DAV Class 7 Maths Chapter 4 Worksheet 2

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1. Find the reciprocals of each of the following

a. (12)5

Solution:

\begin{align*} (12)^5 \\ \end{align*}

\begin{align*} \text{Reciprocal } & = \left(\frac{1}{12}\right)^5 \\ \\ \end{align*}

b. (-9)4

Solution:

\begin{align*} (-9)^4 \\ \end{align*}

\begin{align*} \text{Reciprocal } & = \left(\frac{-1}{9}\right)^4 \\ \\ \end{align*}

c. (2⁄7)3

Solution:

\begin{align*} \left(\frac{2}{7}\right)^3 \\ \end{align*}

\begin{align*} \text{Reciprocal } & = \left(\frac{7}{2}\right)^3 \\ \\ \end{align*}

d. (-3⁄7)7

Solution:

\begin{align*} \left(\frac{-3}{7}\right)^7 \\ \end{align*}

\begin{align*} \text{Reciprocal } & = \left(\frac{-7}{3}\right)^7 \\ \\ \end{align*}

e. (-1⁄15)8

Solution:

\begin{align*} \left(-\frac{1}{15}\right)^8 \\ \end{align*}

\begin{align*} \text{Reciprocal } & = (-15)^8 \\ \\ \end{align*}

f. (-8⁄13)99

Solution:

\begin{align*} \left(-\frac{8}{13}\right)^{99} \end{align*}

\begin{align*} \text{Reciprocal } & = \left(-\frac{13}{8}\right)^{99} \\ \\ \end{align*}

g. (1⁄10)10

Solution:

\begin{align*} \left(\frac{1}{10}\right)^{10} \end{align*}

\begin{align*} \text{Reciprocal } & = (10)^{10} \\ \\ \end{align*}

h. (2⁄3) x (9⁄4)

Solution:

\begin{align*} \frac{2}{3} \times \frac{9}{4} \end{align*}

\begin{align*} & = \frac{\cancel{2}}{\cancel{3}} \times \frac{\cancelto{3}{9}}{\cancelto{2}{4}} \\ \\ & = \left(\frac{3}{2}\right) \\ \\ \text{Reciprocal } & = \left(\frac{2}{3}\right) \\ \\ \end{align*}

i. (1⁄2)2 x 4

Solution:

\begin{align*} \left(\frac{1}{2}\right)^2 \times 4 \end{align*}

\begin{align*} & = \frac{1}{2} \times \frac{1}{2} \times 4 \\ \\ & = \frac{1}{\cancel{4}} \times \cancel{4} \\ \\ & = \left(\frac{1}{1}\right) \\ \\ \text{Reciprocal } & = 1 \\ \\ \end{align*}

j. -(7⁄8)2

Solution:

\begin{align*} -\left(\frac{7}{8}\right)^2 \end{align*}

\begin{align*} \text{Reciprocal } & = -\left(\frac{8}{7}\right)^2 \\ \\ \end{align*}