Algebra Examples

4.6

$4.6$

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.

4 \frac{6}{10}

$4 \frac{6}{10}$

Step 2

Reduce the fractional part of the mixed number.

4 \frac{3}{5}

$4 \frac{3}{5}$

Step 3

Convert

4 \frac{3}{5}

$4 \frac{3}{5}$ to an improper fraction.

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Step 3.1

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

4 + \frac{3}{5}

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

Step 3.2

Add

4

$4$ and

\frac{3}{5}

$\frac{3}{5}$ .

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Step 3.2.1

To write

4

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

\frac{5}{5}

$\frac{5}{5}$ .

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

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

Step 3.2.2

Combine

4

$4$ and

\frac{5}{5}

$\frac{5}{5}$ .

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

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

Step 3.2.3

Combine the numerators over the common denominator.

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

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

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply

4

$4$ by

5

$5$ .

\frac{20 + 3}{5}

$\frac{20 + 3}{5}$

Step 3.2.4.2

Add

20

$20$ and

3

$3$ .

\frac{23}{5}

$\frac{23}{5}$

\frac{23}{5}

$\frac{23}{5}$

\frac{23}{5}

$\frac{23}{5}$

\frac{23}{5}

$\frac{23}{5}$