Basic Math Examples

77.5

$77.5$

Step 1

Convert the decimal number to a fraction by placing the decimal number over a power of ten. Since there is

1

$1$ number to the right of the decimal point, place the decimal number over

10^{1}

$10^{1}$

(10)

$(10)$ . Next, add the whole number to the left of the decimal.

77 \frac{5}{10}

$77 \frac{5}{10}$

Step 2

Reduce the fractional part of the mixed number.

77 \frac{1}{2}

$77 \frac{1}{2}$

Step 3

Convert

77 \frac{1}{2}

$77 \frac{1}{2}$ to an improper fraction.

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Step 3.1

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

77 + \frac{1}{2}

$77 + \frac{1}{2}$

Step 3.2

Add

77

$77$ and

\frac{1}{2}

$\frac{1}{2}$ .

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Step 3.2.1

To write

77

$77$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

77 \cdot \frac{2}{2} + \frac{1}{2}

$77 \cdot \frac{2}{2} + \frac{1}{2}$

Step 3.2.2

Combine

77

$77$ and

\frac{2}{2}

$\frac{2}{2}$ .

\frac{77 \cdot 2}{2} + \frac{1}{2}

$\frac{77 \cdot 2}{2} + \frac{1}{2}$

Step 3.2.3

Combine the numerators over the common denominator.

\frac{77 \cdot 2 + 1}{2}

$\frac{77 \cdot 2 + 1}{2}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply

77

$77$ by

2

$2$ .

\frac{154 + 1}{2}

$\frac{154 + 1}{2}$

Step 3.2.4.2

Add

154

$154$ and

1

$1$ .

\frac{155}{2}

$\frac{155}{2}$

\frac{155}{2}

$\frac{155}{2}$

\frac{155}{2}

$\frac{155}{2}$

\frac{155}{2}

$\frac{155}{2}$