Pre-Algebra Examples

1.8 % \cdot 3.6

$1.8 % \cdot 3.6$

Step 1

Convert all of the decimals to reduced fractions.

\frac{9}{500}, \frac{18}{5}

$\frac{9}{500}, \frac{18}{5}$

Step 2

Find the GCF for the numerators

9, 18

$9, 18$ .

Tap for more steps...

Step 2.1

Find the common factors for the numerical part:

9, 18

$9, 18$

Step 2.2

The factors for

9

$9$ are

1, 3, 9

$1, 3, 9$ .

Tap for more steps...

Step 2.2.1

The factors for

9

$9$ are all numbers between

1

$1$ and

9

$9$ , which divide

9

$9$ evenly.

Check numbers between

1

$1$ and

9

$9$

Step 2.2.2

Find the factor pairs of

9

$9$ where

x \cdot y = 9

$x \cdot y = 9$ .

\begin{array}{c} x & y \\ 1 & 9 \\ 3 & 3 \end{array}

$\begin{array}{c} x & y \\ 1 & 9 \\ 3 & 3 \end{array}$

Step 2.2.3

List the factors for

9

$9$ .

1, 3, 9

$1, 3, 9$

1, 3, 9

$1, 3, 9$

Step 2.3

The factors for

18

$18$ are

1, 2, 3, 6, 9, 18

$1, 2, 3, 6, 9, 18$ .

Tap for more steps...

Step 2.3.1

The factors for

18

$18$ are all numbers between

1

$1$ and

18

$18$ , which divide

18

$18$ evenly.

Check numbers between

1

$1$ and

18

$18$

Step 2.3.2

Find the factor pairs of

18

$18$ where

x \cdot y = 18

$x \cdot y = 18$ .

\begin{array}{c} x & y \\ 1 & 18 \\ 2 & 9 \\ 3 & 6 \end{array}

$\begin{array}{c} x & y \\ 1 & 18 \\ 2 & 9 \\ 3 & 6 \end{array}$

Step 2.3.3

List the factors for

18

$18$ .

1, 2, 3, 6, 9, 18

$1, 2, 3, 6, 9, 18$

1, 2, 3, 6, 9, 18

$1, 2, 3, 6, 9, 18$

Step 2.4

List all the factors for

9, 18

$9, 18$ to find the common factors.

9

$9$ :

1, 3, 9

$1, 3, 9$

18

$18$ :

1, 2, 3, 6, 9, 18

$1, 2, 3, 6, 9, 18$

Step 2.5

The common factors for

9, 18

$9, 18$ are

1, 3, 9

$1, 3, 9$ .

1, 3, 9

$1, 3, 9$

Step 2.6

The GCF (HCF) of the numerical factors

1, 3, 9

$1, 3, 9$ is

9

$9$ .

9

$9$

9

$9$

Step 3

Find the GCF for the denominators

500, 5

$500, 5$ .

Tap for more steps...

Step 3.1

Find the common factors for the numerical part:

500, 5

$500, 5$

Step 3.2

The factors for

500

$500$ are

1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500

$1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500$ .

Tap for more steps...

Step 3.2.1

The factors for

500

$500$ are all numbers between

1

$1$ and

500

$500$ , which divide

500

$500$ evenly.

Check numbers between

1

$1$ and

500

$500$

Step 3.2.2

Find the factor pairs of

500

$500$ where

x \cdot y = 500

$x \cdot y = 500$ .

\begin{array}{c} x & y \\ 1 & 500 \\ 2 & 250 \\ 4 & 125 \\ 5 & 100 \\ 10 & 50 \\ 20 & 25 \end{array}

$\begin{array}{c} x & y \\ 1 & 500 \\ 2 & 250 \\ 4 & 125 \\ 5 & 100 \\ 10 & 50 \\ 20 & 25 \end{array}$

Step 3.2.3

List the factors for

500

$500$ .

1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500

$1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500$

1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500

$1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500$

Step 3.3

The factors for

5

$5$ are

1, 5

$1, 5$ .

Tap for more steps...

Step 3.3.1

The factors for

5

$5$ are all numbers between

1

$1$ and

5

$5$ , which divide

5

$5$ evenly.

Check numbers between

1

$1$ and

5

$5$

Step 3.3.2

Find the factor pairs of

5

$5$ where

x \cdot y = 5

$x \cdot y = 5$ .

\begin{array}{c} x & y \\ 1 & 5 \end{array}

$\begin{array}{c} x & y \\ 1 & 5 \end{array}$

Step 3.3.3

List the factors for

5

$5$ .

1, 5

$1, 5$

1, 5

$1, 5$

Step 3.4

List all the factors for

500, 5

$500, 5$ to find the common factors.

500

$500$ :

1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500

$1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500$

5

$5$ :

1, 5

$1, 5$

Step 3.5

The common factors for

500, 5

$500, 5$ are

1, 5

$1, 5$ .

1, 5

$1, 5$

Step 3.6

The GCF (HCF) of the numerical factors

1, 5

$1, 5$ is

5

$5$ .

5

$5$

5

$5$

Step 4

Determine the GCF for

\frac{9}{500}, \frac{18}{5}

$\frac{9}{500}, \frac{18}{5}$ .

\frac{9}{5}

$\frac{9}{5}$

Step 5

Convert the GCF

\frac{9}{5}

$\frac{9}{5}$ to decimal.

1.8

$1.8$