Pre-Algebra Examples

$4 \frac{7}{8} + 5 \frac{3}{4} + 4 \frac{1}{2} + 4 \frac{3}{8} + \frac{5}{8}$

Step 1

Convert $4 \frac{7}{8}$ to an improper fraction.

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Step 1.1

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

$4 + \frac{7}{8} + 5 \frac{3}{4} + 4 \frac{1}{2} + 4 \frac{3}{8} + \frac{5}{8}$

Step 1.2

Add $4$ and $\frac{7}{8}$ .

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Step 1.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$4 \cdot \frac{8}{8} + \frac{7}{8} + 5 \frac{3}{4} + 4 \frac{1}{2} + 4 \frac{3}{8} + \frac{5}{8}$

Step 1.2.2

Combine $4$ and $\frac{8}{8}$ .

$\frac{4 \cdot 8}{8} + \frac{7}{8} + 5 \frac{3}{4} + 4 \frac{1}{2} + 4 \frac{3}{8} + \frac{5}{8}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{4 \cdot 8 + 7}{8} + 5 \frac{3}{4} + 4 \frac{1}{2} + 4 \frac{3}{8} + \frac{5}{8}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $4$ by $8$ .

$\frac{32 + 7}{8} + 5 \frac{3}{4} + 4 \frac{1}{2} + 4 \frac{3}{8} + \frac{5}{8}$

Step 1.2.4.2

Add $32$ and $7$ .

$\frac{39}{8} + 5 \frac{3}{4} + 4 \frac{1}{2} + 4 \frac{3}{8} + \frac{5}{8}$

Step 2

Convert $5 \frac{3}{4}$ to an improper fraction.

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Step 2.1

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

$\frac{39}{8} + 5 + \frac{3}{4} + 4 \frac{1}{2} + 4 \frac{3}{8} + \frac{5}{8}$

Step 2.2

Add $5$ and $\frac{3}{4}$ .

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Step 2.2.1

To write $5$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{39}{8} + 5 \cdot \frac{4}{4} + \frac{3}{4} + 4 \frac{1}{2} + 4 \frac{3}{8} + \frac{5}{8}$

Step 2.2.2

Combine $5$ and $\frac{4}{4}$ .

$\frac{39}{8} + \frac{5 \cdot 4}{4} + \frac{3}{4} + 4 \frac{1}{2} + 4 \frac{3}{8} + \frac{5}{8}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{39}{8} + \frac{5 \cdot 4 + 3}{4} + 4 \frac{1}{2} + 4 \frac{3}{8} + \frac{5}{8}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $5$ by $4$ .

$\frac{39}{8} + \frac{20 + 3}{4} + 4 \frac{1}{2} + 4 \frac{3}{8} + \frac{5}{8}$

Step 2.2.4.2

Add $20$ and $3$ .

$\frac{39}{8} + \frac{23}{4} + 4 \frac{1}{2} + 4 \frac{3}{8} + \frac{5}{8}$

Step 3

Convert $4 \frac{1}{2}$ to an improper fraction.

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Step 3.1

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

$\frac{39}{8} + \frac{23}{4} + 4 + \frac{1}{2} + 4 \frac{3}{8} + \frac{5}{8}$

Step 3.2

Add $4$ and $\frac{1}{2}$ .

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Step 3.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{39}{8} + \frac{23}{4} + 4 \cdot \frac{2}{2} + \frac{1}{2} + 4 \frac{3}{8} + \frac{5}{8}$

Step 3.2.2

Combine $4$ and $\frac{2}{2}$ .

$\frac{39}{8} + \frac{23}{4} + \frac{4 \cdot 2}{2} + \frac{1}{2} + 4 \frac{3}{8} + \frac{5}{8}$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{39}{8} + \frac{23}{4} + \frac{4 \cdot 2 + 1}{2} + 4 \frac{3}{8} + \frac{5}{8}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $4$ by $2$ .

$\frac{39}{8} + \frac{23}{4} + \frac{8 + 1}{2} + 4 \frac{3}{8} + \frac{5}{8}$

Step 3.2.4.2

Add $8$ and $1$ .

