3 Marks Question

Question 513 Marks

A piece of a wire $\frac{7}{8}\text{metres}$ long broke into two pieces. One piece was $\frac{1}{4}\text{metres}$ long. How long is the other piece?

Answer

Length of the wire $=\frac{7}{8}\text{metres}$
Length of one piece of wire $=\frac{1}{4}\text{metres}$
Let the length of the second piece of wire be $x\ m.$
Therefore, Length of the wire = Length of one piece + Length of the second piece
$\frac{7}{8}\text{metres}=\frac{1}{4}\text{metres}+\text{x}$
$\Rightarrow\text{x}=\frac{7}{8}\text{metres}-\frac{1}{4}\text{metres}$
$\Rightarrow\text{x}=\frac{7\times1}{8\times1}\text{metres}-\frac{1\times2}{4\times2}\text{metres}$
$($because $LCM$ of $8$ and $4$ is $8)$
$\Rightarrow\text{x}=\frac{7}{8}\text{metres}-\frac{2}{8}\text{metres}$
$\Rightarrow\text{x}=\Big(\frac{7-2}{8}\Big)\text{metres}$
$\Rightarrow\text{x}=\frac{5}{8}\text{metres}$
Therefore, the length of the second piece is $\frac{5}{8}\text{m}.$

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Question 523 Marks

Isha read $25$ pages of a book containing $100$ pages. Nagma read $\frac{1}{2}$ of the same book. Who read less?

Answer

Total pages in the book $= 100$
Fraction of the book read by Isha $=\frac{25\div25}{100\div25}=\frac{1}{4}$
(Dividing numerator & denominator by the $HCF$ of $25$ & $100)$
Fraction of the book read by Nagma $=\frac{1}{2}$
Now, compare $\frac{1}{4}\ \&\ \frac{1}{2}$ $L.C.M$ of $4$ & $2$ is $4$
Convert each fraction into equivalent fraction with $4$ as its denominator.
$\frac{1\times1}{4\times1}\ \&\ \frac{1\times2}{2\times2}$ $\frac{1}{4}\ \&\ \frac{2}{4}$
$\frac{1}{4}<\frac{2}{4}$
Therefore, Isha read less.

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Question 533 Marks

Add: $\frac{8}{13}$ and $\frac{2}{3}$

Answer

Given: $\frac{8}{13}$ and $\frac{2}{3}$
$\frac{8}{13}+\frac{2}{3}$
$LCM$ of $13$ and $3$ is $39$,
so we will convert each fraction into an equivalent fraction with denominator $39$.
$=\frac{8\times3}{13\times3}+\frac{2\times13}{3\times13}$
$=\frac{24}{39}+\frac{26}{39}$
$=\frac{24+26}{39}$
$=\frac{50}{39}$

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Question 543 Marks

Add: $\frac{7}{10}$ and $\frac{2}{15}$

Answer

Given: $\frac{7}{10}$ and $\frac{2}{15}$
$\frac{7}{10}+\frac{2}{15}$
$LCM$ of $10$ and $15$ is $30$,
so we will convert each fraction into an equivalent fraction with denominator $30$.
$=\frac{7\times3}{10\times3}+\frac{5\times2}{15\times2}$
$=\frac{21}{30}+\frac{4}{30}$
$=\frac{21+4}{30}$
$=\frac{25}{30}$

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Maths 3 Marks Question