Basic Math Examples

$\frac{1}{2}$ ,

$\frac{3}{8}$ ,

$\frac{5}{16}$ ,

$\frac{3}{4}$

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

$\frac{1}{2}, \frac{3}{8}, \frac{5}{16}, \frac{3}{4}$ .

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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

$2$ has no factors besides

$1$ and

$2$ .

$2$ is a prime number

Step 1.1.3

The prime factors for

$8$ are

$2 \cdot 2 \cdot 2$ .

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Step 1.1.3.1

$8$ has factors of

$2$ and

$4$ .

$2 \cdot 4$

Step 1.1.3.2

$4$ has factors of

$2$ and

$2$ .

$2 \cdot 2 \cdot 2$

Step 1.1.4

The prime factors for

$16$ are

$2 \cdot 2 \cdot 2 \cdot 2$ .

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Step 1.1.4.1

$16$ has factors of

$2$ and

$8$ .

$2 \cdot 8$

Step 1.1.4.2

$8$ has factors of

$2$ and

$4$ .

$2 \cdot 2 \cdot 4$

Step 1.1.4.3

$4$ has factors of

$2$ and

$2$ .

$2 \cdot 2 \cdot 2 \cdot 2$

Step 1.1.5

$4$ has factors of

$2$ and

$2$ .

$2 \cdot 2$

Step 1.1.6

The LCM of

$2, 8, 16, 4$ is the result of multiplying all prime factors the greatest number of times they occur in either number.

$2 \cdot 2 \cdot 2 \cdot 2$

Step 1.1.7

Multiply

$2 \cdot 2 \cdot 2 \cdot 2$ .

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Step 1.1.7.1

Multiply

$2$ by

$2$ .

$4 \cdot 2 \cdot 2$

Step 1.1.7.2

Multiply

$4$ by

$2$ .

$8 \cdot 2$

Step 1.1.7.3

Multiply

$8$ by

$2$ .

$16$

Step 1.2

Multiply each number by

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

$n$ is a number that makes the denominator

$16$ .

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Step 1.2.1

Divide

$16$ by

$2$ .

$8$

Step 1.2.2

Multiply the numerator and denominator of

$\frac{1}{2}$ by

$8$ .

$\frac{1 \cdot 8}{2 \cdot 8}$

Step 1.2.3

Multiply

$8$ by

$1$ .

$\frac{8}{2 \cdot 8}$

Step 1.2.4

Multiply

$2$ by

$8$ .

$\frac{8}{16}$

Step 1.2.5

Divide

$16$ by

$8$ .

$2$

Step 1.2.6

Multiply the numerator and denominator of

$\frac{3}{8}$ by

$2$ .

$\frac{3 \cdot 2}{8 \cdot 2}$

Step 1.2.7

Multiply

$3$ by

$2$ .

$\frac{6}{8 \cdot 2}$

Step 1.2.8

Multiply

$8$ by

$2$ .

$\frac{6}{16}$

Step 1.2.9

Divide

$16$ by

$16$ .

$1$

Step 1.2.10

Multiply the numerator and denominator of

$\frac{5}{16}$ by

$1$ .

$\frac{5 \cdot 1}{16 \cdot 1}$

Step 1.2.11

Multiply

$5$ by

$1$ .

$\frac{5}{16 \cdot 1}$

Step 1.2.12

Multiply

$16$ by

$1$ .

$\frac{5}{16}$

Step 1.2.13

Divide

$16$ by

$4$ .

$4$

Step 1.2.14

Multiply the numerator and denominator of

$\frac{3}{4}$ by

$4$ .

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

Step 1.2.15

Multiply

$3$ by

$4$ .

$\frac{12}{4 \cdot 4}$

Step 1.2.16

Multiply

$4$ by

$4$ .

$\frac{12}{16}$

Step 1.2.17

Write the new list with the same denominators.

$\frac{8}{16}, \frac{6}{16}, \frac{5}{16}, \frac{12}{16}$

Step 2

Since the denominators are equal, arrange the numerators.

$\frac{5}{16}, \frac{6}{16}, \frac{8}{16}, \frac{12}{16}$

Step 3

Replace the fractions with the original fractions.

$\frac{5}{16}, \frac{3}{8}, \frac{1}{2}, \frac{3}{4}$