Question

rewrite the division equation using the multiplicative inverse of 5.
$5m = 50$
$50 \div 5 = m$
$50 \cdot \square = m$
options: $\frac{1}{5}$, $-\frac{1}{5}$

Explanation:

Step1: Recall multiplicative inverse

The multiplicative inverse of a number \(a\) (where \(a
eq0\)) is \(\frac{1}{a}\) because \(a\times\frac{1}{a} = 1\). For \(a = 5\), the multiplicative inverse is \(\frac{1}{5}\).

Step2: Rewrite division as multiplication

We know that dividing by a number is the same as multiplying by its multiplicative inverse. So, \(50\div5\) is the same as \(50\times\frac{1}{5}\) because the multiplicative inverse of \(5\) is \(\frac{1}{5}\). So the equation \(50\div5 = m\) can be rewritten as \(50\times\frac{1}{5}=m\).

Answer:

\(\frac{1}{5}\)