Pre-Algebra Examples

$\frac{12}{5}$ , $2 \frac{5}{12}$ , $\frac{43}{18}$

Step 1

Convert $2 \frac{5}{12}$ to an improper fraction.

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Step 1.1

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

$\frac{12}{5}, 2 + \frac{5}{12}, \frac{43}{18}$

Step 1.2

Add $2$ and $\frac{5}{12}$ .

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Step 1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{12}{12}$ .

$\frac{12}{5}, 2 \cdot \frac{12}{12} + \frac{5}{12}, \frac{43}{18}$

Step 1.2.2

Combine $2$ and $\frac{12}{12}$ .

$\frac{12}{5}, \frac{2 \cdot 12}{12} + \frac{5}{12}, \frac{43}{18}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{12}{5}, \frac{2 \cdot 12 + 5}{12}, \frac{43}{18}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $12$ .

$\frac{12}{5}, \frac{24 + 5}{12}, \frac{43}{18}$

Step 1.2.4.2

Add $24$ and $5$ .

$\frac{12}{5}, \frac{29}{12}, \frac{43}{18}$

Step 2

To find the LCD of a set of numbers $(\frac{12}{5}, \frac{29}{12}, \frac{43}{18})$ , find the LCM of the denominators.

$LCM (5, 12, 18)$

Step 3

Calculate the LCM of first two denominators in the list, $5$ and $12$ .

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Step 3.1

Find the values of the numerical part of each term. Select the largest one, which in this case is $12$ . Multiply them together to get the current total. In this case, the current total is $60$ .

Current Total = $60$

Step 3.2

Multiply the numeric part of the denominators together.

Current Total = $12 + 12 = 24$

Step 3.3

Multiply the numeric part of the denominators together.

Current Total = $24 + 12 = 36$

Step 3.4

Multiply the numeric part of the denominators together.

Current Total = $36 + 12 = 48$

Step 3.5

Multiply the numeric part of the denominators together.

Current Total = $48 + 12 = 60$

Step 3.6

Check each value in the numerical part of each term against the current total. Since the current total is evenly divisible, return it. That is the least common denominator of the numerical part of the fraction.

$60$

Step 4

Calculate the LCM of the previously calculated LCM, $60$ , and the next denominator in the list, $18$ . Since this is the last denominator in the list, the result is the LCD.

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Step 4.1

Find the values of the numerical part of each term. Select the largest one, which in this case is $60$ . Multiply them together to get the current total. In this case, the current total is $1080$ .

Current Total = $1080$

Step 4.2

Multiply the numeric part of the denominators together.

Current Total = $60 + 60 = 120$

Step 4.3

Multiply the numeric part of the denominators together.

Current Total = $120 + 60 = 180$

Step 4.4

$180$