Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

To divide by a fraction, multiply by its reciprocal.

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

Step 1.2

Cancel the common factor of $5$ .

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Step 1.2.1

Cancel the common factor.

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

Step 1.2.2

Rewrite the expression.

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

Step 1.3

Combine $\frac{1}{2}$ and $3$ .

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

Step 1.4

Cancel the common factor of $2$ .

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Step 1.4.1

Factor $2$ out of $4$ .

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

Step 1.4.2

Factor $2$ out of $- 2$ .

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

Step 1.4.3

Cancel the common factor.

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

Step 1.4.4

Rewrite the expression.

$\frac{3}{4} - \frac{3}{2} + \frac{1}{2} \cdot - 1 - 1 \div \frac{- 5}{6} + 7$

Step 1.5

Combine $\frac{1}{2}$ and $- 1$ .

$\frac{3}{4} - \frac{3}{2} + \frac{- 1}{2} - 1 \div \frac{- 5}{6} + 7$

Step 1.6

Move the negative in front of the fraction.

$\frac{3}{4} - \frac{3}{2} - \frac{1}{2} - 1 \div \frac{- 5}{6} + 7$

Step 1.7

To divide by a fraction, multiply by its reciprocal.

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

Step 1.8

Multiply $\frac{6}{- 5}$ by $1$ .

$\frac{3}{4} - \frac{3}{2} - \frac{1}{2} - \frac{6}{- 5} + 7$

Step 1.9

Move the negative in front of the fraction.

$\frac{3}{4} - \frac{3}{2} - \frac{1}{2} - - \frac{6}{5} + 7$

Step 1.10

Multiply $- - \frac{6}{5}$ .

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Step 1.10.1

Multiply $- 1$ by $- 1$ .

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

Step 1.10.2

Multiply $\frac{6}{5}$ by $1$ .

$\frac{3}{4} - \frac{3}{2} - \frac{1}{2} + \frac{6}{5} + 7$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$7 + \frac{3}{4} + \frac{- 3 - 1}{2} + \frac{6}{5}$

Step 2.2

Subtract $1$ from $- 3$ .

$7 + \frac{3}{4} + \frac{- 4}{2} + \frac{6}{5}$

Step 3

Find the common denominator.

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Step 3.1

Write $7$ as a fraction with denominator $1$ .

$\frac{7}{1} + \frac{3}{4} + \frac{- 4}{2} + \frac{6}{5}$

Step 3.2

Multiply $\frac{7}{1}$ by $\frac{20}{20}$ .

$\frac{7}{1} \cdot \frac{20}{20} + \frac{3}{4} + \frac{- 4}{2} + \frac{6}{5}$

Step 3.3

Multiply $\frac{7}{1}$ by $\frac{20}{20}$ .

$\frac{7 \cdot 20}{20} + \frac{3}{4} + \frac{- 4}{2} + \frac{6}{5}$

Step 3.4

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

$\frac{7 \cdot 20}{20} + \frac{3}{4} \cdot \frac{5}{5} + \frac{- 4}{2} + \frac{6}{5}$

Step 3.5

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

$\frac{7 \cdot 20}{20} + \frac{3 \cdot 5}{4 \cdot 5} + \frac{- 4}{2} + \frac{6}{5}$

Step 3.6

Multiply $\frac{- 4}{2}$ by $\frac{10}{10}$ .

$\frac{7 \cdot 20}{20} + \frac{3 \cdot 5}{4 \cdot 5} + \frac{- 4}{2} \cdot \frac{10}{10} + \frac{6}{5}$

Step 3.7

Multiply $\frac{- 4}{2}$ by $\frac{10}{10}$ .

$\frac{7 \cdot 20}{20} + \frac{3 \cdot 5}{4 \cdot 5} + \frac{- 4 \cdot 10}{2 \cdot 10} + \frac{6}{5}$

Step 3.8

Multiply $\frac{6}{5}$ by $\frac{4}{4}$ .

$\frac{7 \cdot 20}{20} + \frac{3 \cdot 5}{4 \cdot 5} + \frac{- 4 \cdot 10}{2 \cdot 10} + \frac{6}{5} \cdot \frac{4}{4}$

Step 3.9

Multiply $\frac{6}{5}$ by $\frac{4}{4}$ .

$\frac{7 \cdot 20}{20} + \frac{3 \cdot 5}{4 \cdot 5} + \frac{- 4 \cdot 10}{2 \cdot 10} + \frac{6 \cdot 4}{5 \cdot 4}$

Step 3.10

Multiply $4$ by $5$ .

$\frac{7 \cdot 20}{20} + \frac{3 \cdot 5}{20} + \frac{- 4 \cdot 10}{2 \cdot 10} + \frac{6 \cdot 4}{5 \cdot 4}$

Step 3.11

Multiply $2$ by $10$ .

$\frac{7 \cdot 20}{20} + \frac{3 \cdot 5}{20} + \frac{- 4 \cdot 10}{20} + \frac{6 \cdot 4}{5 \cdot 4}$

Step 3.12

Reorder the factors of $5 \cdot 4$ .

$\frac{7 \cdot 20}{20} + \frac{3 \cdot 5}{20} + \frac{- 4 \cdot 10}{20} + \frac{6 \cdot 4}{4 \cdot 5}$

Step 3.13

Multiply $4$ by $5$ .

$\frac{7 \cdot 20}{20} + \frac{3 \cdot 5}{20} + \frac{- 4 \cdot 10}{20} + \frac{6 \cdot 4}{20}$

Step 4

Combine the numerators over the common denominator.

$\frac{7 \cdot 20 + 3 \cdot 5 - 4 \cdot 10 + 6 \cdot 4}{20}$

Step 5

Simplify each term.

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Step 5.1

Multiply $7$ by $20$ .

$\frac{140 + 3 \cdot 5 - 4 \cdot 10 + 6 \cdot 4}{20}$

Step 5.2

Multiply $3$ by $5$ .

$\frac{140 + 15 - 4 \cdot 10 + 6 \cdot 4}{20}$

Step 5.3

Multiply $- 4$ by $10$ .

$\frac{140 + 15 - 40 + 6 \cdot 4}{20}$

Step 5.4

Multiply $6$ by $4$ .

$\frac{140 + 15 - 40 + 24}{20}$

Step 6

Simplify by adding and subtracting.

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Step 6.1

Add $140$ and $15$ .

$\frac{155 - 40 + 24}{20}$

Step 6.2

Subtract $40$ from $155$ .

$\frac{115 + 24}{20}$

Step 6.3

Add $115$ and $24$ .

$\frac{139}{20}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{139}{20}$

Decimal Form:

$6.95$

Mixed Number Form:

$6 \frac{19}{20}$