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Is 0.2 the multiplicative inverse of
2(1)/(2) ? Why or why not?

Is $0$ . $2$ the multiplicative inverse of $2 \frac{1}{2}$ ? Why or why not?

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Reciprocals and multiplicative inverses

Full solution

Q. Is

0

.

2

the multiplicative inverse of

2 \frac{1}{2}

? Why or why not?

Convert to Improper Fraction: To find the multiplicative inverse of a number, we need to find a number that, when multiplied with the original number, gives a product of $1$ . Let's first convert the mixed number $2\left(\frac{1}{2}\right)$ to an improper fraction. $\newline$ $2\left(\frac{1}{2}\right) = 2 + \frac{1}{2}$ $\newline$ $= \frac{2\times 2}{2} + \frac{1}{2}$ $\newline$ $= \frac{4}{2} + \frac{1}{2}$ $\newline$ $= \frac{4 + 1}{2}$ $\newline$ $= \frac{5}{2}$
Find Multiplicative Inverse: Now, let's find the multiplicative inverse of $\frac{5}{2}$ . The multiplicative inverse of a fraction is obtained by flipping the numerator and the denominator. $\newline$ The multiplicative inverse of $\frac{5}{2}$ is $\frac{2}{5}$ .
Check Multiplicative Inverse: Next, we need to check if $0.2$ is equal to the multiplicative inverse we found, which is $\frac{2}{5}$ . To compare, we can convert $0.2$ to a fraction. $0.2 = \frac{2}{10}$ Now, simplify the fraction $\frac{2}{10}$ . $\frac{2}{10} = \frac{1}{5}$
Compare Fractions: We can see that $\frac{1}{5}$ is not equal to $\frac{2}{5}$ . Therefore, $0.2$ is not the multiplicative inverse of $2\left(\frac{1}{2}\right)$ .

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