Basic Math Examples

\frac{3}{7}

$\frac{3}{7}$ ,

\frac{1}{2}

$\frac{1}{2}$ ,

\frac{2}{3}

$\frac{2}{3}$ least to greatest

Step 1

Write all of the fractions over the common denominator.

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Step 1.1

Find the LCM for the denominators of

\frac{3}{7}, \frac{1}{2}, \frac{2}{3}

$\frac{3}{7}, \frac{1}{2}, \frac{2}{3}$ .

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Step 1.1.1

The LCM is the smallest positive number that all of the numbers divide into evenly.

1. List the prime factors of each number.

2. Multiply each factor the greatest number of times it occurs in either number.

Step 1.1.2

Since

7

$7$ has no factors besides

1

$1$ and

7

$7$ .

7

$7$ is a prime number

Step 1.1.3

Since

2

$2$ has no factors besides

1

$1$ and

2

$2$ .

2

$2$ is a prime number

Step 1.1.4

Since

3

$3$ has no factors besides

1

$1$ and

3

$3$ .

3

$3$ is a prime number

Step 1.1.5

The LCM of

7, 2, 3

$7, 2, 3$ is the result of multiplying all prime factors the greatest number of times they occur in either number.

2 \cdot 3 \cdot 7

$2 \cdot 3 \cdot 7$

Step 1.1.6

Multiply

2 \cdot 3 \cdot 7

$2 \cdot 3 \cdot 7$ .

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Step 1.1.6.1

Multiply

2

$2$ by

3

$3$ .

6 \cdot 7

$6 \cdot 7$

Step 1.1.6.2

Multiply

6

$6$ by

7

$7$ .

42

$42$

42

$42$

42

$42$

Step 1.2

Multiply each number by

\frac{n}{n}

$\frac{n}{n}$ , where

n

$n$ is a number that makes the denominator

42

$42$ .

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Step 1.2.1

Divide

42

$42$ by

7

$7$ .

6

$6$

Step 1.2.2

Multiply the numerator and denominator of

\frac{3}{7}

$\frac{3}{7}$ by

6

$6$ .

\frac{3 \cdot 6}{7 \cdot 6}

$\frac{3 \cdot 6}{7 \cdot 6}$

Step 1.2.3

Multiply

3

$3$ by

6

$6$ .

\frac{18}{7 \cdot 6}

$\frac{18}{7 \cdot 6}$

Step 1.2.4

Multiply

7

$7$ by

6

$6$ .

\frac{18}{42}

$\frac{18}{42}$

Step 1.2.5

Divide

42

$42$ by

2

$2$ .

21

$21$

Step 1.2.6

Multiply the numerator and denominator of

\frac{1}{2}

$\frac{1}{2}$ by

21

$21$ .

\frac{1 \cdot 21}{2 \cdot 21}

$\frac{1 \cdot 21}{2 \cdot 21}$

Step 1.2.7

Multiply

21

$21$ by

1

$1$ .

\frac{21}{2 \cdot 21}

$\frac{21}{2 \cdot 21}$

Step 1.2.8

Multiply

2

$2$ by

21

$21$ .

\frac{21}{42}

$\frac{21}{42}$

Step 1.2.9

Divide

42

$42$ by

3

$3$ .

14

$14$

Step 1.2.10

Multiply the numerator and denominator of

\frac{2}{3}

$\frac{2}{3}$ by

14

$14$ .

\frac{2 \cdot 14}{3 \cdot 14}

$\frac{2 \cdot 14}{3 \cdot 14}$

Step 1.2.11

Multiply

2

$2$ by

14

$14$ .

\frac{28}{3 \cdot 14}

$\frac{28}{3 \cdot 14}$

Step 1.2.12

Multiply

3

$3$ by

14

$14$ .

\frac{28}{42}

$\frac{28}{42}$

Step 1.2.13

Write the new list with the same denominators.

\frac{18}{42}, \frac{21}{42}, \frac{28}{42}

$\frac{18}{42}, \frac{21}{42}, \frac{28}{42}$

\frac{18}{42}, \frac{21}{42}, \frac{28}{42}

$\frac{18}{42}, \frac{21}{42}, \frac{28}{42}$

\frac{18}{42}, \frac{21}{42}, \frac{28}{42}

$\frac{18}{42}, \frac{21}{42}, \frac{28}{42}$

Step 2

Since the denominators are equal, arrange the numerators.

\frac{18}{42}, \frac{21}{42}, \frac{28}{42}

$\frac{18}{42}, \frac{21}{42}, \frac{28}{42}$

Step 3

Replace the fractions with the original fractions.

\frac{3}{7}, \frac{1}{2}, \frac{2}{3}

$\frac{3}{7}, \frac{1}{2}, \frac{2}{3}$