Basic Math Examples

$\frac{86 y}{100} + \frac{87 (100 - 83.1 - y)}{100} = 14.602$

Step 1

Simplify $\frac{86 y}{100} + \frac{87 (100 - 83.1 - y)}{100}$ .

Tap for more steps...

Step 1.1

Combine the numerators over the common denominator.

$\frac{86 y + 87 (100 - 83.1 - y)}{100} = 14.602$

Step 1.2

Simplify each term.

Tap for more steps...

Step 1.2.1

Subtract $83.1$ from $100$ .

$\frac{86 y + 87 (16.9 - y)}{100} = 14.602$

Step 1.2.2

Apply the distributive property.

$\frac{86 y + 87 \cdot 16.9 + 87 (- y)}{100} = 14.602$

Step 1.2.3

Multiply $87$ by $16.9$ .

$\frac{86 y + 1470.3 + 87 (- y)}{100} = 14.602$

Step 1.2.4

Multiply $- 1$ by $87$ .

$\frac{86 y + 1470.3 - 87 y}{100} = 14.602$

Step 1.3

Simplify terms.

Tap for more steps...

Step 1.3.1

Subtract $87 y$ from $86 y$ .

$\frac{- y + 1470.3}{100} = 14.602$

Step 1.3.2

Factor $0.1$ out of $- y + 1470.3$ .

Tap for more steps...

Step 1.3.2.1

Factor $0.1$ out of $- y$ .

$\frac{0.1 (- 10 y) + 1470.3}{100} = 14.602$

Step 1.3.2.2

Factor $0.1$ out of $1470.3$ .

$\frac{0.1 (- 10 y) + 0.1 (14703)}{100} = 14.602$

Step 1.3.2.3

Factor $0.1$ out of $0.1 (- 10 y) + 0.1 (14703)$ .

$\frac{0.1 (- 10 y + 14703)}{100} = 14.602$

Step 1.3.3

Factor $100$ out of $100$ .

$\frac{0.1 (- 10 y + 14703)}{100 (1)} = 14.602$

Step 1.4

Separate fractions.

$\frac{0.1}{100} \cdot \frac{- 10 y + 14703}{1} = 14.602$

Step 1.5

Divide $0.1$ by $100$ .

$0.001 \frac{- 10 y + 14703}{1} = 14.602$

Step 1.6

Cancel the common factor of $0.001$ .

Tap for more steps...

Step 1.6.1

Factor $0.001$ out of $1$ .

$0.001 \frac{- 10 y + 14703}{0.001 \cdot 1000} = 14.602$

Step 1.6.2

Cancel the common factor.

$0.001 \frac{- 10 y + 14703}{0.001 \cdot 1000} = 14.602$

Step 1.6.3

Rewrite the expression.

$\frac{- 10 y + 14703}{1000} = 14.602$

Step 1.7

Factor $- 1$ out of $- 10 y$ .

$\frac{- (10 y) + 14703}{1000} = 14.602$

Step 1.8

Rewrite $14703$ as $- 1 (- 14703)$ .

$\frac{- (10 y) - 1 (- 14703)}{1000} = 14.602$

Step 1.9

Factor $- 1$ out of $- (10 y) - 1 (- 14703)$ .

$\frac{- (10 y - 14703)}{1000} = 14.602$

Step 1.10

Simplify the expression.

Tap for more steps...

Step 1.10.1

Rewrite $- (10 y - 14703)$ as $- 1 (10 y - 14703)$ .

$\frac{- 1 (10 y - 14703)}{1000} = 14.602$

Step 1.10.2

Move the negative in front of the fraction.

$- \frac{10 y - 14703}{1000} = 14.602$

Step 2

Multiply both sides of the equation by $- 1000$ .

$- 1000 (- \frac{10 y - 14703}{1000}) = - 1000 \cdot 14.602$

Step 3

Simplify both sides of the equation.

Tap for more steps...

Step 3.1

Simplify the left side.

Tap for more steps...

Step 3.1.1

Simplify $- 1000 (- \frac{10 y - 14703}{1000})$ .

Tap for more steps...

Step 3.1.1.1

Cancel the common factor of $1000$ .

Tap for more steps...

Step 3.1.1.1.1

Move the leading negative in $- \frac{10 y - 14703}{1000}$ into the numerator.

$- 1000 \frac{- (10 y - 14703)}{1000} = - 1000 \cdot 14.602$

Step 3.1.1.1.2

Factor $1000$ out of $- 1000$ .

$1000 (- 1) \frac{- (10 y - 14703)}{1000} = - 1000 \cdot 14.602$

Step 3.1.1.1.3

Cancel the common factor.

$1000 \cdot - 1 \frac{- (10 y - 14703)}{1000} = - 1000 \cdot 14.602$

Step 3.1.1.1.4

Rewrite the expression.

$- - (10 y - 14703) = - 1000 \cdot 14.602$

Step 3.1.1.2

Multiply.

Tap for more steps...

Step 3.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 (10 y - 14703) = - 1000 \cdot 14.602$

Step 3.1.1.2.2

Multiply $10 y - 14703$ by $1$ .

$10 y - 14703 = - 1000 \cdot 14.602$

Step 3.2

Simplify the right side.

Tap for more steps...

Step 3.2.1

Multiply $- 1000$ by $14.602$ .

$10 y - 14703 = - 14602$

Step 4

Move all terms not containing $y$ to the right side of the equation.

Tap for more steps...

Step 4.1

Add $14703$ to both sides of the equation.

$10 y = - 14602 + 14703$

Step 4.2

Add $- 14602$ and $14703$ .

$10 y = 101$

Step 5

Divide each term in $10 y = 101$ by $10$ and simplify.

Tap for more steps...

Step 5.1

Divide each term in $10 y = 101$ by $10$ .

$\frac{10 y}{10} = \frac{101}{10}$

Step 5.2

Simplify the left side.

Tap for more steps...

Step 5.2.1

Cancel the common factor of $10$ .

Tap for more steps...

Step 5.2.1.1

Cancel the common factor.

$\frac{10 y}{10} = \frac{101}{10}$

Step 5.2.1.2

Divide $y$ by $1$ .

$y = \frac{101}{10}$

Step 5.3

Simplify the right side.

Tap for more steps...

Step 5.3.1

Cancel the common factor of $101$ and $10$ .

Tap for more steps...

Step 5.3.1.1

Rewrite $101$ as $1 (101)$ .

$y = \frac{1 (101)}{10}$

Step 5.3.1.2

Cancel the common factors.

Tap for more steps...

Step 5.3.1.2.1

Rewrite $10$ as $1 (10)$ .

$y = \frac{1 \cdot 101}{1 \cdot 10}$

Step 5.3.1.2.2

Cancel the common factor.

$y = \frac{1 \cdot 101}{1 \cdot 10}$

Step 5.3.1.2.3

Rewrite the expression.

$y = \frac{101}{10}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$y = \frac{101}{10}$

Decimal Form:

$y = 10.1$

Mixed Number Form:

$y = 10 \frac{1}{10}$