Basic Math Examples

$\frac{1}{4} \cdot (b t) + 6 b t - \frac{1}{9} \cdot (b t)$

Step 1

Simplify each term.

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Step 1.1

Multiply $\frac{1}{4} (b t)$ .

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Step 1.1.1

Combine $b$ and $\frac{1}{4}$ .

$\frac{b}{4} t + 6 b t - \frac{1}{9} \cdot (b t)$

Step 1.1.2

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

$\frac{b t}{4} + 6 b t - \frac{1}{9} \cdot (b t)$

Step 1.2

Multiply $- \frac{1}{9} (b t)$ .

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Step 1.2.1

Combine $b$ and $\frac{1}{9}$ .

$\frac{b t}{4} + 6 b t - \frac{b}{9} t$

Step 1.2.2

Combine $t$ and $\frac{b}{9}$ .

$\frac{b t}{4} + 6 b t - \frac{t b}{9}$

Step 2

To write $6 b t$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{b t}{4} + 6 b t \cdot \frac{4}{4} - \frac{t b}{9}$

Step 3

Simplify terms.

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Step 3.1

Combine $6 b t$ and $\frac{4}{4}$ .

$\frac{b t}{4} + \frac{6 b t \cdot 4}{4} - \frac{t b}{9}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{b t + 6 b t \cdot 4}{4} - \frac{t b}{9}$

Step 4

Simplify each term.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Factor $b t$ out of $b t + 6 b t \cdot 4$ .

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Step 4.1.1.1

Factor $b t$ out of $b t$ .

$\frac{b t (1) + 6 b t \cdot 4}{4} - \frac{t b}{9}$

Step 4.1.1.2

Factor $b t$ out of $6 b t \cdot 4$ .

$\frac{b t (1) + b t (6 \cdot 4)}{4} - \frac{t b}{9}$

Step 4.1.1.3

Factor $b t$ out of $b t (1) + b t (6 \cdot 4)$ .

$\frac{b t (1 + 6 \cdot 4)}{4} - \frac{t b}{9}$

Step 4.1.2

Multiply $6$ by $4$ .

$\frac{b t (1 + 24)}{4} - \frac{t b}{9}$

Step 4.1.3

Add $1$ and $24$ .

$\frac{b t \cdot 25}{4} - \frac{t b}{9}$

Step 4.2

Move $25$ to the left of $b t$ .

$\frac{25 b t}{4} - \frac{t b}{9}$

Step 5

To write $\frac{25 b t}{4}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{25 b t}{4} \cdot \frac{9}{9} - \frac{t b}{9}$

Step 6

To write $- \frac{t b}{9}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{25 b t}{4} \cdot \frac{9}{9} - \frac{t b}{9} \cdot \frac{4}{4}$

Step 7

Write each expression with a common denominator of $36$ , by multiplying each by an appropriate factor of $1$ .

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Step 7.1

Multiply $\frac{25 b t}{4}$ by $\frac{9}{9}$ .

$\frac{25 b t \cdot 9}{4 \cdot 9} - \frac{t b}{9} \cdot \frac{4}{4}$

Step 7.2

Multiply $4$ by $9$ .

$\frac{25 b t \cdot 9}{36} - \frac{t b}{9} \cdot \frac{4}{4}$

Step 7.3

Multiply $\frac{t b}{9}$ by $\frac{4}{4}$ .

$\frac{25 b t \cdot 9}{36} - \frac{t b \cdot 4}{9 \cdot 4}$

Step 7.4

Multiply $9$ by $4$ .

$\frac{25 b t \cdot 9}{36} - \frac{t b \cdot 4}{36}$

Step 8

Combine the numerators over the common denominator.

$\frac{25 b t \cdot 9 - t b \cdot 4}{36}$

Step 9

Simplify the numerator.

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Step 9.1

Factor $b t$ out of $25 b t \cdot 9 - t b \cdot 4$ .

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Step 9.1.1

Factor $b t$ out of $25 b t \cdot 9$ .

$\frac{b t (25 \cdot 9) - t b \cdot 4}{36}$

Step 9.1.2

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

$\frac{b t (25 \cdot 9) + b t (- 1 \cdot 4)}{36}$

Step 9.1.3

Factor $b t$ out of $b t (25 \cdot 9) + b t (- 1 \cdot 4)$ .

$\frac{b t (25 \cdot 9 - 1 \cdot 4)}{36}$

Step 9.2

Combine exponents.

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Step 9.2.1

Multiply $25$ by $9$ .

$\frac{b t (225 - 1 \cdot 4)}{36}$

Step 9.2.2

Multiply $- 1$ by $4$ .

$\frac{b t (225 - 4)}{36}$

Step 9.3

Subtract $4$ from $225$ .

$\frac{b t \cdot 221}{36}$

Step 10

Move $221$ to the left of $b t$ .

$\frac{221 b t}{36}$