Basic Math Examples

$75 \cdot \frac{t}{60} = 60 \cdot \frac{t + 14}{60}$

Step 1

Simplify $75 \cdot \frac{t}{60}$ .

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Step 1.1

Rewrite.

$0 + 0 + 75 \cdot \frac{t}{60} = 60 \cdot \frac{t + 14}{60}$

Step 1.2

Simplify by adding zeros.

$75 \cdot \frac{t}{60} = 60 \cdot \frac{t + 14}{60}$

Step 1.3

Cancel the common factor of $15$ .

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Step 1.3.1

Factor $15$ out of $75$ .

$15 (5) \cdot \frac{t}{60} = 60 \cdot \frac{t + 14}{60}$

Step 1.3.2

Factor $15$ out of $60$ .

$15 \cdot 5 \cdot \frac{t}{15 \cdot 4} = 60 \cdot \frac{t + 14}{60}$

Step 1.3.3

Cancel the common factor.

$15 \cdot 5 \cdot \frac{t}{15 \cdot 4} = 60 \cdot \frac{t + 14}{60}$

Step 1.3.4

Rewrite the expression.

$5 \cdot \frac{t}{4} = 60 \cdot \frac{t + 14}{60}$

$\frac{5 t}{4} = 60 \cdot \frac{t + 14}{60}$

Step 2

Cancel the common factor of $60$ .

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Step 2.1

Cancel the common factor.

$\frac{5 t}{4} = 60 \cdot \frac{t + 14}{60}$

Step 2.2

Rewrite the expression.

$\frac{5 t}{4} = t + 14$

Step 3

Move all terms containing $t$ to the left side of the equation.

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Step 3.1

Subtract $t$ from both sides of the equation.

$\frac{5 t}{4} - t = 14$

Step 3.2

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

$\frac{5 t}{4} - t \cdot \frac{4}{4} = 14$

Step 3.3

Combine $- t$ and $\frac{4}{4}$ .

$\frac{5 t}{4} + \frac{- t \cdot 4}{4} = 14$

Step 3.4

Combine the numerators over the common denominator.

$\frac{5 t - t \cdot 4}{4} = 14$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Factor $t$ out of $5 t - t \cdot 4$ .

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Step 3.5.1.1

Factor $t$ out of $5 t$ .

$\frac{t \cdot 5 - t \cdot 4}{4} = 14$

Step 3.5.1.2

Factor $t$ out of $- t \cdot 4$ .

$\frac{t \cdot 5 + t (- 1 \cdot 4)}{4} = 14$

Step 3.5.1.3

Factor $t$ out of $t \cdot 5 + t (- 1 \cdot 4)$ .

$\frac{t (5 - 1 \cdot 4)}{4} = 14$

Step 3.5.2

Multiply $- 1$ by $4$ .

$\frac{t (5 - 4)}{4} = 14$

Step 3.5.3

Subtract $4$ from $5$ .

$\frac{t \cdot 1}{4} = 14$

Step 3.6

Multiply $t$ by $1$ .

$\frac{t}{4} = 14$

Step 4

Multiply both sides of the equation by $4$ .

$4 \frac{t}{4} = 4 \cdot 14$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Cancel the common factor of $4$ .

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Step 5.1.1.1

Cancel the common factor.

$4 \frac{t}{4} = 4 \cdot 14$

Step 5.1.1.2

Rewrite the expression.

$t = 4 \cdot 14$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $4$ by $14$ .

$t = 56$