Basic Math Examples

$16 \frac{1}{10} - \frac{8 y}{5} = 7 \frac{1}{2}$

Step 1

Simplify the left side.

Tap for more steps...

Step 1.1

Convert $16 \frac{1}{10}$ to an improper fraction.

Tap for more steps...

Step 1.1.1

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

$16 + \frac{1}{10} - \frac{8 y}{5} = 7 \frac{1}{2}$

Step 1.1.2

Add $16$ and $\frac{1}{10}$ .

Tap for more steps...

Step 1.1.2.1

To write $16$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$16 \cdot \frac{10}{10} + \frac{1}{10} - \frac{8 y}{5} = 7 \frac{1}{2}$

Step 1.1.2.2

Combine $16$ and $\frac{10}{10}$ .

$\frac{16 \cdot 10}{10} + \frac{1}{10} - \frac{8 y}{5} = 7 \frac{1}{2}$

Step 1.1.2.3

Combine the numerators over the common denominator.

$\frac{16 \cdot 10 + 1}{10} - \frac{8 y}{5} = 7 \frac{1}{2}$

Step 1.1.2.4

Simplify the numerator.

Tap for more steps...

Step 1.1.2.4.1

Multiply $16$ by $10$ .

$\frac{160 + 1}{10} - \frac{8 y}{5} = 7 \frac{1}{2}$

Step 1.1.2.4.2

Add $160$ and $1$ .

$\frac{161}{10} - \frac{8 y}{5} = 7 \frac{1}{2}$

Step 2

Simplify the right side.

Tap for more steps...

Step 2.1

Convert $7 \frac{1}{2}$ to an improper fraction.

Tap for more steps...

Step 2.1.1

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

$\frac{161}{10} - \frac{8 y}{5} = 7 + \frac{1}{2}$

Step 2.1.2

Add $7$ and $\frac{1}{2}$ .

Tap for more steps...

Step 2.1.2.1

To write $7$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{161}{10} - \frac{8 y}{5} = 7 \cdot \frac{2}{2} + \frac{1}{2}$

Step 2.1.2.2

Combine $7$ and $\frac{2}{2}$ .

$\frac{161}{10} - \frac{8 y}{5} = \frac{7 \cdot 2}{2} + \frac{1}{2}$

Step 2.1.2.3

Combine the numerators over the common denominator.

$\frac{161}{10} - \frac{8 y}{5} = \frac{7 \cdot 2 + 1}{2}$

Step 2.1.2.4

Simplify the numerator.

Tap for more steps...

Step 2.1.2.4.1

Multiply $7$ by $2$ .

$\frac{161}{10} - \frac{8 y}{5} = \frac{14 + 1}{2}$

Step 2.1.2.4.2

Add $14$ and $1$ .

$\frac{161}{10} - \frac{8 y}{5} = \frac{15}{2}$

Step 3

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

Tap for more steps...

Step 3.1

Subtract $\frac{161}{10}$ from both sides of the equation.

$- \frac{8 y}{5} = \frac{15}{2} - \frac{161}{10}$

Step 3.2

To write $\frac{15}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{8 y}{5} = \frac{15}{2} \cdot \frac{5}{5} - \frac{161}{10}$

Step 3.3

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.3.1

Multiply $\frac{15}{2}$ by $\frac{5}{5}$ .

$- \frac{8 y}{5} = \frac{15 \cdot 5}{2 \cdot 5} - \frac{161}{10}$

Step 3.3.2

Multiply $2$ by $5$ .

$- \frac{8 y}{5} = \frac{15 \cdot 5}{10} - \frac{161}{10}$

Step 3.4

Combine the numerators over the common denominator.

$- \frac{8 y}{5} = \frac{15 \cdot 5 - 161}{10}$

Step 3.5

Simplify the numerator.

Tap for more steps...

Step 3.5.1

Multiply $15$ by $5$ .

$- \frac{8 y}{5} = \frac{75 - 161}{10}$

Step 3.5.2

Subtract $161$ from $75$ .

$- \frac{8 y}{5} = \frac{- 86}{10}$

Step 3.6

Cancel the common factor of $- 86$ and $10$ .

Tap for more steps...

Step 3.6.1

Factor $2$ out of $- 86$ .

$- \frac{8 y}{5} = \frac{2 (- 43)}{10}$

Step 3.6.2

Cancel the common factors.

Tap for more steps...

Step 3.6.2.1

Factor $2$ out of $10$ .

$- \frac{8 y}{5} = \frac{2 \cdot - 43}{2 \cdot 5}$

Step 3.6.2.2

Cancel the common factor.

$- \frac{8 y}{5} = \frac{2 \cdot - 43}{2 \cdot 5}$

Step 3.6.2.3

Rewrite the expression.

$- \frac{8 y}{5} = \frac{- 43}{5}$

Step 3.7

Move the negative in front of the fraction.

$- \frac{8 y}{5} = - \frac{43}{5}$

Step 4

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- 8 y = - 43$

Step 5

Divide each term in $- 8 y = - 43$ by $- 8$ and simplify.

Tap for more steps...

Step 5.1

Divide each term in $- 8 y = - 43$ by $- 8$ .

$\frac{- 8 y}{- 8} = \frac{- 43}{- 8}$

Step 5.2

Simplify the left side.

Tap for more steps...

Step 5.2.1

Cancel the common factor of $- 8$ .

Tap for more steps...

Step 5.2.1.1

Cancel the common factor.

$\frac{- 8 y}{- 8} = \frac{- 43}{- 8}$

Step 5.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 43}{- 8}$

Step 5.3

Simplify the right side.

Tap for more steps...

Step 5.3.1

Dividing two negative values results in a positive value.

$y = \frac{43}{8}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$y = \frac{43}{8}$

Decimal Form:

$y = 5.375$

Mixed Number Form:

$y = 5 \frac{3}{8}$