Basic Math Examples

$- \frac{7}{8} y - \frac{1}{8} \cdot 100 + \frac{1}{4} \cdot \frac{1}{8} \cdot y - 135$

Step 1

Simplify each term.

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Step 1.1

Combine $y$ and $\frac{7}{8}$ .

$- \frac{y \cdot 7}{8} - \frac{1}{8} \cdot 100 + \frac{1}{4} \cdot \frac{1}{8} \cdot y - 135$

Step 1.2

Move $7$ to the left of $y$ .

$- \frac{7 \cdot y}{8} - \frac{1}{8} \cdot 100 + \frac{1}{4} \cdot \frac{1}{8} \cdot y - 135$

Step 1.3

Cancel the common factor of $4$ .

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Step 1.3.1

Move the leading negative in $- \frac{1}{8}$ into the numerator.

$- \frac{7 y}{8} + \frac{- 1}{8} \cdot 100 + \frac{1}{4} \cdot \frac{1}{8} \cdot y - 135$

Step 1.3.2

Factor $4$ out of $8$ .

$- \frac{7 y}{8} + \frac{- 1}{4 (2)} \cdot 100 + \frac{1}{4} \cdot \frac{1}{8} \cdot y - 135$

Step 1.3.3

Factor $4$ out of $100$ .

$- \frac{7 y}{8} + \frac{- 1}{4 \cdot 2} \cdot (4 \cdot 25) + \frac{1}{4} \cdot \frac{1}{8} \cdot y - 135$

Step 1.3.4

Cancel the common factor.

$- \frac{7 y}{8} + \frac{- 1}{4 \cdot 2} \cdot (4 \cdot 25) + \frac{1}{4} \cdot \frac{1}{8} \cdot y - 135$

Step 1.3.5

Rewrite the expression.

$- \frac{7 y}{8} + \frac{- 1}{2} \cdot 25 + \frac{1}{4} \cdot \frac{1}{8} \cdot y - 135$

Step 1.4

Combine $\frac{- 1}{2}$ and $25$ .

$- \frac{7 y}{8} + \frac{- 1 \cdot 25}{2} + \frac{1}{4} \cdot \frac{1}{8} \cdot y - 135$

Step 1.5

Multiply $- 1$ by $25$ .

$- \frac{7 y}{8} + \frac{- 25}{2} + \frac{1}{4} \cdot \frac{1}{8} \cdot y - 135$

Step 1.6

Move the negative in front of the fraction.

$- \frac{7 y}{8} - \frac{25}{2} + \frac{1}{4} \cdot \frac{1}{8} \cdot y - 135$

Step 1.7

Multiply $\frac{1}{4} \cdot \frac{1}{8}$ .

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Step 1.7.1

Multiply $\frac{1}{4}$ by $\frac{1}{8}$ .

$- \frac{7 y}{8} - \frac{25}{2} + \frac{1}{4 \cdot 8} \cdot y - 135$

Step 1.7.2

Multiply $4$ by $8$ .

$- \frac{7 y}{8} - \frac{25}{2} + \frac{1}{32} \cdot y - 135$

Step 1.8

Combine $\frac{1}{32}$ and $y$ .

$- \frac{7 y}{8} - \frac{25}{2} + \frac{y}{32} - 135$

Step 2

To write $- \frac{7 y}{8}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{7 y}{8} \cdot \frac{4}{4} + \frac{y}{32} - \frac{25}{2} - 135$

Step 3

Write each expression with a common denominator of $32$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{7 y}{8}$ by $\frac{4}{4}$ .

$- \frac{7 y \cdot 4}{8 \cdot 4} + \frac{y}{32} - \frac{25}{2} - 135$

Step 3.2

Multiply $8$ by $4$ .

$- \frac{7 y \cdot 4}{32} + \frac{y}{32} - \frac{25}{2} - 135$

Step 4

Combine the numerators over the common denominator.

$\frac{- 7 y \cdot 4 + y}{32} - \frac{25}{2} - 135$

Step 5

Find the common denominator.

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Step 5.1

Multiply $\frac{25}{2}$ by $\frac{16}{16}$ .

$\frac{- 7 y \cdot 4 + y}{32} - (\frac{25}{2} \cdot \frac{16}{16}) - 135$

Step 5.2

Multiply $\frac{25}{2}$ by $\frac{16}{16}$ .

$\frac{- 7 y \cdot 4 + y}{32} - \frac{25 \cdot 16}{2 \cdot 16} - 135$

Step 5.3

Write $- 135$ as a fraction with denominator $1$ .

$\frac{- 7 y \cdot 4 + y}{32} - \frac{25 \cdot 16}{2 \cdot 16} + \frac{- 135}{1}$

Step 5.4

Multiply $\frac{- 135}{1}$ by $\frac{32}{32}$ .

$\frac{- 7 y \cdot 4 + y}{32} - \frac{25 \cdot 16}{2 \cdot 16} + \frac{- 135}{1} \cdot \frac{32}{32}$

Step 5.5

Multiply $\frac{- 135}{1}$ by $\frac{32}{32}$ .

$\frac{- 7 y \cdot 4 + y}{32} - \frac{25 \cdot 16}{2 \cdot 16} + \frac{- 135 \cdot 32}{32}$

Step 5.6

Multiply $2$ by $16$ .

$\frac{- 7 y \cdot 4 + y}{32} - \frac{25 \cdot 16}{32} + \frac{- 135 \cdot 32}{32}$

Step 6

Combine the numerators over the common denominator.

$\frac{- 7 y \cdot 4 + y - 25 \cdot 16 - 135 \cdot 32}{32}$

Step 7

Simplify each term.

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Step 7.1

Multiply $4$ by $- 7$ .

$\frac{- 28 y + y - 25 \cdot 16 - 135 \cdot 32}{32}$

Step 7.2

Multiply $- 25$ by $16$ .

$\frac{- 28 y + y - 400 - 135 \cdot 32}{32}$

Step 7.3

Multiply $- 135$ by $32$ .

$\frac{- 28 y + y - 400 - 4320}{32}$

Step 8

Simplify terms.

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Step 8.1

Add $- 28 y$ and $y$ .

$\frac{- 27 y - 400 - 4320}{32}$

Step 8.2

Subtract $4320$ from $- 400$ .

$\frac{- 27 y - 4720}{32}$

Step 8.3

Factor $- 1$ out of $- 27 y$ .

$\frac{- (27 y) - 4720}{32}$

Step 8.4

Rewrite $- 4720$ as $- 1 (4720)$ .

$\frac{- (27 y) - 1 (4720)}{32}$

Step 8.5

Factor $- 1$ out of $- (27 y) - 1 (4720)$ .

$\frac{- (27 y + 4720)}{32}$

Step 8.6

Simplify the expression.

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Step 8.6.1

Rewrite $- (27 y + 4720)$ as $- 1 (27 y + 4720)$ .

$\frac{- 1 (27 y + 4720)}{32}$

Step 8.6.2

Move the negative in front of the fraction.

$- \frac{27 y + 4720}{32}$