Pre-Algebra Examples

$68$ , $\frac{1}{12} + 62$ , $\frac{8}{9}$

Step 1

Simplify each term.

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Step 1.1

To write $62$ as a fraction with a common denominator, multiply by $\frac{12}{12}$ .

$68, \frac{1}{12} + 62 \cdot \frac{12}{12}, \frac{8}{9}$

Step 1.2

Combine $62$ and $\frac{12}{12}$ .

$68, \frac{1}{12} + \frac{62 \cdot 12}{12}, \frac{8}{9}$

Step 1.3

Combine the numerators over the common denominator.

$68, \frac{1 + 62 \cdot 12}{12}, \frac{8}{9}$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Multiply $62$ by $12$ .

$68, \frac{1 + 744}{12}, \frac{8}{9}$

Step 1.4.2

Add $1$ and $744$ .

$68, \frac{745}{12}, \frac{8}{9}$

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 $68, 745, 8$ .

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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

The prime factors for $68$ are $2 \cdot 2 \cdot 17$ .

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Step 3.2.1

$68$ has factors of $2$ and $34$ .

$2 \cdot 34$

Step 3.2.2

$34$ has factors of $2$ and $17$ .

$2 \cdot 2 \cdot 17$

Step 3.3

$745$ has factors of $5$ and $149$ .

$5 \cdot 149$

Step 3.4

The prime factors for $8$ are $2 \cdot 2 \cdot 2$ .

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Step 3.4.1

$8$ has factors of $2$ and $4$ .

$2 \cdot 4$

Step 3.4.2

$4$ has factors of $2$ and $2$ .

$2 \cdot 2 \cdot 2$

Step 3.5

The LCM of $68, 745, 8$ is the result of multiplying all prime factors the greatest number of times they occur in either number.

$2 \cdot 2 \cdot 2 \cdot 5 \cdot 17 \cdot 149$

Step 3.6

Multiply $2 \cdot 2 \cdot 2 \cdot 5 \cdot 17 \cdot 149$ .

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Step 3.6.1

Multiply $2$ by $2$ .

$4 \cdot 2 \cdot 5 \cdot 17 \cdot 149$

Step 3.6.2

Multiply $4$ by $2$ .

$8 \cdot 5 \cdot 17 \cdot 149$

Step 3.6.3

Multiply $8$ by $5$ .

$40 \cdot 17 \cdot 149$

Step 3.6.4

Multiply $40$ by $17$ .

$680 \cdot 149$

Step 3.6.5

Multiply $680$ by $149$ .

$101320$

Step 4

Find the GCF of the denominators $1, 12, 9$ .

$GCF (1, 12, 9) = 1$

Step 5

Divide $101320$ by $1$ .

$101320$