Numerical: Fractions & Decimals MCQ — 14 Practice Questions with Answers

Explanation

To compare fractions and decimals, convert all values to decimals on the same scale. We have 7/12 = 0.5833..., 3/5 = 0.60, 0.62 is already a decimal, and 5/8 = 0.625. Now compare the decimal values: 0.5833... is the smallest, followed by 0.60, then 0.62, and finally 0.625. Therefore the ascending order is 7/12 < 3/5 < 0.62 < 5/8.

Explanation

Use the fraction forms of the recurring decimals because fractions make the addition exact and simple. We know 0.333... = 1/3. Also, 0.166... means 0.1 + 0.066..., which is 1/10 + 1/15 = 1/6; commonly, 1 ÷ 6 = 0.166.... Now add the fractions: 1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2 = 0.5. Thus the assertion is true, the reason is true, and the reason correctly explains the assertion.

Explanation

To compare fractions and decimals, first write all values as decimals using value = numerator ÷ denominator. 11/12 = 0.9166..., 0.91 is already 0.910, 9/10 = 0.900, and 0.909 is 0.909. Now compare place by place after aligning the decimal places. The tenths digits are all 9 except 11/12 also has a larger hundredths part. So 0.9166... is greater than 0.910, 0.909 and 0.900. Therefore the greatest number among the four given values is 11/12.

Explanation

Convert each fraction separately, using an equivalent denominator where possible. For 3/8, multiply numerator and denominator by 125: 3/8 = 375/1000 = 0.375. For 7/20, multiply by 5: 7/20 = 35/100 = 0.35. For 11/25, multiply by 4: 11/25 = 44/100 = 0.44. For 9/16, since 1/16 = 0.0625, 9/16 = 9 × 0.0625 = 0.5625. Thus the correct matching is option C.

Explanation

Convert each fraction separately so that no value is guessed by appearance. For 3/4, make the denominator 100: 3/4 = 75/100 = 0.75. For 7/20, multiply numerator and denominator by 5, so 7/20 = 35/100 = 0.35. For 5/8, divide 5 by 8 or use 5/8 = 625/1000 = 0.625. Thus the correct matching is 3/4 = 0.75, 7/20 = 0.35 and 5/8 = 0.625.