NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 4: Fractions & Decimals - Problems and Solutions
Question 88

Question. 88

Arrange the fractions \(\dfrac{6}{7},\ \dfrac{7}{8},\ \dfrac{4}{5},\ \dfrac{3}{4}\) in descending order.

Answer:

\(\dfrac{7}{8} > \dfrac{6}{7} > \dfrac{4}{5} > \dfrac{3}{4}\)

Detailed Answer with Explanation:

  1. Find a common denominator.
    The denominators are (7, 8, 5, 4). A common multiple is (280).

  2. Change each fraction to a denominator of (280).

    (displaystyle rac{6}{7}= rac{6 imes 40}{7 imes 40}= rac{240}{280})

    (displaystyle rac{7}{8}= rac{7 imes 35}{8 imes 35}= rac{245}{280})

    (displaystyle rac{4}{5}= rac{4 imes 56}{5 imes 56}= rac{224}{280})

    (displaystyle rac{3}{4}= rac{3 imes 70}{4 imes 70}= rac{210}{280})

  3. Compare the numerators (bigger numerator means bigger fraction).
    (245 > 240 > 224 > 210)

  4. Write the fractions in descending order.
    (displaystyle rac{7}{8} > rac{6}{7} > rac{4}{5} > rac{3}{4})

  5. (Quick check with decimals)
    ( rac{7}{8}=0.875, rac{6}{7}approx0.857, rac{4}{5}=0.8, rac{3}{4}=0.75) — same order.

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