{300} = \frac{75 \div 75}{300 \div 75} = \frac{1}{4}$

Answer: 1:4

₹2400 is to be shared between Ravi and Sita in the ratio 5:3. How much does each get?

Solution: Total parts = 5 + 3 = 8 parts.

Value of 1 part = $\frac{2400}{8} = \text{₹}300$

Ravi’s share = 5 parts = 5 × 300 = ₹1500

Sita’s share = 3 parts = 3 × 300 = ₹900

Check: 1500 + 900 = 2400 ✓

Example 3 — Check Proportion (2 marks)

Are 4, 12, 7, 21 in proportion?

Solution: Check if $a:b = c:d$ , i.e., $4:12 = 7:21$ .

$\frac{4}{12} = \frac{1}{3}$ and $\frac{7}{21} = \frac{1}{3}$ . ✓

Alternatively, check: extremes product = $4 \times 21 = 84$ ; means product = $12 \times 7 = 84$ . ✓

Yes, 4, 12, 7, 21 are in proportion.

Example 4 — Missing Term in Proportion (2 marks)

Find $x$ if $3:x = 9:15$ .

Solution: Product of extremes = Product of means:

$3 \times 15 = x \times 9$

$45 = 9x$

$x = 5$

Difficulty Distribution

Difficulty	%	Topics
Easy	45%	Finding ratio, simplest form, check proportion
Medium	40%	Sharing in ratio, find missing term
Hard	15%	Multi-step word problems, combining ratios

Expert Strategy

For ratio questions: Always check if units are the same before taking ratio. 50 paise to ₹2 → convert to 50 paise : 200 paise = 1:4. Forgetting to convert is the single biggest error.

For proportion word problems: Identify whether it is direct proportion (both increase together) or inverse proportion (one increases, other decreases — covered in Class 8). For Class 7, most are direct.

For sharing problems: Total parts = sum of ratio terms. Find one part’s value, then multiply. Always verify by checking the shares add to the total.

For “find the fourth proportional” type questions: if $a:b::c:x$ , then $x = \frac{b \times c}{a}$ . Cross-multiply and solve. This works for ALL proportion problems.

Common Traps

Trap 1: Comparing quantities in different units. Always convert to the same unit before forming a ratio. Ratio of 2 hours to 30 minutes = ratio of 120 minutes to 30 minutes = 4:1. Many students write 2:30 directly.

Trap 2: Dividing the total by the ratio incorrectly. If ratio is 3:5, total parts = 8 (not 3+5 = 8… this is correct, but students sometimes use 3×5 = 15 as total). Total parts = sum of ratio terms.

Trap 3: Reversing extremes and means in proportion. In $a:b::c:d$ , product of EXTREMES ( $a \times d$ ) = product of MEANS ( $b \times c$ ). The extremes are the OUTER terms (first and last), not the inner ones.