Basic Math Examples

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

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

Step 1

Convert

4 \frac{3}{8}

$4 \frac{3}{8}$ to an improper fraction.

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Step 1.1

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

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

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

Step 1.2

Add

4

$4$ and

\frac{3}{8}

$\frac{3}{8}$ .

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Step 1.2.1

To write

4

$4$ as a fraction with a common denominator, multiply by

\frac{8}{8}

$\frac{8}{8}$ .

4 \cdot \frac{8}{8} + \frac{3}{8} + 2 \frac{3}{4}

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

Step 1.2.2

Combine

4

$4$ and

\frac{8}{8}

$\frac{8}{8}$ .

\frac{4 \cdot 8}{8} + \frac{3}{8} + 2 \frac{3}{4}

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

Step 1.2.3

Combine the numerators over the common denominator.

\frac{4 \cdot 8 + 3}{8} + 2 \frac{3}{4}

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

4

$4$ by

8

$8$ .

\frac{32 + 3}{8} + 2 \frac{3}{4}

$\frac{32 + 3}{8} + 2 \frac{3}{4}$

Step 1.2.4.2

Add

32

$32$ and

3

$3$ .

\frac{35}{8} + 2 \frac{3}{4}

$\frac{35}{8} + 2 \frac{3}{4}$

\frac{35}{8} + 2 \frac{3}{4}

$\frac{35}{8} + 2 \frac{3}{4}$

\frac{35}{8} + 2 \frac{3}{4}

$\frac{35}{8} + 2 \frac{3}{4}$

\frac{35}{8} + 2 \frac{3}{4}

$\frac{35}{8} + 2 \frac{3}{4}$

Step 2

Convert

2 \frac{3}{4}

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

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Step 2.1

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

\frac{35}{8} + 2 + \frac{3}{4}

$\frac{35}{8} + 2 + \frac{3}{4}$

Step 2.2

Add

2

$2$ and

\frac{3}{4}

$\frac{3}{4}$ .

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Step 2.2.1

To write

2

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

\frac{4}{4}

$\frac{4}{4}$ .

\frac{35}{8} + 2 \cdot \frac{4}{4} + \frac{3}{4}

$\frac{35}{8} + 2 \cdot \frac{4}{4} + \frac{3}{4}$

Step 2.2.2

Combine

2

$2$ and

\frac{4}{4}

$\frac{4}{4}$ .

\frac{35}{8} + \frac{2 \cdot 4}{4} + \frac{3}{4}

$\frac{35}{8} + \frac{2 \cdot 4}{4} + \frac{3}{4}$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{35}{8} + \frac{2 \cdot 4 + 3}{4}

$\frac{35}{8} + \frac{2 \cdot 4 + 3}{4}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

2

$2$ by

4

$4$ .

\frac{35}{8} + \frac{8 + 3}{4}

$\frac{35}{8} + \frac{8 + 3}{4}$

Step 2.2.4.2

Add

8

$8$ and

3

$3$ .

\frac{35}{8} + \frac{11}{4}

$\frac{35}{8} + \frac{11}{4}$

\frac{35}{8} + \frac{11}{4}

$\frac{35}{8} + \frac{11}{4}$

\frac{35}{8} + \frac{11}{4}

$\frac{35}{8} + \frac{11}{4}$

\frac{35}{8} + \frac{11}{4}

$\frac{35}{8} + \frac{11}{4}$

Step 3

To write

\frac{11}{4}

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

\frac{2}{2}

$\frac{2}{2}$ .

\frac{35}{8} + \frac{11}{4} \cdot \frac{2}{2}

$\frac{35}{8} + \frac{11}{4} \cdot \frac{2}{2}$

Step 4

Write each expression with a common denominator of

8

$8$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 4.1

Multiply

\frac{11}{4}

$\frac{11}{4}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{35}{8} + \frac{11 \cdot 2}{4 \cdot 2}

$\frac{35}{8} + \frac{11 \cdot 2}{4 \cdot 2}$

Step 4.2

Multiply

4

$4$ by

2

$2$ .

\frac{35}{8} + \frac{11 \cdot 2}{8}

$\frac{35}{8} + \frac{11 \cdot 2}{8}$

\frac{35}{8} + \frac{11 \cdot 2}{8}

$\frac{35}{8} + \frac{11 \cdot 2}{8}$

Step 5

Combine the numerators over the common denominator.

\frac{35 + 11 \cdot 2}{8}

$\frac{35 + 11 \cdot 2}{8}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply

11

$11$ by

2

$2$ .

\frac{35 + 22}{8}

$\frac{35 + 22}{8}$

Step 6.2

Add

35

$35$ and

22

$22$ .

\frac{57}{8}

$\frac{57}{8}$

\frac{57}{8}

$\frac{57}{8}$

Step 7

The result can be shown in multiple forms.

Exact Form:

\frac{57}{8}

$\frac{57}{8}$

Decimal Form:

7.125

$7.125$

Mixed Number Form:

7 \frac{1}{8}

$7 \frac{1}{8}$