Basic Math Examples

$\frac{z - 7}{8 y} + \frac{y}{5 z}$

Step 1

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

$\frac{z - 7}{8 y} \cdot \frac{5 z}{5 z} + \frac{y}{5 z}$

Step 2

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

$\frac{z - 7}{8 y} \cdot \frac{5 z}{5 z} + \frac{y}{5 z} \cdot \frac{8 y}{8 y}$

Step 3

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

Tap for more steps...

Step 3.1

Multiply $\frac{z - 7}{8 y}$ by $\frac{5 z}{5 z}$ .

$\frac{(z - 7) (5 z)}{8 y (5 z)} + \frac{y}{5 z} \cdot \frac{8 y}{8 y}$

Step 3.2

Multiply $5$ by $8$ .

$\frac{(z - 7) (5 z)}{40 y z} + \frac{y}{5 z} \cdot \frac{8 y}{8 y}$

Step 3.3

Multiply $\frac{y}{5 z}$ by $\frac{8 y}{8 y}$ .

$\frac{(z - 7) (5 z)}{40 y z} + \frac{y (8 y)}{5 z (8 y)}$

Step 3.4

Multiply $8$ by $5$ .

$\frac{(z - 7) (5 z)}{40 y z} + \frac{y (8 y)}{40 z y}$

Step 3.5

Reorder the factors of $40 z y$ .

$\frac{(z - 7) (5 z)}{40 y z} + \frac{y (8 y)}{40 y z}$

Step 4

Combine the numerators over the common denominator.

$\frac{(z - 7) (5 z) + y (8 y)}{40 y z}$

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

Apply the distributive property.

$\frac{(z \cdot 5 - 7 \cdot 5) z + y (8 y)}{40 y z}$

Step 5.2

Move $5$ to the left of $z$ .

$\frac{(5 \cdot z - 7 \cdot 5) z + y (8 y)}{40 y z}$

Step 5.3

Multiply $- 7$ by $5$ .

$\frac{(5 \cdot z - 35) z + y (8 y)}{40 y z}$

Step 5.4

Apply the distributive property.

$\frac{5 z \cdot z - 35 z + y (8 y)}{40 y z}$

Step 5.5

Multiply $z$ by $z$ by adding the exponents.

Tap for more steps...

Step 5.5.1

Move $z$ .

$\frac{5 (z \cdot z) - 35 z + y (8 y)}{40 y z}$

Step 5.5.2

Multiply $z$ by $z$ .

$\frac{5 z^{2} - 35 z + y (8 y)}{40 y z}$

Step 5.6

Rewrite using the commutative property of multiplication.

$\frac{5 z^{2} - 35 z + 8 y \cdot y}{40 y z}$

Step 5.7

Multiply $y$ by $y$ by adding the exponents.

Tap for more steps...

Step 5.7.1

Move $y$ .

$\frac{5 z^{2} - 35 z + 8 (y \cdot y)}{40 y z}$

Step 5.7.2

Multiply $y$ by $y$ .

$\frac{5 z^{2} - 35 z + 8 y^{2}}{40 y z}$