$\frac{39}{8} + \frac{23}{4} + \frac{9}{2} + 4 \frac{3}{8} + \frac{5}{8}$

Step 4

Convert $4 \frac{3}{8}$ to an improper fraction.

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Step 4.1

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

$\frac{39}{8} + \frac{23}{4} + \frac{9}{2} + 4 + \frac{3}{8} + \frac{5}{8}$

Step 4.2

Add $4$ and $\frac{3}{8}$ .

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Step 4.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{39}{8} + \frac{23}{4} + \frac{9}{2} + 4 \cdot \frac{8}{8} + \frac{3}{8} + \frac{5}{8}$

Step 4.2.2

Combine $4$ and $\frac{8}{8}$ .

$\frac{39}{8} + \frac{23}{4} + \frac{9}{2} + \frac{4 \cdot 8}{8} + \frac{3}{8} + \frac{5}{8}$

Step 4.2.3

Combine the numerators over the common denominator.

$\frac{39}{8} + \frac{23}{4} + \frac{9}{2} + \frac{4 \cdot 8 + 3}{8} + \frac{5}{8}$

Step 4.2.4

Simplify the numerator.

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Step 4.2.4.1

Multiply $4$ by $8$ .

$\frac{39}{8} + \frac{23}{4} + \frac{9}{2} + \frac{32 + 3}{8} + \frac{5}{8}$

Step 4.2.4.2

Add $32$ and $3$ .

$\frac{39}{8} + \frac{23}{4} + \frac{9}{2} + \frac{35}{8} + \frac{5}{8}$

Step 5

Combine the numerators over the common denominator.

$\frac{39 + 35 + 5}{8} + \frac{23}{4} + \frac{9}{2}$

Step 6

Simplify by adding numbers.

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Step 6.1

Add $39$ and $35$ .

$\frac{74 + 5}{8} + \frac{23}{4} + \frac{9}{2}$

Step 6.2

Add $74$ and $5$ .

$\frac{79}{8} + \frac{23}{4} + \frac{9}{2}$

Step 7

Find the common denominator.

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Step 7.1

Multiply $\frac{23}{4}$ by $\frac{2}{2}$ .

$\frac{79}{8} + \frac{23}{4} \cdot \frac{2}{2} + \frac{9}{2}$

Step 7.2

Multiply $\frac{23}{4}$ by $\frac{2}{2}$ .

$\frac{79}{8} + \frac{23 \cdot 2}{4 \cdot 2} + \frac{9}{2}$

Step 7.3

Multiply $\frac{9}{2}$ by $\frac{4}{4}$ .

$\frac{79}{8} + \frac{23 \cdot 2}{4 \cdot 2} + \frac{9}{2} \cdot \frac{4}{4}$

Step 7.4

Multiply $\frac{9}{2}$ by $\frac{4}{4}$ .

$\frac{79}{8} + \frac{23 \cdot 2}{4 \cdot 2} + \frac{9 \cdot 4}{2 \cdot 4}$

Step 7.5

Reorder the factors of $4 \cdot 2$ .

$\frac{79}{8} + \frac{23 \cdot 2}{2 \cdot 4} + \frac{9 \cdot 4}{2 \cdot 4}$

Step 7.6

Multiply $2$ by $4$ .

$\frac{79}{8} + \frac{23 \cdot 2}{8} + \frac{9 \cdot 4}{2 \cdot 4}$

Step 7.7

Multiply $2$ by $4$ .

$\frac{79}{8} + \frac{23 \cdot 2}{8} + \frac{9 \cdot 4}{8}$

Step 8

Combine the numerators over the common denominator.

$\frac{79 + 23 \cdot 2 + 9 \cdot 4}{8}$

Step 9

Simplify each term.

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Step 9.1

Multiply $23$ by $2$ .

$\frac{79 + 46 + 9 \cdot 4}{8}$

Step 9.2

Multiply $9$ by $4$ .

$\frac{79 + 46 + 36}{8}$

Step 10

Simplify by adding numbers.

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Step 10.1

Add $79$ and $46$ .

$\frac{125 + 36}{8}$

Step 10.2

Add $125$ and $36$ .

$\frac{161}{8}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\frac{161}{8}$

Decimal Form:

$20.125$

Mixed Number Form:

$20 \frac{1}{8}$