Basic Math Examples

$- \frac{7}{8} + 1 \frac{1}{6} \cdot 1 \frac{4}{5}$

Step 1

Convert $1 \frac{1}{6}$ to an improper fraction.

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Step 1.1

A mixed number is an addition of its whole and fractional parts.

$- \frac{7}{8} + (1 + \frac{1}{6}) \cdot 1 \frac{4}{5}$

Step 1.2

Add $1$ and $\frac{1}{6}$ .

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Step 1.2.1

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

$- \frac{7}{8} + (\frac{6}{6} + \frac{1}{6}) \cdot 1 \frac{4}{5}$

Step 1.2.2

Combine the numerators over the common denominator.

$- \frac{7}{8} + \frac{6 + 1}{6} \cdot 1 \frac{4}{5}$

Step 1.2.3

Add $6$ and $1$ .

$- \frac{7}{8} + \frac{7}{6} \cdot 1 \frac{4}{5}$

Step 2

Convert $1 \frac{4}{5}$ to an improper fraction.

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Step 2.1

A mixed number is an addition of its whole and fractional parts.

$- \frac{7}{8} + \frac{7}{6} \cdot (1 + \frac{4}{5})$

Step 2.2

Add $1$ and $\frac{4}{5}$ .

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Step 2.2.1

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

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

Step 2.2.2

Combine the numerators over the common denominator.

$- \frac{7}{8} + \frac{7}{6} \cdot \frac{5 + 4}{5}$

Step 2.2.3

Add $5$ and $4$ .

$- \frac{7}{8} + \frac{7}{6} \cdot \frac{9}{5}$

Step 3

Simplify each term.

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Step 3.1

Cancel the common factor of $3$ .

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Step 3.1.1

Factor $3$ out of $6$ .

$- \frac{7}{8} + \frac{7}{3 (2)} \cdot \frac{9}{5}$

Step 3.1.2

Factor $3$ out of $9$ .

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

Step 3.1.3

Cancel the common factor.

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

Step 3.1.4

Rewrite the expression.

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

Step 3.2

Multiply $\frac{7}{2}$ by $\frac{3}{5}$ .

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

Step 3.3

Multiply $7$ by $3$ .

$- \frac{7}{8} + \frac{21}{2 \cdot 5}$

Step 3.4

Multiply $2$ by $5$ .

$- \frac{7}{8} + \frac{21}{10}$

Step 4

To write $- \frac{7}{8}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{7}{8} \cdot \frac{5}{5} + \frac{21}{10}$

Step 5

To write $\frac{21}{10}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{7}{8} \cdot \frac{5}{5} + \frac{21}{10} \cdot \frac{4}{4}$

Step 6

Write each expression with a common denominator of $40$ , by multiplying each by an appropriate factor of $1$ .

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Step 6.1

Multiply $\frac{7}{8}$ by $\frac{5}{5}$ .

$- \frac{7 \cdot 5}{8 \cdot 5} + \frac{21}{10} \cdot \frac{4}{4}$

Step 6.2

Multiply $8$ by $5$ .

$- \frac{7 \cdot 5}{40} + \frac{21}{10} \cdot \frac{4}{4}$

Step 6.3

Multiply $\frac{21}{10}$ by $\frac{4}{4}$ .

$- \frac{7 \cdot 5}{40} + \frac{21 \cdot 4}{10 \cdot 4}$

Step 6.4

Multiply $10$ by $4$ .

$- \frac{7 \cdot 5}{40} + \frac{21 \cdot 4}{40}$

Step 7

Combine the numerators over the common denominator.

$\frac{- 7 \cdot 5 + 21 \cdot 4}{40}$

Step 8

Simplify the numerator.

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Step 8.1

Multiply $- 7$ by $5$ .

$\frac{- 35 + 21 \cdot 4}{40}$

Step 8.2

Multiply $21$ by $4$ .

$\frac{- 35 + 84}{40}$

Step 8.3

Add $- 35$ and $84$ .

$\frac{49}{40}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{49}{40}$

Decimal Form:

$1.225$

Mixed Number Form:

$1 \frac{9}{40}$