Basic Math Examples

$c + \frac{4}{5} = 3 \frac{3}{4}$

Step 1

Simplify the right side.

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Step 1.1

Convert $3 \frac{3}{4}$ to an improper fraction.

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Step 1.1.1

A mixed number is an addition of its whole and fractional parts.

$c + \frac{4}{5} = 3 + \frac{3}{4}$

Step 1.1.2

Add $3$ and $\frac{3}{4}$ .

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Step 1.1.2.1

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

$c + \frac{4}{5} = 3 \cdot \frac{4}{4} + \frac{3}{4}$

Step 1.1.2.2

Combine $3$ and $\frac{4}{4}$ .

$c + \frac{4}{5} = \frac{3 \cdot 4}{4} + \frac{3}{4}$

Step 1.1.2.3

Combine the numerators over the common denominator.

$c + \frac{4}{5} = \frac{3 \cdot 4 + 3}{4}$

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $3$ by $4$ .

$c + \frac{4}{5} = \frac{12 + 3}{4}$

Step 1.1.2.4.2

Add $12$ and $3$ .

$c + \frac{4}{5} = \frac{15}{4}$

Step 2

Move all terms not containing $c$ to the right side of the equation.

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Step 2.1

Subtract $\frac{4}{5}$ from both sides of the equation.

$c = \frac{15}{4} - \frac{4}{5}$

Step 2.2

To write $\frac{15}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$c = \frac{15}{4} \cdot \frac{5}{5} - \frac{4}{5}$

Step 2.3

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

$c = \frac{15}{4} \cdot \frac{5}{5} - \frac{4}{5} \cdot \frac{4}{4}$

Step 2.4

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

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Step 2.4.1

Multiply $\frac{15}{4}$ by $\frac{5}{5}$ .

$c = \frac{15 \cdot 5}{4 \cdot 5} - \frac{4}{5} \cdot \frac{4}{4}$

Step 2.4.2

Multiply $4$ by $5$ .

$c = \frac{15 \cdot 5}{20} - \frac{4}{5} \cdot \frac{4}{4}$

Step 2.4.3

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

$c = \frac{15 \cdot 5}{20} - \frac{4 \cdot 4}{5 \cdot 4}$

Step 2.4.4

Multiply $5$ by $4$ .

$c = \frac{15 \cdot 5}{20} - \frac{4 \cdot 4}{20}$

Step 2.5

Combine the numerators over the common denominator.

$c = \frac{15 \cdot 5 - 4 \cdot 4}{20}$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply $15$ by $5$ .

$c = \frac{75 - 4 \cdot 4}{20}$

Step 2.6.2

Multiply $- 4$ by $4$ .

$c = \frac{75 - 16}{20}$

Step 2.6.3

Subtract $16$ from $75$ .

$c = \frac{59}{20}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$c = \frac{59}{20}$

Decimal Form:

$c = 2.95$

Mixed Number Form:

$c = 2 \frac{19}{20}$