Basic Math Examples

$\frac{t}{16} + \frac{3}{4} = \frac{5}{8}$

Step 1

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

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Step 1.1

Subtract $\frac{3}{4}$ from both sides of the equation.

$\frac{t}{16} = \frac{5}{8} - \frac{3}{4}$

Step 1.2

To write $- \frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{t}{16} = \frac{5}{8} - \frac{3}{4} \cdot \frac{2}{2}$

Step 1.3

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{3}{4}$ by $\frac{2}{2}$ .

$\frac{t}{16} = \frac{5}{8} - \frac{3 \cdot 2}{4 \cdot 2}$

Step 1.3.2

Multiply $4$ by $2$ .

$\frac{t}{16} = \frac{5}{8} - \frac{3 \cdot 2}{8}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{t}{16} = \frac{5 - 3 \cdot 2}{8}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $- 3$ by $2$ .

$\frac{t}{16} = \frac{5 - 6}{8}$

Step 1.5.2

Subtract $6$ from $5$ .

$\frac{t}{16} = \frac{- 1}{8}$

Step 1.6

Move the negative in front of the fraction.

$\frac{t}{16} = - \frac{1}{8}$

Step 2

Multiply both sides of the equation by $16$ .

$16 \frac{t}{16} = 16 (- \frac{1}{8})$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $16$ .

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Step 3.1.1.1

Cancel the common factor.

$16 \frac{t}{16} = 16 (- \frac{1}{8})$

Step 3.1.1.2

Rewrite the expression.

$t = 16 (- \frac{1}{8})$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $16 (- \frac{1}{8})$ .

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Step 3.2.1.1

Cancel the common factor of $8$ .

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Step 3.2.1.1.1

Move the leading negative in $- \frac{1}{8}$ into the numerator.

$t = 16 (\frac{- 1}{8})$

Step 3.2.1.1.2

Factor $8$ out of $16$ .

$t = 8 (2) \frac{- 1}{8}$

Step 3.2.1.1.3

Cancel the common factor.

$t = 8 \cdot 2 \frac{- 1}{8}$

Step 3.2.1.1.4

Rewrite the expression.

$t = 2 \cdot - 1$

Step 3.2.1.2

Multiply $2$ by $- 1$ .

$t = - 2$