Basic Math Examples

$\frac{2}{3} - \frac{1}{2} \cdot (\frac{5}{6} - \frac{7}{4})$

Step 1

Simplify each term.

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Step 1.1

To write $\frac{5}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{2}{3} - \frac{1}{2} \cdot (\frac{5}{6} \cdot \frac{2}{2} - \frac{7}{4})$

Step 1.2

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

$\frac{2}{3} - \frac{1}{2} \cdot (\frac{5}{6} \cdot \frac{2}{2} - \frac{7}{4} \cdot \frac{3}{3})$

Step 1.3

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{5}{6}$ by $\frac{2}{2}$ .

$\frac{2}{3} - \frac{1}{2} \cdot (\frac{5 \cdot 2}{6 \cdot 2} - \frac{7}{4} \cdot \frac{3}{3})$

Step 1.3.2

Multiply $6$ by $2$ .

$\frac{2}{3} - \frac{1}{2} \cdot (\frac{5 \cdot 2}{12} - \frac{7}{4} \cdot \frac{3}{3})$

Step 1.3.3

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

$\frac{2}{3} - \frac{1}{2} \cdot (\frac{5 \cdot 2}{12} - \frac{7 \cdot 3}{4 \cdot 3})$

Step 1.3.4

Multiply $4$ by $3$ .

$\frac{2}{3} - \frac{1}{2} \cdot (\frac{5 \cdot 2}{12} - \frac{7 \cdot 3}{12})$

Step 1.4

Combine the numerators over the common denominator.

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

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $5$ by $2$ .

$\frac{2}{3} - \frac{1}{2} \cdot \frac{10 - 7 \cdot 3}{12}$

Step 1.5.2

Multiply $- 7$ by $3$ .

$\frac{2}{3} - \frac{1}{2} \cdot \frac{10 - 21}{12}$

Step 1.5.3

Subtract $21$ from $10$ .

$\frac{2}{3} - \frac{1}{2} \cdot \frac{- 11}{12}$

Step 1.6

Move the negative in front of the fraction.

$\frac{2}{3} - \frac{1}{2} \cdot (- \frac{11}{12})$

Step 1.7

Multiply $- \frac{1}{2} (- \frac{11}{12})$ .

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Step 1.7.1

Multiply $- 1$ by $- 1$ .

$\frac{2}{3} + 1 (\frac{1}{2}) \frac{11}{12}$

Step 1.7.2

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

$\frac{2}{3} + \frac{1}{2} \cdot \frac{11}{12}$

Step 1.7.3

Multiply $\frac{1}{2}$ by $\frac{11}{12}$ .

$\frac{2}{3} + \frac{11}{2 \cdot 12}$

Step 1.7.4

Multiply $2$ by $12$ .

$\frac{2}{3} + \frac{11}{24}$

Step 2

To write $\frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{2}{3} \cdot \frac{8}{8} + \frac{11}{24}$

Step 3

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

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Step 3.1

Multiply $\frac{2}{3}$ by $\frac{8}{8}$ .

$\frac{2 \cdot 8}{3 \cdot 8} + \frac{11}{24}$

Step 3.2

Multiply $3$ by $8$ .

$\frac{2 \cdot 8}{24} + \frac{11}{24}$

Step 4

Combine the numerators over the common denominator.

$\frac{2 \cdot 8 + 11}{24}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $2$ by $8$ .

$\frac{16 + 11}{24}$

Step 5.2

Add $16$ and $11$ .

$\frac{27}{24}$

Step 6

Cancel the common factor of $27$ and $24$ .

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Step 6.1

Factor $3$ out of $27$ .

$\frac{3 (9)}{24}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $3$ out of $24$ .

$\frac{3 \cdot 9}{3 \cdot 8}$

Step 6.2.2

Cancel the common factor.

$\frac{3 \cdot 9}{3 \cdot 8}$

Step 6.2.3

Rewrite the expression.

$\frac{9}{8}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{9}{8}$

Decimal Form:

$1.125$

Mixed Number Form:

$1 \frac{1}{8}$