Pre-Algebra Examples

$5 \frac{1}{3} - 3 \frac{9}{18}$

Step 1

Convert $5 \frac{1}{3}$ to an improper fraction.

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Step 1.1

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

$5 + \frac{1}{3} - 3 \frac{9}{18}$

Step 1.2

Add $5$ and $\frac{1}{3}$ .

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Step 1.2.1

To write $5$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$5 \cdot \frac{3}{3} + \frac{1}{3} - 3 \frac{9}{18}$

Step 1.2.2

Combine $5$ and $\frac{3}{3}$ .

$\frac{5 \cdot 3}{3} + \frac{1}{3} - 3 \frac{9}{18}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{5 \cdot 3 + 1}{3} - 3 \frac{9}{18}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $5$ by $3$ .

$\frac{15 + 1}{3} - 3 \frac{9}{18}$

Step 1.2.4.2

Add $15$ and $1$ .

$\frac{16}{3} - 3 \frac{9}{18}$

Step 2

Convert $3 \frac{9}{18}$ to an improper fraction.

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Step 2.1

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

$\frac{16}{3} - (3 + \frac{9}{18})$

Step 2.2

Add $3$ and $\frac{9}{18}$ .

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Step 2.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{18}{18}$ .

$\frac{16}{3} - (3 \cdot \frac{18}{18} + \frac{9}{18})$

Step 2.2.2

Combine $3$ and $\frac{18}{18}$ .

$\frac{16}{3} - (\frac{3 \cdot 18}{18} + \frac{9}{18})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{16}{3} - \frac{3 \cdot 18 + 9}{18}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $3$ by $18$ .

$\frac{16}{3} - \frac{54 + 9}{18}$

Step 2.2.4.2

Add $54$ and $9$ .

$\frac{16}{3} - \frac{63}{18}$

Step 3

Cancel the common factor of $63$ and $18$ .

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Step 3.1

Factor $9$ out of $63$ .

$\frac{16}{3} - \frac{9 (7)}{18}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $9$ out of $18$ .

$\frac{16}{3} - \frac{9 \cdot 7}{9 \cdot 2}$

Step 3.2.2

Cancel the common factor.

$\frac{16}{3} - \frac{9 \cdot 7}{9 \cdot 2}$

Step 3.2.3

Rewrite the expression.

$\frac{16}{3} - \frac{7}{2}$

Step 4

To write $\frac{16}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{16}{3} \cdot \frac{2}{2} - \frac{7}{2}$

Step 5

To write $- \frac{7}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{16}{3} \cdot \frac{2}{2} - \frac{7}{2} \cdot \frac{3}{3}$

Step 6

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 6.1

Multiply $\frac{16}{3}$ by $\frac{2}{2}$ .

$\frac{16 \cdot 2}{3 \cdot 2} - \frac{7}{2} \cdot \frac{3}{3}$

Step 6.2

Multiply $3$ by $2$ .

$\frac{16 \cdot 2}{6} - \frac{7}{2} \cdot \frac{3}{3}$

Step 6.3

Multiply $\frac{7}{2}$ by $\frac{3}{3}$ .

$\frac{16 \cdot 2}{6} - \frac{7 \cdot 3}{2 \cdot 3}$

Step 6.4

Multiply $2$ by $3$ .

$\frac{16 \cdot 2}{6} - \frac{7 \cdot 3}{6}$

Step 7

Combine the numerators over the common denominator.

$\frac{16 \cdot 2 - 7 \cdot 3}{6}$

Step 8

Simplify the numerator.

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Step 8.1

Multiply $16$ by $2$ .

$\frac{32 - 7 \cdot 3}{6}$

Step 8.2

Multiply $- 7$ by $3$ .

$\frac{32 - 21}{6}$

Step 8.3

Subtract $21$ from $32$ .

$\frac{11}{6}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{11}{6}$

Decimal Form:

$1.8\overline{3}$

Mixed Number Form:

$1 \frac{5}{6}$