Basic Math Examples

$24 (\frac{7}{4} + \frac{t - 5}{3})$

Step 1

To write $\frac{7}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$24 (\frac{7}{4} \cdot \frac{3}{3} + \frac{t - 5}{3})$

Step 2

To write $\frac{t - 5}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$24 (\frac{7}{4} \cdot \frac{3}{3} + \frac{t - 5}{3} \cdot \frac{4}{4})$

Step 3

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{7}{4}$ by $\frac{3}{3}$ .

$24 (\frac{7 \cdot 3}{4 \cdot 3} + \frac{t - 5}{3} \cdot \frac{4}{4})$

Step 3.2

Multiply $4$ by $3$ .

$24 (\frac{7 \cdot 3}{12} + \frac{t - 5}{3} \cdot \frac{4}{4})$

Step 3.3

Multiply $\frac{t - 5}{3}$ by $\frac{4}{4}$ .

$24 (\frac{7 \cdot 3}{12} + \frac{(t - 5) \cdot 4}{3 \cdot 4})$

Step 3.4

Multiply $3$ by $4$ .

$24 (\frac{7 \cdot 3}{12} + \frac{(t - 5) \cdot 4}{12})$

Step 4

Combine the numerators over the common denominator.

$24 \frac{7 \cdot 3 + (t - 5) \cdot 4}{12}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $7$ by $3$ .

$24 \frac{21 + (t - 5) \cdot 4}{12}$

Step 5.2

Apply the distributive property.

$24 \frac{21 + t \cdot 4 - 5 \cdot 4}{12}$

Step 5.3

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

$24 \frac{21 + 4 \cdot t - 5 \cdot 4}{12}$

Step 5.4

Multiply $- 5$ by $4$ .

$24 \frac{21 + 4 \cdot t - 20}{12}$

Step 5.5

Subtract $20$ from $21$ .

$24 \frac{4 t + 1}{12}$

Step 6

Simplify terms.

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Step 6.1

Cancel the common factor of $12$ .

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Step 6.1.1

Factor $12$ out of $24$ .

$12 (2) \frac{4 t + 1}{12}$

Step 6.1.2

Cancel the common factor.

$12 \cdot 2 \frac{4 t + 1}{12}$

Step 6.1.3

Rewrite the expression.

$2 (4 t + 1)$

Step 6.2

Apply the distributive property.

$2 (4 t) + 2 \cdot 1$

Step 6.3

Multiply.

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Step 6.3.1

Multiply $4$ by $2$ .

$8 t + 2 \cdot 1$

Step 6.3.2

Multiply $2$ by $1$ .

$8 t + 2$