Basic Math Examples

$\frac{5}{7} - \frac{2}{3} \cdot (\frac{1}{3} + \frac{3}{8})$

Step 1

Simplify each term.

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Step 1.1

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{5}{7} - \frac{2}{3} \cdot (\frac{1}{3} \cdot \frac{8}{8} + \frac{3}{8})$

Step 1.2

To write $\frac{3}{8}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{5}{7} - \frac{2}{3} \cdot (\frac{1}{3} \cdot \frac{8}{8} + \frac{3}{8} \cdot \frac{3}{3})$

Step 1.3

Write each expression with a common denominator of $24$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{1}{3}$ by $\frac{8}{8}$ .

$\frac{5}{7} - \frac{2}{3} \cdot (\frac{8}{3 \cdot 8} + \frac{3}{8} \cdot \frac{3}{3})$

Step 1.3.2

Multiply $3$ by $8$ .

$\frac{5}{7} - \frac{2}{3} \cdot (\frac{8}{24} + \frac{3}{8} \cdot \frac{3}{3})$

Step 1.3.3

Multiply $\frac{3}{8}$ by $\frac{3}{3}$ .

$\frac{5}{7} - \frac{2}{3} \cdot (\frac{8}{24} + \frac{3 \cdot 3}{8 \cdot 3})$

Step 1.3.4

Multiply $8$ by $3$ .

$\frac{5}{7} - \frac{2}{3} \cdot (\frac{8}{24} + \frac{3 \cdot 3}{24})$

Step 1.4

Combine the numerators over the common denominator.

$\frac{5}{7} - \frac{2}{3} \cdot \frac{8 + 3 \cdot 3}{24}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $3$ by $3$ .

$\frac{5}{7} - \frac{2}{3} \cdot \frac{8 + 9}{24}$

Step 1.5.2

Add $8$ and $9$ .

$\frac{5}{7} - \frac{2}{3} \cdot \frac{17}{24}$

Step 1.6

Cancel the common factor of $2$ .

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Step 1.6.1

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$\frac{5}{7} + \frac{- 2}{3} \cdot \frac{17}{24}$

Step 1.6.2

Factor $2$ out of $- 2$ .

$\frac{5}{7} + \frac{2 (- 1)}{3} \cdot \frac{17}{24}$

Step 1.6.3

Factor $2$ out of $24$ .

$\frac{5}{7} + \frac{2 \cdot - 1}{3} \cdot \frac{17}{2 \cdot 12}$

Step 1.6.4

Cancel the common factor.

$\frac{5}{7} + \frac{2 \cdot - 1}{3} \cdot \frac{17}{2 \cdot 12}$

Step 1.6.5

Rewrite the expression.

$\frac{5}{7} + \frac{- 1}{3} \cdot \frac{17}{12}$

Step 1.7

Multiply $\frac{- 1}{3}$ by $\frac{17}{12}$ .

$\frac{5}{7} + \frac{- 1 \cdot 17}{3 \cdot 12}$

Step 1.8

Multiply $- 1$ by $17$ .

$\frac{5}{7} + \frac{- 17}{3 \cdot 12}$

Step 1.9

Multiply $3$ by $12$ .

$\frac{5}{7} + \frac{- 17}{36}$

Step 1.10

Move the negative in front of the fraction.

$\frac{5}{7} - \frac{17}{36}$

Step 2

To write $\frac{5}{7}$ as a fraction with a common denominator, multiply by $\frac{36}{36}$ .

$\frac{5}{7} \cdot \frac{36}{36} - \frac{17}{36}$

Step 3

To write $- \frac{17}{36}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{5}{7} \cdot \frac{36}{36} - \frac{17}{36} \cdot \frac{7}{7}$

Step 4

Write each expression with a common denominator of $252$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{5}{7}$ by $\frac{36}{36}$ .

$\frac{5 \cdot 36}{7 \cdot 36} - \frac{17}{36} \cdot \frac{7}{7}$

Step 4.2

Multiply $7$ by $36$ .

$\frac{5 \cdot 36}{252} - \frac{17}{36} \cdot \frac{7}{7}$

Step 4.3

Multiply $\frac{17}{36}$ by $\frac{7}{7}$ .

$\frac{5 \cdot 36}{252} - \frac{17 \cdot 7}{36 \cdot 7}$

Step 4.4

Multiply $36$ by $7$ .

$\frac{5 \cdot 36}{252} - \frac{17 \cdot 7}{252}$

Step 5

Combine the numerators over the common denominator.

$\frac{5 \cdot 36 - 17 \cdot 7}{252}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $5$ by $36$ .

$\frac{180 - 17 \cdot 7}{252}$

Step 6.2

Multiply $- 17$ by $7$ .

$\frac{180 - 119}{252}$

Step 6.3

Subtract $119$ from $180$ .

$\frac{61}{252}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{61}{252}$

Decimal Form:

$0.24206349 \dots$