Find two fractions whose ratio is $3 : 4$ and whose sum is $\frac{7}{8}$ .

hard 3 marks Class 7 · Mathematics · Fractions and Decimals

Answer

\frac{3}{8}\text{ and }\frac{1}{2}

The correct answer is \frac{3}{8}\text{ and }\frac{1}{2} — Hence the required fractions are $\frac{3}{8}$ and $\frac{1}{2}$ .

Step-by-step solution

Let the two fractions be $3 x$ and $4 x$ because their ratio is $3 : 4$ .
Use the sum condition: $3 x + 4 x = \frac{7}{8}$ , which simplifies to $7 x = \frac{7}{8}$ .
Solve for $x$ by dividing both sides by 7: $x = \frac{7}{8} \times \frac{1}{7} = \frac{1}{8}$ .
Substitute $x$ back to find the fractions: $3 x = 3 \times \frac{1}{8} = \frac{3}{8}$ and $4 x = 4 \times \frac{1}{8} = \frac{4}{8} = \frac{1}{2}$ .
Hence the required fractions are $\frac{3}{8}$ and $\frac{1}{2}$ .

Common mistake: Setting up equations incorrectly

Concept tested: Ratio and sum of fractions