Pre-Algebra Examples

$7$ , $- 6 \frac{1}{3}$

Step 1

Convert $6 \frac{1}{3}$ to an improper fraction.

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Step 1.1

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

$7, - (6 + \frac{1}{3})$

Step 1.2

Add $6$ and $\frac{1}{3}$ .

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Step 1.2.1

To write $6$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$7, - (6 \cdot \frac{3}{3} + \frac{1}{3})$

Step 1.2.2

Combine $6$ and $\frac{3}{3}$ .

$7, - (\frac{6 \cdot 3}{3} + \frac{1}{3})$

Step 1.2.3

Combine the numerators over the common denominator.

$7, - \frac{6 \cdot 3 + 1}{3}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $6$ by $3$ .

$7, - \frac{18 + 1}{3}$

Step 1.2.4.2

Add $18$ and $1$ .

$7, - \frac{19}{3}$

Step 2

To find the LCM for a list of fractions such as $LCM (\frac{a}{b}, \frac{c}{d})$ using GCF:

1. Find the LCM of $a$ and $c$ .

2. Find the GCF of $b$ and $d$ .

3. $LCM (\frac{a}{b}, \frac{c}{d}) = \frac{LCM (a, c)}{GCF (b, d)}$ .

Step 3

Calculate the LCM of the numerators $7, - 19$ .

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Step 3.1

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 3.2

Since the LCM is the smallest positive number, $LCM (7, - 19) = LCM (7, 19)$

Step 3.3

Since $7$ has no factors besides $1$ and $7$ .

$7$ is a prime number

Step 3.4

Since $19$ has no factors besides $1$ and $19$ .

$19$ is a prime number

Step 3.5

The LCM of $7, 19$ is the result of multiplying all prime factors the greatest number of times they occur in either number.

$7 \cdot 19$

Step 3.6

Multiply $7$ by $19$ .

$133$

Step 4

Find the GCF of the denominators $1, 3$ .

$GCF (1, 3) = 1$

Step 5

Divide $133$ by $1$ .

$133$