Pre-Algebra Examples

$\frac{4}{3} - (\frac{3}{4} - \frac{8}{5} \div \frac{6}{7})$

Step 1

Simplify each term.

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Step 1.1

Simplify each term.

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Step 1.1.1

To divide by a fraction, multiply by its reciprocal.

$\frac{4}{3} - (\frac{3}{4} - (\frac{8}{5} \cdot \frac{7}{6}))$

Step 1.1.2

Cancel the common factor of $2$ .

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Step 1.1.2.1

Factor $2$ out of $8$ .

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

Step 1.1.2.2

Factor $2$ out of $6$ .

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

Step 1.1.2.3

Cancel the common factor.

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

Step 1.1.2.4

Rewrite the expression.

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

Step 1.1.3

Multiply $\frac{4}{5}$ by $\frac{7}{3}$ .

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

Step 1.1.4

Multiply $4$ by $7$ .

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

Step 1.1.5

Multiply $5$ by $3$ .

$\frac{4}{3} - (\frac{3}{4} - \frac{28}{15})$

Step 1.2

To write $\frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{15}{15}$ .

$\frac{4}{3} - (\frac{3}{4} \cdot \frac{15}{15} - \frac{28}{15})$

Step 1.3

To write $- \frac{28}{15}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{4}{3} - (\frac{3}{4} \cdot \frac{15}{15} - \frac{28}{15} \cdot \frac{4}{4})$

Step 1.4

Write each expression with a common denominator of $60$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{3}{4}$ by $\frac{15}{15}$ .

$\frac{4}{3} - (\frac{3 \cdot 15}{4 \cdot 15} - \frac{28}{15} \cdot \frac{4}{4})$

Step 1.4.2

Multiply $4$ by $15$ .

$\frac{4}{3} - (\frac{3 \cdot 15}{60} - \frac{28}{15} \cdot \frac{4}{4})$

Step 1.4.3

Multiply $\frac{28}{15}$ by $\frac{4}{4}$ .

$\frac{4}{3} - (\frac{3 \cdot 15}{60} - \frac{28 \cdot 4}{15 \cdot 4})$

Step 1.4.4

Multiply $15$ by $4$ .

$\frac{4}{3} - (\frac{3 \cdot 15}{60} - \frac{28 \cdot 4}{60})$

Step 1.5

Combine the numerators over the common denominator.

$\frac{4}{3} - \frac{3 \cdot 15 - 28 \cdot 4}{60}$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Multiply $3$ by $15$ .

$\frac{4}{3} - \frac{45 - 28 \cdot 4}{60}$

Step 1.6.2

Multiply $- 28$ by $4$ .

$\frac{4}{3} - \frac{45 - 112}{60}$

Step 1.6.3

Subtract $112$ from $45$ .

$\frac{4}{3} - \frac{- 67}{60}$

Step 1.7

Move the negative in front of the fraction.

$\frac{4}{3} - - \frac{67}{60}$

Step 1.8

Multiply $- - \frac{67}{60}$ .

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Step 1.8.1

Multiply $- 1$ by $- 1$ .

$\frac{4}{3} + 1 (\frac{67}{60})$

Step 1.8.2

Multiply $\frac{67}{60}$ by $1$ .

$\frac{4}{3} + \frac{67}{60}$

Step 2

To write $\frac{4}{3}$ as a fraction with a common denominator, multiply by $\frac{20}{20}$ .

$\frac{4}{3} \cdot \frac{20}{20} + \frac{67}{60}$

Step 3

Write each expression with a common denominator of $60$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{4}{3}$ by $\frac{20}{20}$ .

$\frac{4 \cdot 20}{3 \cdot 20} + \frac{67}{60}$

Step 3.2

Multiply $3$ by $20$ .

$\frac{4 \cdot 20}{60} + \frac{67}{60}$

Step 4

Combine the numerators over the common denominator.

$\frac{4 \cdot 20 + 67}{60}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $4$ by $20$ .

$\frac{80 + 67}{60}$

Step 5.2

Add $80$ and $67$ .

$\frac{147}{60}$

Step 6

Cancel the common factor of $147$ and $60$ .

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Step 6.1

Factor $3$ out of $147$ .

$\frac{3 (49)}{60}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $3$ out of $60$ .

$\frac{3 \cdot 49}{3 \cdot 20}$

Step 6.2.2

Cancel the common factor.

$\frac{3 \cdot 49}{3 \cdot 20}$

Step 6.2.3

Rewrite the expression.

$\frac{49}{20}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{49}{20}$

Decimal Form:

$2.45$

Mixed Number Form:

$2 \frac{9}{20}$