Basic Math Examples

$2 \frac{3}{4} + 2 \frac{3}{5}$

Step 1

Convert

$2 \frac{3}{4}$ to an improper fraction.

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Step 1.1

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

$2 + \frac{3}{4} + 2 \frac{3}{5}$

Step 1.2

Add

$2$ and

$\frac{3}{4}$ .

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Step 1.2.1

To write

$2$ as a fraction with a common denominator, multiply by

$\frac{4}{4}$ .

$2 \cdot \frac{4}{4} + \frac{3}{4} + 2 \frac{3}{5}$

Step 1.2.2

Combine

$2$ and

$\frac{4}{4}$ .

$\frac{2 \cdot 4}{4} + \frac{3}{4} + 2 \frac{3}{5}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{2 \cdot 4 + 3}{4} + 2 \frac{3}{5}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$2$ by

$4$ .

$\frac{8 + 3}{4} + 2 \frac{3}{5}$

Step 1.2.4.2

Add

$8$ and

$3$ .

$\frac{11}{4} + 2 \frac{3}{5}$

Step 2

Convert

$2 \frac{3}{5}$ to an improper fraction.

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Step 2.1

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

$\frac{11}{4} + 2 + \frac{3}{5}$

Step 2.2

Add

$2$ and

$\frac{3}{5}$ .

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Step 2.2.1

To write

$2$ as a fraction with a common denominator, multiply by

$\frac{5}{5}$ .

$\frac{11}{4} + 2 \cdot \frac{5}{5} + \frac{3}{5}$

Step 2.2.2

Combine

$2$ and

$\frac{5}{5}$ .

$\frac{11}{4} + \frac{2 \cdot 5}{5} + \frac{3}{5}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{11}{4} + \frac{2 \cdot 5 + 3}{5}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

$2$ by

$5$ .

$\frac{11}{4} + \frac{10 + 3}{5}$

Step 2.2.4.2

Add

$10$ and

$3$ .

$\frac{11}{4} + \frac{13}{5}$

Step 3

To write

$\frac{11}{4}$ as a fraction with a common denominator, multiply by

$\frac{5}{5}$ .

$\frac{11}{4} \cdot \frac{5}{5} + \frac{13}{5}$

Step 4

To write

$\frac{13}{5}$ as a fraction with a common denominator, multiply by

$\frac{4}{4}$ .

$\frac{11}{4} \cdot \frac{5}{5} + \frac{13}{5} \cdot \frac{4}{4}$

Step 5

Write each expression with a common denominator of

$20$ , by multiplying each by an appropriate factor of

$1$ .

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Step 5.1

Multiply

$\frac{11}{4}$ by

$\frac{5}{5}$ .

$\frac{11 \cdot 5}{4 \cdot 5} + \frac{13}{5} \cdot \frac{4}{4}$

Step 5.2

Multiply

$4$ by

$5$ .

$\frac{11 \cdot 5}{20} + \frac{13}{5} \cdot \frac{4}{4}$

Step 5.3

Multiply

$\frac{13}{5}$ by

$\frac{4}{4}$ .

$\frac{11 \cdot 5}{20} + \frac{13 \cdot 4}{5 \cdot 4}$

Step 5.4

Multiply

$5$ by

$4$ .

$\frac{11 \cdot 5}{20} + \frac{13 \cdot 4}{20}$

Step 6

Combine the numerators over the common denominator.

$\frac{11 \cdot 5 + 13 \cdot 4}{20}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply

$11$ by

$5$ .

$\frac{55 + 13 \cdot 4}{20}$

Step 7.2

Multiply

$13$ by

$4$ .

$\frac{55 + 52}{20}$

Step 7.3

Add

$55$ and

$52$ .

$\frac{107}{20}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{107}{20}$

Decimal Form:

$5.35$

Mixed Number Form:

$5 \frac{7}{20}$