NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 4: Fractions & Decimals - Fill in the Blanks (Relation)

Question 67

We want to compare \(\tfrac{8}{15}\) and \(\tfrac{95}{14}\).

Both are positive fractions. We can compare them using cross-multiplication.

1. Multiply the first numerator by the second denominator:
   \(8 \times 14 = 112\).
2. Multiply the second numerator by the first denominator:
   \(95 \times 15 = 1425\).
3. Compare the two products:
   \(112 < 1425\).

When \(a, b, c, d > 0\), if \(a \times d < c \times b\), then \(\tfrac{a}{b} < \tfrac{c}{d}\).

So, \(\tfrac{8}{15} < \tfrac{95}{14}\).

(Quick check with decimals, optional)
\(8 \div 15 \approx 0.53\) and \(95 \div 14 \approx 6.79\).
Since \(0.53 < 6.79\), the result is the same.