NCERT Solutions Class 7 Mathematics Fractions and Decimals Ex 2.1

Question: 6. Salil wants to put a picture in a frame. The picture is 7³⁄₅ cm wide. To fit in the frame the picture cannot be more than 7³⁄₁₀ cm wide. How much should the picture be trimmed?

Answer :
Given: The width of the picture = 7³⁄₅ cm and the width of picture frame = 7³⁄₁₀ cm

Therefore, the picture should be trimmed = ³⁄₅ – ³⁄₁₀ = ³⁸⁄₅–⁷³⁄₁₀

= (^(76–73)⁄₁₀) = ³⁄₁₀ cm

Thus, the picture should be trimmed by ³⁄₁₀ cm.

Question: 7.Ritu ate ³⁄₅ part of an apple and the remaining apple was eaten by her brother Somu. How much part of the apple did Somu eat? Who had the larger share? By how much?

Answer :
The part of an apple eaten by Ritu = ³⁄₅

The part of an apple eaten by Somu = 1–³⁄₅=^(5-3)⁄₅ = ²⁄₅

Comparing the parts of apple eaten by both Ritu and Somu ³⁄₅ > ²⁄₅

Larger share will be more by ³⁄₅ – ²⁄₅ = ¹⁄₅ part.

Thus, Ritu’s part is ¹⁄₅ more than Somu’s part.

Question: 8.Michael finished colouring a picture in ⁷⁄₁₂ hour. Vaibhav finished colouring the same picture in ³⁄₄ hour. Who worked longer? By what fraction was it longer?

Answer :
Time taken by Michael to colour the picture = ⁷⁄₁₂ hour

Time taken by Vaibhav to colour the picture = ³⁄₄ hour

Converting both fractions in like fractions, ⁷⁄₁₂ and ^(3×3)⁄_(4×3) = ⁹⁄₁₂

Here, ⁷⁄₁₂ < ⁹⁄₁₂ ⇒ ⁷⁄₁₂ < ³⁄₄

Thus, Vaibhav worked longer time.

Vaibhav worked longer time by ³⁄₄ – ⁷⁄₁₂ = ^{(9 – 7)}⁄₁₂ = ²⁄₁₂ = ¹⁄₆ hour.

Thus, Vaibhav took ¹⁄₆ hour more than Michael.