Question

a piece of wire 7/8 metre long broke into two pieces. one piece was 1/4 mere long. how long is the other piece. ​

Answer 1

Given : ↴

$\sf \: A \: piece \: of \: wire \: \cfrac{7}{8} \: metre \: long \: is \: broken \: into \: two \: pieces.$

$\sf \: One \: piece \: was \: \cfrac{1}{4} \: metre \: long.$

To Find : ↴

$\sf \: We \: have \: to \: find \: the \: length \: of \: another \: piece.$

So, Let's Start : ↴

$\sf \: Let \: the \: another \: piece \:of \: the \:wire \: be \: x.$

$\sf \: \longrightarrow \: \cfrac{1}{4} \: + \: x \: = \: \cfrac{7}{8}$

$\sf \: \longrightarrow \: x \: = \: \cfrac{7}{8} \: - \: \cfrac{1}{4}$

$\sf \: Now \: we \: have \: to \: make \: the \: denominator \: same.$

$\longrightarrow \: \cfrac{7}{8} \: - \: \bigg( \cfrac{1}{4} \: \times \: \cfrac{2}{2} \: = \: \cfrac{2}{8} \bigg)$

$\sf \longrightarrow \:x \: = \cfrac{7 \: - \: 2}{8}$

$\sf \longrightarrow \:x \: = \cfrac{5}{8} \: \: metre$

$\sf \: Answer \: = \: \cfrac{5}{8} \: \: metre$

$\sf \: So, \: the \: length \: of \: the \: another \: piece \: of \: the \: wire \: is \: : \: \cfrac{5}{8} \: \: metre$

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Let's verify our Answer : ↴

$\sf \: \longrightarrow \: \cfrac{5}{8} \: + \: \cfrac{1}{4} \: = \: \cfrac{7}{8}$

$\sf \longrightarrow \: \cfrac{5 \: + \: 2}{8} \: = \: \cfrac{7}{8}$

$\sf \:Hence \:our\: Answer\: is\: correct.$