Basic Math Examples

$(\frac{3}{4} - \frac{5}{7}) \cdot (\frac{2}{4} + \frac{3}{5})$

Step 1

To write $\frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$(\frac{3}{4} \cdot \frac{7}{7} - \frac{5}{7}) \cdot (\frac{2}{4} + \frac{3}{5})$

Step 2

To write $- \frac{5}{7}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$(\frac{3}{4} \cdot \frac{7}{7} - \frac{5}{7} \cdot \frac{4}{4}) \cdot (\frac{2}{4} + \frac{3}{5})$

Step 3

Write each expression with a common denominator of $28$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{3}{4}$ by $\frac{7}{7}$ .

$(\frac{3 \cdot 7}{4 \cdot 7} - \frac{5}{7} \cdot \frac{4}{4}) \cdot (\frac{2}{4} + \frac{3}{5})$

Step 3.2

Multiply $4$ by $7$ .

$(\frac{3 \cdot 7}{28} - \frac{5}{7} \cdot \frac{4}{4}) \cdot (\frac{2}{4} + \frac{3}{5})$

Step 3.3

Multiply $\frac{5}{7}$ by $\frac{4}{4}$ .

$(\frac{3 \cdot 7}{28} - \frac{5 \cdot 4}{7 \cdot 4}) \cdot (\frac{2}{4} + \frac{3}{5})$

Step 3.4

Multiply $7$ by $4$ .

$(\frac{3 \cdot 7}{28} - \frac{5 \cdot 4}{28}) \cdot (\frac{2}{4} + \frac{3}{5})$

Step 4

Combine the numerators over the common denominator.

$\frac{3 \cdot 7 - 5 \cdot 4}{28} \cdot (\frac{2}{4} + \frac{3}{5})$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $3$ by $7$ .

$\frac{21 - 5 \cdot 4}{28} \cdot (\frac{2}{4} + \frac{3}{5})$

Step 5.2

Multiply $- 5$ by $4$ .

$\frac{21 - 20}{28} \cdot (\frac{2}{4} + \frac{3}{5})$

Step 5.3

Subtract $20$ from $21$ .

$\frac{1}{28} \cdot (\frac{2}{4} + \frac{3}{5})$

Step 6

Cancel the common factor of $2$ and $4$ .

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Step 6.1

Factor $2$ out of $2$ .

$\frac{1}{28} \cdot (\frac{2 (1)}{4} + \frac{3}{5})$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $2$ out of $4$ .

$\frac{1}{28} \cdot (\frac{2 \cdot 1}{2 \cdot 2} + \frac{3}{5})$

Step 6.2.2

Cancel the common factor.

$\frac{1}{28} \cdot (\frac{2 \cdot 1}{2 \cdot 2} + \frac{3}{5})$

Step 6.2.3

Rewrite the expression.

$\frac{1}{28} \cdot (\frac{1}{2} + \frac{3}{5})$

Step 7

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{1}{28} \cdot (\frac{1}{2} \cdot \frac{5}{5} + \frac{3}{5})$

Step 8

To write $\frac{3}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{1}{28} \cdot (\frac{1}{2} \cdot \frac{5}{5} + \frac{3}{5} \cdot \frac{2}{2})$

Step 9

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 9.1

Multiply $\frac{1}{2}$ by $\frac{5}{5}$ .

$\frac{1}{28} \cdot (\frac{5}{2 \cdot 5} + \frac{3}{5} \cdot \frac{2}{2})$

Step 9.2

Multiply $2$ by $5$ .

$\frac{1}{28} \cdot (\frac{5}{10} + \frac{3}{5} \cdot \frac{2}{2})$

Step 9.3

Multiply $\frac{3}{5}$ by $\frac{2}{2}$ .

$\frac{1}{28} \cdot (\frac{5}{10} + \frac{3 \cdot 2}{5 \cdot 2})$

Step 9.4

Multiply $5$ by $2$ .

$\frac{1}{28} \cdot (\frac{5}{10} + \frac{3 \cdot 2}{10})$

Step 10

Combine the numerators over the common denominator.

$\frac{1}{28} \cdot \frac{5 + 3 \cdot 2}{10}$

Step 11

Simplify the numerator.

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Step 11.1

Multiply $3$ by $2$ .

$\frac{1}{28} \cdot \frac{5 + 6}{10}$

Step 11.2

Add $5$ and $6$ .

$\frac{1}{28} \cdot \frac{11}{10}$

Step 12

Multiply $\frac{1}{28} \cdot \frac{11}{10}$ .

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Step 12.1

Multiply $\frac{1}{28}$ by $\frac{11}{10}$ .

$\frac{11}{28 \cdot 10}$

Step 12.2

Multiply $28$ by $10$ .

$\frac{11}{280}$

Step 13

The result can be shown in multiple forms.

Exact Form:

$\frac{11}{280}$

Decimal Form:

$0.03928571 \dots$