Basic Math Examples

$\frac{6}{5} (a) + a = 77$

Step 1

Simplify $\frac{6}{5} a + a$ .

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Step 1.1

Combine $\frac{6}{5}$ and $a$ .

$\frac{6 a}{5} + a = 77$

Step 1.2

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

$\frac{6 a}{5} + a \cdot \frac{5}{5} = 77$

Step 1.3

Simplify terms.

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Step 1.3.1

Combine $a$ and $\frac{5}{5}$ .

$\frac{6 a}{5} + \frac{a \cdot 5}{5} = 77$

Step 1.3.2

Combine the numerators over the common denominator.

$\frac{6 a + a \cdot 5}{5} = 77$

Step 1.4

Simplify the numerator.

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Step 1.4.1

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

$\frac{6 a + 5 \cdot a}{5} = 77$

Step 1.4.2

Add $6 a$ and $5 a$ .

$\frac{11 a}{5} = 77$

Step 2

Multiply both sides of the equation by $\frac{5}{11}$ .

$\frac{5}{11} \cdot \frac{11 a}{5} = \frac{5}{11} \cdot 77$

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

Simplify $\frac{5}{11} \cdot \frac{11 a}{5}$ .

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Step 3.1.1.1

Cancel the common factor of $5$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{5}{11} \cdot \frac{11 a}{5} = \frac{5}{11} \cdot 77$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{11} (11 a) = \frac{5}{11} \cdot 77$

Step 3.1.1.2

Cancel the common factor of $11$ .

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Step 3.1.1.2.1

Factor $11$ out of $11 a$ .

$\frac{1}{11} (11 (a)) = \frac{5}{11} \cdot 77$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{11} (11 a) = \frac{5}{11} \cdot 77$

Step 3.1.1.2.3

Rewrite the expression.

$a = \frac{5}{11} \cdot 77$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{5}{11} \cdot 77$ .

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Step 3.2.1.1

Cancel the common factor of $11$ .

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Step 3.2.1.1.1

Factor $11$ out of $77$ .

$a = \frac{5}{11} \cdot (11 (7))$

Step 3.2.1.1.2

Cancel the common factor.

$a = \frac{5}{11} \cdot (11 \cdot 7)$

Step 3.2.1.1.3

Rewrite the expression.

$a = 5 \cdot 7$

Step 3.2.1.2

Multiply $5$ by $7$ .

$a = 35$