Question

What number is missing to make the following statement true? 8/11=7 ?/15

Answer 1

First we need to rewrite the mixed number (7 ?/15)​ on the right of the equation as a fraction, we can do it like this:

1. multiply the whole number part (7) by the fraction's denominator

7 * 15 = 105

2. Add that to the numerator (?)

105 + ?

3. write the result on top of the denominator

(105 + ?)/ 15

Now that we converted the mixed number on the right side, we can rewrite the equation like this:

8/11 = (105 + ?)/ 15

From this expression, we can solve for ? by following these steps:

1. multiply both sides of the equation by 15:

$\begin{gathered} \frac{8}{11}\times15=\frac{(105+?)}{15}\times15 \\ \frac{8\times15}{11}=(105+?)\times\frac{15}{15} \\ \frac{120}{11}=(105+?)\times1 \\ \frac{120}{11}=105+? \end{gathered}$

2. Subtract 105 on both sides:

$\begin{gathered} \frac{120}{11}=105+? \\ \frac{120}{11}-105=105-105+? \\ \frac{120}{11}-105=0+? \\ \frac{120}{11}-105=? \end{gathered}$

3. Solve the subtraction on the left side by multiplying and dividing 105 by 11:

$\begin{gathered} \frac{120}{11}-\frac{105\times11}{11}=? \\ \frac{120}{11}-\frac{1155}{11}=? \\ ?=\frac{120-1155}{11} \\ ?=\frac{-1035}{11} \end{gathered}$

Then, ? is:

$-\frac{1035}{11}=-94\frac{1}{11}$