Pre-Algebra Examples

$\frac{7}{3} + \frac{3}{8} \cdot (- \frac{5}{9}) - \frac{5}{3} \div (- \frac{4}{7})$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $3$ .

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Step 1.1.1

Move the leading negative in $- \frac{5}{9}$ into the numerator.

$\frac{7}{3} + \frac{3}{8} \cdot \frac{- 5}{9} - \frac{5}{3} \div (- \frac{4}{7})$

Step 1.1.2

Factor $3$ out of $9$ .

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

Step 1.1.3

Cancel the common factor.

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

Step 1.1.4

Rewrite the expression.

$\frac{7}{3} + \frac{1}{8} \cdot \frac{- 5}{3} - \frac{5}{3} \div (- \frac{4}{7})$

Step 1.2

Multiply $\frac{1}{8}$ by $\frac{- 5}{3}$ .

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

Step 1.3

Multiply $8$ by $3$ .

$\frac{7}{3} + \frac{- 5}{24} - \frac{5}{3} \div (- \frac{4}{7})$

Step 1.4

Move the negative in front of the fraction.

$\frac{7}{3} - \frac{5}{24} - \frac{5}{3} \div (- \frac{4}{7})$

Step 1.5

To divide by a fraction, multiply by its reciprocal.

$\frac{7}{3} - \frac{5}{24} - (\frac{5}{3} (- \frac{7}{4}))$

Step 1.6

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

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Step 1.6.1

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

$\frac{7}{3} - \frac{5}{24} - - \frac{5 \cdot 7}{3 \cdot 4}$

Step 1.6.2

Multiply $5$ by $7$ .

$\frac{7}{3} - \frac{5}{24} - - \frac{35}{3 \cdot 4}$

Step 1.6.3

Multiply $3$ by $4$ .

$\frac{7}{3} - \frac{5}{24} - - \frac{35}{12}$

Step 1.7

Multiply $- - \frac{35}{12}$ .

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Step 1.7.1

Multiply $- 1$ by $- 1$ .

$\frac{7}{3} - \frac{5}{24} + 1 (\frac{35}{12})$

Step 1.7.2

Multiply $\frac{35}{12}$ by $1$ .

$\frac{7}{3} - \frac{5}{24} + \frac{35}{12}$

Step 2

Find the common denominator.

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Step 2.1

Multiply $\frac{7}{3}$ by $\frac{8}{8}$ .

$\frac{7}{3} \cdot \frac{8}{8} - \frac{5}{24} + \frac{35}{12}$

Step 2.2

Multiply $\frac{7}{3}$ by $\frac{8}{8}$ .

$\frac{7 \cdot 8}{3 \cdot 8} - \frac{5}{24} + \frac{35}{12}$

Step 2.3

Multiply $\frac{35}{12}$ by $\frac{2}{2}$ .

$\frac{7 \cdot 8}{3 \cdot 8} - \frac{5}{24} + \frac{35}{12} \cdot \frac{2}{2}$

Step 2.4

Multiply $\frac{35}{12}$ by $\frac{2}{2}$ .

$\frac{7 \cdot 8}{3 \cdot 8} - \frac{5}{24} + \frac{35 \cdot 2}{12 \cdot 2}$

Step 2.5

Multiply $3$ by $8$ .

$\frac{7 \cdot 8}{24} - \frac{5}{24} + \frac{35 \cdot 2}{12 \cdot 2}$

Step 2.6

Reorder the factors of $12 \cdot 2$ .

$\frac{7 \cdot 8}{24} - \frac{5}{24} + \frac{35 \cdot 2}{2 \cdot 12}$

Step 2.7

Multiply $2$ by $12$ .

$\frac{7 \cdot 8}{24} - \frac{5}{24} + \frac{35 \cdot 2}{24}$

Step 3

Combine the numerators over the common denominator.

$\frac{7 \cdot 8 - 5 + 35 \cdot 2}{24}$

Step 4

Simplify each term.

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Step 4.1

Multiply $7$ by $8$ .

$\frac{56 - 5 + 35 \cdot 2}{24}$

Step 4.2

Multiply $35$ by $2$ .

$\frac{56 - 5 + 70}{24}$

Step 5

Simplify by adding and subtracting.

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Step 5.1

Subtract $5$ from $56$ .

$\frac{51 + 70}{24}$

Step 5.2

Add $51$ and $70$ .

$\frac{121}{24}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{121}{24}$

Decimal Form:

$5.041\overline{6}$

Mixed Number Form:

$5 \frac{1}{24}$