Pre-Algebra Examples

$\frac{4}{5}$ , $\frac{7}{10}$ , $\frac{13}{20}$

Step 1

Write all of the fractions over the common denominator.

Tap for more steps...

Step 1.1

Find the LCM for the denominators of $\frac{4}{5}, \frac{7}{10}, \frac{13}{20}$ .

Tap for more steps...

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 $5$ has no factors besides $1$ and $5$ .

$5$ is a prime number

Step 1.1.3

$10$ has factors of $2$ and $5$ .

$2 \cdot 5$

Step 1.1.4

The prime factors for $20$ are $2 \cdot 2 \cdot 5$ .

Tap for more steps...

Step 1.1.4.1

$20$ has factors of $2$ and $10$ .

$2 \cdot 10$

Step 1.1.4.2

$10$ has factors of $2$ and $5$ .

$2 \cdot 2 \cdot 5$

Step 1.1.5

Multiply $2 \cdot 2 \cdot 5$ .

Tap for more steps...

Step 1.1.5.1

Multiply $2$ by $2$ .

$4 \cdot 5$

Step 1.1.5.2

Multiply $4$ by $5$ .

$20$

Step 1.2

Multiply each number by $\frac{n}{n}$ , where $n$ is a number that makes the denominator $20$ .

Tap for more steps...

Step 1.2.1

Divide $20$ by $5$ .

$4$

Step 1.2.2

Multiply the numerator and denominator of $\frac{4}{5}$ by $4$ .

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

Step 1.2.3

Multiply $4$ by $4$ .

$\frac{16}{5 \cdot 4}$

Step 1.2.4

Multiply $5$ by $4$ .

$\frac{16}{20}$

Step 1.2.5

Divide $20$ by $10$ .

$2$

Step 1.2.6

Multiply the numerator and denominator of $\frac{7}{10}$ by $2$ .

$\frac{7 \cdot 2}{10 \cdot 2}$

Step 1.2.7

Multiply $7$ by $2$ .

$\frac{14}{10 \cdot 2}$

Step 1.2.8

Multiply $10$ by $2$ .

$\frac{14}{20}$

Step 1.2.9

Divide $20$ by $20$ .

$1$

Step 1.2.10

Multiply the numerator and denominator of $\frac{13}{20}$ by $1$ .

$\frac{13 \cdot 1}{20 \cdot 1}$

Step 1.2.11

Multiply $13$ by $1$ .

$\frac{13}{20 \cdot 1}$

Step 1.2.12

Multiply $20$ by $1$ .

$\frac{13}{20}$

Step 1.2.13

Write the new list with the same denominators.

$\frac{16}{20}, \frac{14}{20}, \frac{13}{20}$

Step 2

Since the denominators are equal, arrange the numerators.

$\frac{13}{20}, \frac{14}{20}, \frac{16}{20}$

Step 3

Replace the fractions with the original fractions.

$\frac{13}{20}, \frac{7}{10}, \frac{4}{5}$