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Ex 2.1 Q1 Fractions and Decimals Solution- NCERT Maths Class 7

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Question

 Solve: -

a) \(\begin{align}\;2 - \frac{3}{5} \end{align}\)

b) \(\begin{align}\;4 + \frac{7}{8}\end{align}\)

c) \(\begin{align}\;\frac{3}{5} + \frac{2}{7}\end{align}\)

d) \(\begin{align}\;\frac{9}{{11}} - \frac{4}{{15}}\end{align}\)

e) \(\begin{align}\;\frac{7}{{10}} + \frac{2}{5} + \frac{3}{2}\end{align}\)

f) \(\begin{align}\;2\frac{2}{3} + 3\frac{1}{2}\end{align}\)

g) \(\begin{align}\;8\frac{1}{2} - 3\frac{5}{8}\end{align}\)

 Video Solution
Fractions And Decimals
Ex 2.1 | Question 1

Text Solution

What is known?

Expression in unlike fraction.

What is unknown?

Sum/difference.

Reasoning:

Convert following fractions into like fraction (fractions with same denominator) then find sum or difference by adding or subtracting numerator.

Steps:

a)

\(\begin{align}2 - \frac{3}{5} &= \frac{2}{1} - \frac{3}{5} \\&= \frac{{10 - 3}}{5} \\&= \frac{7}{5}\\&( \text{improper fraction})\end{align}\)

Converting into mixed fraction, we get

\[\begin{align} = 1\frac{2}{5}\end{align}\]

b)

\(\begin{align}4 + \frac{7}{8}& = \frac{4}{1} + \frac{7}{8} \\&= \frac{{32 + 7}}{8} \\&= \frac{{39}}{8} \\& (\text{improper fraction})\end{align}\)

Converting into mixed fraction, we get

\[\begin{align} = 4\frac{7}{8}\end{align}\]

c)

\(\begin{align}\frac{3}{5} + \frac{2}{7} &= \frac{{21 + 10}}{{35}} \\&= \frac{{31}}{{35}}\end{align}\)

d)

\(\begin{align}\frac{9}{{11}} - \frac{4}{{15}} &= \frac{{135 - 44}}{{165}} \\&= \frac{{91}}{{165}}\end{align}\)

e)

\(\begin{align}\frac{7}{{10}} + \frac{2}{5} + \frac{3}{2} &= \frac{{7 + 4 + 15}}{{10}} \\&= \frac{{26}}{{10}} \\&= \frac{{13}}{5}\\&({\text{improper fraction}})\end{align}\)

Converting into mixed fraction, we get

\[\begin{align} = 2\frac{3}{5}\end{align}\]

f)

\(\begin{align}2\frac{2}{3} + 3\frac{1}{2} &= \frac{8}{3} + \frac{7}{2} \\&= \frac{{16 + 21}}{6} \\&= \frac{{37}}{6}\\&({\text{improper fraction}})\end{align}\)

Converting into mixed fraction, we get

\[\begin{align} = 6\frac{1}{6}\end{align}\]

g)

\(\begin{align}8\frac{1}{2} - 3\frac{5}{8} &= \frac{{17}}{2} - \frac{{29}}{8} \\&= \frac{{68 - 29}}{8} \\&= \frac{{39}}{8}\\&(\text{improper fraction})\end{align}\)

Converting into mixed fraction, we get

\[ \begin{align}= 4\frac{7}{8}\end{align}\]

  
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