Question

Find $x$ in the following:
$6\frac{7}{15} + x = 8\frac{3}{5}$

• A. $2\frac{2}{15}$
• B. $2\frac{3}{15}$
• C. $6\frac{3}{5}$
• D. $5\frac{4}{5}$

Answer 1

Answer:

$2\frac{2}{15}$

The value of $x$ is $2\frac{2}{15}$ (or $\frac{32}{15}$).

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1: Isolate $x$

To find the value of $x$, subtract the mixed fraction on the left side from the right side:
$x = 8\frac{3}{5} - 6\frac{7}{15}$

2: Separate whole numbers and fractions

You can subtract the whole numbers and the fractions separately:

• Whole numbers:
  $8 - 6 = 2$

• Fractions:
  $\frac{3}{5} - \frac{7}{15}$

3: Find a common denominator

The Lowest Common Multiple (LCM) of 5 and 15 is 15. Convert $\frac{3}{5}$ to have a denominator of 15:
$\frac{3 \times 3}{5 \times 3} = \frac{9}{15}$

Now, subtract the fractions:
$\frac{9}{15} - \frac{7}{15} = \frac{2}{15}$

4: Combine the results

Put the whole number and fraction back together:
$x = 2\frac{2}{15}$

To express it as an improper fraction:
$x = \frac{(2 \times 15) + 2}{15} = \frac{32}{15}=2\frac{2}{15}$