Pre-Algebra Examples

$\frac{t}{60} + \frac{t}{65} = 1$

Step 1

Simplify $\frac{t}{60} + \frac{t}{65}$ .

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Step 1.1

To write $\frac{t}{60}$ as a fraction with a common denominator, multiply by $\frac{13}{13}$ .

$\frac{t}{60} \cdot \frac{13}{13} + \frac{t}{65} = 1$

Step 1.2

To write $\frac{t}{65}$ as a fraction with a common denominator, multiply by $\frac{12}{12}$ .

$\frac{t}{60} \cdot \frac{13}{13} + \frac{t}{65} \cdot \frac{12}{12} = 1$

Step 1.3

Write each expression with a common denominator of $780$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{t}{60}$ by $\frac{13}{13}$ .

$\frac{t \cdot 13}{60 \cdot 13} + \frac{t}{65} \cdot \frac{12}{12} = 1$

Step 1.3.2

Multiply $60$ by $13$ .

$\frac{t \cdot 13}{780} + \frac{t}{65} \cdot \frac{12}{12} = 1$

Step 1.3.3

Multiply $\frac{t}{65}$ by $\frac{12}{12}$ .

$\frac{t \cdot 13}{780} + \frac{t \cdot 12}{65 \cdot 12} = 1$

Step 1.3.4

Multiply $65$ by $12$ .

$\frac{t \cdot 13}{780} + \frac{t \cdot 12}{780} = 1$

Step 1.4

Combine the numerators over the common denominator.

$\frac{t \cdot 13 + t \cdot 12}{780} = 1$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Move $13$ to the left of $t$ .

$\frac{13 \cdot t + t \cdot 12}{780} = 1$

Step 1.5.2

Move $12$ to the left of $t$ .

$\frac{13 t + 12 \cdot t}{780} = 1$

Step 1.5.3

Add $13 t$ and $12 t$ .

$\frac{25 t}{780} = 1$

Step 1.6

Cancel the common factor of $25$ and $780$ .

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Step 1.6.1

Factor $5$ out of $25 t$ .

$\frac{5 (5 t)}{780} = 1$

Step 1.6.2

Cancel the common factors.

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Step 1.6.2.1

Factor $5$ out of $780$ .

$\frac{5 (5 t)}{5 (156)} = 1$

Step 1.6.2.2

Cancel the common factor.

$\frac{5 (5 t)}{5 \cdot 156} = 1$

Step 1.6.2.3

Rewrite the expression.

$\frac{5 t}{156} = 1$

Step 2

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

$t \approx 31.2$

Step 3