Basic Math Examples

\frac{31}{2} + 1 \frac{3}{4}

$\frac{31}{2} + 1 \frac{3}{4}$

Step 1

Convert

1 \frac{3}{4}

$1 \frac{3}{4}$ to an improper fraction.

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Step 1.1

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

\frac{31}{2} + 1 + \frac{3}{4}

$\frac{31}{2} + 1 + \frac{3}{4}$

Step 1.2

Add

1

$1$ and

\frac{3}{4}

$\frac{3}{4}$ .

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Step 1.2.1

Write

1

$1$ as a fraction with a common denominator.

\frac{31}{2} + \frac{4}{4} + \frac{3}{4}

$\frac{31}{2} + \frac{4}{4} + \frac{3}{4}$

Step 1.2.2

Combine the numerators over the common denominator.

\frac{31}{2} + \frac{4 + 3}{4}

$\frac{31}{2} + \frac{4 + 3}{4}$

Step 1.2.3

Add

4

$4$ and

3

$3$ .

\frac{31}{2} + \frac{7}{4}

$\frac{31}{2} + \frac{7}{4}$

\frac{31}{2} + \frac{7}{4}

$\frac{31}{2} + \frac{7}{4}$

\frac{31}{2} + \frac{7}{4}

$\frac{31}{2} + \frac{7}{4}$

Step 2

To write

\frac{31}{2}

$\frac{31}{2}$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{31}{2} \cdot \frac{2}{2} + \frac{7}{4}

$\frac{31}{2} \cdot \frac{2}{2} + \frac{7}{4}$

Step 3

Write each expression with a common denominator of

4

$4$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 3.1

Multiply

\frac{31}{2}

$\frac{31}{2}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{31 \cdot 2}{2 \cdot 2} + \frac{7}{4}

$\frac{31 \cdot 2}{2 \cdot 2} + \frac{7}{4}$

Step 3.2

Multiply

2

$2$ by

2

$2$ .

\frac{31 \cdot 2}{4} + \frac{7}{4}

$\frac{31 \cdot 2}{4} + \frac{7}{4}$

\frac{31 \cdot 2}{4} + \frac{7}{4}

$\frac{31 \cdot 2}{4} + \frac{7}{4}$

Step 4

Combine the numerators over the common denominator.

\frac{31 \cdot 2 + 7}{4}

$\frac{31 \cdot 2 + 7}{4}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply

31

$31$ by

2

$2$ .

\frac{62 + 7}{4}

$\frac{62 + 7}{4}$

Step 5.2

Add

62

$62$ and

7

$7$ .

\frac{69}{4}

$\frac{69}{4}$

\frac{69}{4}

$\frac{69}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

\frac{69}{4}

$\frac{69}{4}$

Decimal Form:

17.25

$17.25$

Mixed Number Form:

17 \frac{1}{4}

$17 \frac{1}{4}$