Pre-Algebra Examples

$\frac{t}{4} + \frac{t}{5} = 1$

Step 1

Simplify $\frac{t}{4} + \frac{t}{5}$ .

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Step 1.1

To write $\frac{t}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{t}{4} \cdot \frac{5}{5} + \frac{t}{5} = 1$

Step 1.2

To write $\frac{t}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{t}{4} \cdot \frac{5}{5} + \frac{t}{5} \cdot \frac{4}{4} = 1$

Step 1.3

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{t}{4}$ by $\frac{5}{5}$ .

$\frac{t \cdot 5}{4 \cdot 5} + \frac{t}{5} \cdot \frac{4}{4} = 1$

Step 1.3.2

Multiply $4$ by $5$ .

$\frac{t \cdot 5}{20} + \frac{t}{5} \cdot \frac{4}{4} = 1$

Step 1.3.3

Multiply $\frac{t}{5}$ by $\frac{4}{4}$ .

$\frac{t \cdot 5}{20} + \frac{t \cdot 4}{5 \cdot 4} = 1$

Step 1.3.4

Multiply $5$ by $4$ .

$\frac{t \cdot 5}{20} + \frac{t \cdot 4}{20} = 1$

Step 1.4

Combine the numerators over the common denominator.

$\frac{t \cdot 5 + t \cdot 4}{20} = 1$

Step 1.5

Simplify the numerator.

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Step 1.5.1

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

$\frac{5 \cdot t + t \cdot 4}{20} = 1$

Step 1.5.2

Move $4$ to the left of $t$ .

$\frac{5 t + 4 \cdot t}{20} = 1$

Step 1.5.3

Add $5 t$ and $4 t$ .

$\frac{9 t}{20} = 1$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$t = \frac{20}{9}$

Step 3