Ratios & Proportions (Advanced) • Topic 1 of 2

Solving Proportions Using Cross-Multiplication

A proportion says two ratios are equal: a/b = c/d (where b and d are not zero).

Cross-multiplication rule: If a/b = c/d, then a x d = b x c.

Real-life example: If 3 apples cost $6, how much do 5 apples cost?

3/6 = 5/x => 3x = 30 => x = 10

Step	Action
1	Set up the proportion: a/b = c/d
2	Cross-multiply: a x d = b x c
3	Solve for the unknown variable
4	Check: does the answer make sense?

CROSS-MULTIPLICATION DIAGRAM:

    a      c
    -  =   -
    b      d

    a x d = b x c

Example: 5/8 = 15/x
    5 x x = 8 x 15
    5x = 120
    x = 24

Solved Examples

Worked Example

Solve: 5/8 = 15/x

Solution5 x x = 8 x 15 => 5x = 120 => x = 24

Worked Example

A recipe needs 2 cups of flour for 3 cookies. How many cups for 12 cookies?

Solution2/3 = x/12 => 2 x 12 = 3 x x => 24 = 3x => x = 8 cups

Worked Example

On a map, 1 cm = 5 km. Two cities are 8 cm apart on the map. Actual distance?

Solution1/5 = 8/x => 1 x x = 5 x 8 => x = 40 km

Key Points

Proportion = two equal ratios
Cross-multiply: a x d = b x c
Solve for unknown by dividing both sides
Always check: does your answer make sense?

Quick Check — 4 MCQs

Tap an option to check your answer0 / 4

Q1.In the proportion $\tfrac{a}{b}=\tfrac{c}{d}$, cross-multiplication gives:

Explanation: $ad=bc$.

Q2.If $\tfrac34=\tfrac{x}{8}$, then $x=$

Explanation: $3\times8=4x\Rightarrow x=6$.

Q3.Solve $\tfrac{x}{3}=\tfrac{4}{6}$:

Explanation: $6x=12\Rightarrow x=2$.

Q4.Are $\tfrac23$ and $\tfrac69$ in proportion?

Explanation: $2\times9=3\times6$.

Practice more MCQs → 📝 Assignment · 35 marks