Pre-Algebra Examples

$2 \frac{3}{32} + 1 \frac{31}{32} + 2 \frac{21}{32} \div 3$

Step 1

Convert $2 \frac{3}{32}$ to an improper fraction.

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Step 1.1

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

$2 + \frac{3}{32} + 1 \frac{31}{32} + 2 \frac{21}{32} \div 3$

Step 1.2

Add $2$ and $\frac{3}{32}$ .

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Step 1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{32}{32}$ .

$2 \cdot \frac{32}{32} + \frac{3}{32} + 1 \frac{31}{32} + 2 \frac{21}{32} \div 3$

Step 1.2.2

Combine $2$ and $\frac{32}{32}$ .

$\frac{2 \cdot 32}{32} + \frac{3}{32} + 1 \frac{31}{32} + 2 \frac{21}{32} \div 3$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{2 \cdot 32 + 3}{32} + 1 \frac{31}{32} + 2 \frac{21}{32} \div 3$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $32$ .

$\frac{64 + 3}{32} + 1 \frac{31}{32} + 2 \frac{21}{32} \div 3$

Step 1.2.4.2

Add $64$ and $3$ .

$\frac{67}{32} + 1 \frac{31}{32} + 2 \frac{21}{32} \div 3$

Step 2

Convert $1 \frac{31}{32}$ to an improper fraction.

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Step 2.1

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

$\frac{67}{32} + 1 + \frac{31}{32} + 2 \frac{21}{32} \div 3$

Step 2.2

Add $1$ and $\frac{31}{32}$ .

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Step 2.2.1

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

$\frac{67}{32} + \frac{32}{32} + \frac{31}{32} + 2 \frac{21}{32} \div 3$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{67}{32} + \frac{32 + 31}{32} + 2 \frac{21}{32} \div 3$

Step 2.2.3

Add $32$ and $31$ .

$\frac{67}{32} + \frac{63}{32} + 2 \frac{21}{32} \div 3$

Step 3

Convert $2 \frac{21}{32}$ to an improper fraction.

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Step 3.1

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

$\frac{67}{32} + \frac{63}{32} + (2 + \frac{21}{32}) \div 3$

Step 3.2

Add $2$ and $\frac{21}{32}$ .

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Step 3.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{32}{32}$ .

$\frac{67}{32} + \frac{63}{32} + (2 \cdot \frac{32}{32} + \frac{21}{32}) \div 3$

Step 3.2.2

Combine $2$ and $\frac{32}{32}$ .

$\frac{67}{32} + \frac{63}{32} + (\frac{2 \cdot 32}{32} + \frac{21}{32}) \div 3$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{67}{32} + \frac{63}{32} + \frac{2 \cdot 32 + 21}{32} \div 3$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $2$ by $32$ .

$\frac{67}{32} + \frac{63}{32} + \frac{64 + 21}{32} \div 3$

Step 3.2.4.2

Add $64$ and $21$ .

$\frac{67}{32} + \frac{63}{32} + \frac{85}{32} \div 3$

Step 4

Combine fractions.

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Step 4.1

Combine the numerators over the common denominator.

$\frac{67 + 63}{32} + \frac{\frac{85}{32}}{3}$

Step 4.2

Add $67$ and $63$ .

$\frac{130}{32} + \frac{\frac{85}{32}}{3}$

Step 5

Simplify each term.

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Step 5.1

Cancel the common factor of $130$ and $32$ .

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Step 5.1.1

Factor $2$ out of $130$ .

$\frac{2 (65)}{32} + \frac{\frac{85}{32}}{3}$

Step 5.1.2

Cancel the common factors.

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Step 5.1.2.1

Factor $2$ out of $32$ .

$\frac{2 \cdot 65}{2 \cdot 16} + \frac{\frac{85}{32}}{3}$

Step 5.1.2.2

Cancel the common factor.

$\frac{2 \cdot 65}{2 \cdot 16} + \frac{\frac{85}{32}}{3}$

Step 5.1.2.3

Rewrite the expression.

$\frac{65}{16} + \frac{\frac{85}{32}}{3}$

Step 5.2

Multiply the numerator by the reciprocal of the denominator.

$\frac{65}{16} + \frac{85}{32} \cdot \frac{1}{3}$

Step 5.3

Multiply $\frac{85}{32} \cdot \frac{1}{3}$ .

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Step 5.3.1

Multiply $\frac{85}{32}$ by $\frac{1}{3}$ .

$\frac{65}{16} + \frac{85}{32 \cdot 3}$

Step 5.3.2

Multiply $32$ by $3$ .

$\frac{65}{16} + \frac{85}{96}$

Step 6

To write $\frac{65}{16}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{65}{16} \cdot \frac{6}{6} + \frac{85}{96}$

Step 7

Write each expression with a common denominator of $96$ , by multiplying each by an appropriate factor of $1$ .

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Step 7.1

Multiply $\frac{65}{16}$ by $\frac{6}{6}$ .

$\frac{65 \cdot 6}{16 \cdot 6} + \frac{85}{96}$

Step 7.2

Multiply $16$ by $6$ .

$\frac{65 \cdot 6}{96} + \frac{85}{96}$

Step 8

Combine the numerators over the common denominator.

$\frac{65 \cdot 6 + 85}{96}$

Step 9

Simplify the numerator.

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Step 9.1

Multiply $65$ by $6$ .

$\frac{390 + 85}{96}$

Step 9.2

Add $390$ and $85$ .

$\frac{475}{96}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{475}{96}$

Decimal Form:

$4.94791\overline{6}$

Mixed Number Form:

$4 \frac{91}{96}$