Question

What is title=" \frac{x}{7} = \frac{4}{5} " alt=" \frac{x}{7} = \frac{4}{5} " align="absmiddle" class="latex-formula">

Answer 1

Multply both sides of the equation by 7.

$\dfrac{x}{7}\cdot 7=\dfrac{4}{5}\cdot 7\\\\x=\dfrac{28}{5}=5.6$

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When the variable is in the numerator of a proportion like this, you can solve it by multiplying by that denominator. That multiplication cancels the denominator and gives you the value of the variable.

In general, you multiply by the reciprocal of the coefficient of x. When that coefficient is 1/7, you multiply by 7/1. Of course, you know that 7/7 = 1 and that x/1 = x.