Basic Math Examples

$\frac{78 + 25}{78 - 65} - \frac{65 - θ}{65 - 50}$

Step 1

Add $78$ and $25$ .

$\frac{103}{78 - 65} - \frac{65 - θ}{65 - 50}$

Step 2

Simplify each term.

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Step 2.1

Subtract $65$ from $78$ .

$\frac{103}{13} - \frac{65 - θ}{65 - 50}$

Step 2.2

Subtract $50$ from $65$ .

$\frac{103}{13} - \frac{65 - θ}{15}$

Step 3

To write $\frac{103}{13}$ as a fraction with a common denominator, multiply by $\frac{15}{15}$ .

$\frac{103}{13} \cdot \frac{15}{15} - \frac{65 - θ}{15}$

Step 4

To write $- \frac{65 - θ}{15}$ as a fraction with a common denominator, multiply by $\frac{13}{13}$ .

$\frac{103}{13} \cdot \frac{15}{15} - \frac{65 - θ}{15} \cdot \frac{13}{13}$

Step 5

Write each expression with a common denominator of $195$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{103}{13}$ by $\frac{15}{15}$ .

$\frac{103 \cdot 15}{13 \cdot 15} - \frac{65 - θ}{15} \cdot \frac{13}{13}$

Step 5.2

Multiply $13$ by $15$ .

$\frac{103 \cdot 15}{195} - \frac{65 - θ}{15} \cdot \frac{13}{13}$

Step 5.3

Multiply $\frac{65 - θ}{15}$ by $\frac{13}{13}$ .

$\frac{103 \cdot 15}{195} - \frac{(65 - θ) \cdot 13}{15 \cdot 13}$

Step 5.4

Multiply $15$ by $13$ .

$\frac{103 \cdot 15}{195} - \frac{(65 - θ) \cdot 13}{195}$

Step 6

Combine the numerators over the common denominator.

$\frac{103 \cdot 15 - (65 - θ) \cdot 13}{195}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $103$ by $15$ .

$\frac{1545 - (65 - θ) \cdot 13}{195}$

Step 7.2

Apply the distributive property.

$\frac{1545 + (- 1 \cdot 65 - - θ) \cdot 13}{195}$

Step 7.3

Multiply $- 1$ by $65$ .

$\frac{1545 + (- 65 - - θ) \cdot 13}{195}$

Step 7.4

Multiply $- - θ$ .

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Step 7.4.1

Multiply $- 1$ by $- 1$ .

$\frac{1545 + (- 65 + 1 θ) \cdot 13}{195}$

Step 7.4.2

Multiply $θ$ by $1$ .

$\frac{1545 + (- 65 + θ) \cdot 13}{195}$

Step 7.5

Apply the distributive property.

$\frac{1545 - 65 \cdot 13 + θ \cdot 13}{195}$

Step 7.6

Multiply $- 65$ by $13$ .

$\frac{1545 - 845 + θ \cdot 13}{195}$

Step 7.7

Move $13$ to the left of $θ$ .

$\frac{1545 - 845 + 13 \cdot θ}{195}$

Step 7.8

Subtract $845$ from $1545$ .

$\frac{700 + 13 θ}{195}$