Pre-Algebra Examples

$3 + 7 \div 2 + 4$ , $3 - 1 \div 7 - 14$

Step 1

Simplify each polynomial.

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Step 1.1

Find the common denominator.

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Step 1.1.1

Write $3$ as a fraction with denominator $1$ .

$\frac{3}{1} + 7 \div 2 + 4, 3 - 1 \div 7 - 14$

Step 1.1.2

Multiply $\frac{3}{1}$ by $\frac{2}{2}$ .

$\frac{3}{1} \cdot \frac{2}{2} + 7 \div 2 + 4, 3 - 1 \div 7 - 14$

Step 1.1.3

Multiply $\frac{3}{1}$ by $\frac{2}{2}$ .

$\frac{3 \cdot 2}{2} + 7 \div 2 + 4, 3 - 1 \div 7 - 14$

Step 1.1.4

Write $4$ as a fraction with denominator $1$ .

$\frac{3 \cdot 2}{2} + 7 \div 2 + \frac{4}{1}, 3 - 1 \div 7 - 14$

Step 1.1.5

Multiply $\frac{4}{1}$ by $\frac{2}{2}$ .

$\frac{3 \cdot 2}{2} + 7 \div 2 + \frac{4}{1} \cdot \frac{2}{2}, 3 - 1 \div 7 - 14$

Step 1.1.6

Multiply $\frac{4}{1}$ by $\frac{2}{2}$ .

$\frac{3 \cdot 2}{2} + 7 \div 2 + \frac{4 \cdot 2}{2}, 3 - 1 \div 7 - 14$

Step 1.2

Combine the numerators over the common denominator.

$\frac{3 \cdot 2 + 7 + 4 \cdot 2}{2}, 3 - 1 \div 7 - 14$

Step 1.3

Simplify each term.

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Step 1.3.1

Multiply $3$ by $2$ .

$\frac{6 + 7 + 4 \cdot 2}{2}, 3 - 1 \div 7 - 14$

Step 1.3.2

Multiply $4$ by $2$ .

$\frac{6 + 7 + 8}{2}, 3 - 1 \div 7 - 14$

Step 1.4

Simplify by adding numbers.

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Step 1.4.1

Add $6$ and $7$ .

$\frac{13 + 8}{2}, 3 - 1 \div 7 - 14$

Step 1.4.2

Add $13$ and $8$ .

$\frac{21}{2}, 3 - 1 \div 7 - 14$

Step 1.5

Find the common denominator.

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Step 1.5.1

Write $3$ as a fraction with denominator $1$ .

$\frac{21}{2}, \frac{3}{1} - 1 \div 7 - 14$

Step 1.5.2

Multiply $\frac{3}{1}$ by $\frac{7}{7}$ .

$\frac{21}{2}, \frac{3}{1} \cdot \frac{7}{7} - 1 \div 7 - 14$

Step 1.5.3

Multiply $\frac{3}{1}$ by $\frac{7}{7}$ .

$\frac{21}{2}, \frac{3 \cdot 7}{7} - 1 \div 7 - 14$

Step 1.5.4

Write $- 14$ as a fraction with denominator $1$ .

$\frac{21}{2}, \frac{3 \cdot 7}{7} - 1 \div 7 + \frac{- 14}{1}$

Step 1.5.5

Multiply $\frac{- 14}{1}$ by $\frac{7}{7}$ .

$\frac{21}{2}, \frac{3 \cdot 7}{7} - 1 \div 7 + \frac{- 14}{1} \cdot \frac{7}{7}$

Step 1.5.6

Multiply $\frac{- 14}{1}$ by $\frac{7}{7}$ .

$\frac{21}{2}, \frac{3 \cdot 7}{7} - 1 \div 7 + \frac{- 14 \cdot 7}{7}$

Step 1.6

Combine the numerators over the common denominator.

$\frac{21}{2}, \frac{3 \cdot 7 - 1 - 14 \cdot 7}{7}$

Step 1.7

Simplify each term.

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Step 1.7.1

Multiply $3$ by $7$ .

$\frac{21}{2}, \frac{21 - 1 - 14 \cdot 7}{7}$

Step 1.7.2

Multiply $- 14$ by $7$ .

$\frac{21}{2}, \frac{21 - 1 - 98}{7}$

Step 1.8

Simplify the expression.

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Step 1.8.1

Subtract $1$ from $21$ .

$\frac{21}{2}, \frac{20 - 98}{7}$

Step 1.8.2

Subtract $98$ from $20$ .

$\frac{21}{2}, \frac{- 78}{7}$

Step 1.8.3

Move the negative in front of the fraction.

$\frac{21}{2}, - \frac{78}{7}$

Step 2

To find the LCD of a set of numbers $(\frac{21}{2}, - \frac{78}{7})$ , find the LCM of the denominators.

$LCM (2, 7)$

Step 3

Calculate the LCM of first two denominators in the list, $2$ and $7$ .

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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 $7$ . Multiply them together to get the current total. In this case, the current total is $14$ .

Current Total = $14$

Step 3.2

Multiply the numeric part of the denominators together.

Current Total = $7 + 7 = 14$

Step 3.3

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.

$14$