Question

by what number should 1 2/6 be divided to get 6/8

Answer 1

Answer:

$\rm{\circ\;The\;required\;number\;is\;1\dfrac{7}{9}.}$

Step-by-step explanation:

To Find:

$\sf{\circ\;1\dfrac{2}{6}\;\div\; ?=\dfrac{6}{8}}$

Let us assume:

• The number to be divided be x.

According to the question:

$\sf{\implies 1\dfrac{2}{6}\;\div\;x=\dfrac{6}{8}}$

Solving further,

$\sf{\implies \dfrac{8}{6}\times\dfrac{1}{x}=\dfrac{6}{8}}$

Reducing the numbers,

$\sf{\implies \dfrac{4}{3}\times\dfrac{1}{x}=\dfrac{3}{4}}$

Transposing 4/3 from LHS to RHS and changing its sign,

$\sf{\implies \dfrac{1}{x}=\dfrac{3}{4}\div\dfrac{4}{3}}$

$\sf{\implies \dfrac{1}{x}=\dfrac{3}{4}\times\dfrac{3}{4}}$

Multiplying,

$\sf{\implies \dfrac{1}{x}=\dfrac{9}{16}}$

$\sf{\implies x=\dfrac{16}{9}}$

$\sf{\implies x=1\dfrac{7}{9}}$

Hence,

$\bf{\circ\;x=1\dfrac{7}{9}}$

Verification:

Substituting the value of x to the equation,

LHS:

$\sf{\longmapsto1\dfrac{2}{6}\div1\dfrac{7}{9}}$

$\sf{\longmapsto\dfrac{8}{6}\div\dfrac{16}{9}}$

$\sf{\longmapsto\dfrac{8}{6}\times\dfrac{9}{16}}$

$\sf{\longmapsto\dfrac{1}{6}\times\dfrac{9}{2}}$

$\sf{\longmapsto\dfrac{9}{12}}$

$\sf{\longmapsto\dfrac{9\div3}{12\div3}}$

$\sf{\longmapsto\dfrac{3}{4}}$

RHS:

$\sf{\longmapsto\dfrac{6}{8}}$

$\sf{\longmapsto\dfrac{6\div2}{8\div2}}$

$\sf{\longmapsto\dfrac{3}{4}}$

As,

• LHS = RHS

Hence, Verified.