Pre-Algebra Examples

$8 \frac{3}{4} + 10 \frac{1}{2} + 9 \frac{1}{8} + 7 \frac{1}{4} + 8 \frac{3}{4}$

Step 1

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

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Step 1.1

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

$8 + \frac{3}{4} + 10 \frac{1}{2} + 9 \frac{1}{8} + 7 \frac{1}{4} + 8 \frac{3}{4}$

Step 1.2

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

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Step 1.2.1

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

$8 \cdot \frac{4}{4} + \frac{3}{4} + 10 \frac{1}{2} + 9 \frac{1}{8} + 7 \frac{1}{4} + 8 \frac{3}{4}$

Step 1.2.2

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

$\frac{8 \cdot 4}{4} + \frac{3}{4} + 10 \frac{1}{2} + 9 \frac{1}{8} + 7 \frac{1}{4} + 8 \frac{3}{4}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{8 \cdot 4 + 3}{4} + 10 \frac{1}{2} + 9 \frac{1}{8} + 7 \frac{1}{4} + 8 \frac{3}{4}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $8$ by $4$ .

$\frac{32 + 3}{4} + 10 \frac{1}{2} + 9 \frac{1}{8} + 7 \frac{1}{4} + 8 \frac{3}{4}$

Step 1.2.4.2

Add $32$ and $3$ .

$\frac{35}{4} + 10 \frac{1}{2} + 9 \frac{1}{8} + 7 \frac{1}{4} + 8 \frac{3}{4}$

Step 2

Convert $10 \frac{1}{2}$ to an improper fraction.

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Step 2.1

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

$\frac{35}{4} + 10 + \frac{1}{2} + 9 \frac{1}{8} + 7 \frac{1}{4} + 8 \frac{3}{4}$

Step 2.2

Add $10$ and $\frac{1}{2}$ .

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Step 2.2.1

To write $10$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{35}{4} + 10 \cdot \frac{2}{2} + \frac{1}{2} + 9 \frac{1}{8} + 7 \frac{1}{4} + 8 \frac{3}{4}$

Step 2.2.2

Combine $10$ and $\frac{2}{2}$ .

$\frac{35}{4} + \frac{10 \cdot 2}{2} + \frac{1}{2} + 9 \frac{1}{8} + 7 \frac{1}{4} + 8 \frac{3}{4}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{35}{4} + \frac{10 \cdot 2 + 1}{2} + 9 \frac{1}{8} + 7 \frac{1}{4} + 8 \frac{3}{4}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $10$ by $2$ .

$\frac{35}{4} + \frac{20 + 1}{2} + 9 \frac{1}{8} + 7 \frac{1}{4} + 8 \frac{3}{4}$

Step 2.2.4.2

Add $20$ and $1$ .

$\frac{35}{4} + \frac{21}{2} + 9 \frac{1}{8} + 7 \frac{1}{4} + 8 \frac{3}{4}$

Step 3

Convert $9 \frac{1}{8}$ to an improper fraction.

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Step 3.1

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

$\frac{35}{4} + \frac{21}{2} + 9 + \frac{1}{8} + 7 \frac{1}{4} + 8 \frac{3}{4}$

Step 3.2

Add $9$ and $\frac{1}{8}$ .

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Step 3.2.1

To write $9$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{35}{4} + \frac{21}{2} + 9 \cdot \frac{8}{8} + \frac{1}{8} + 7 \frac{1}{4} + 8 \frac{3}{4}$

Step 3.2.2

Combine $9$ and $\frac{8}{8}$ .

$\frac{35}{4} + \frac{21}{2} + \frac{9 \cdot 8}{8} + \frac{1}{8} + 7 \frac{1}{4} + 8 \frac{3}{4}$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{35}{4} + \frac{21}{2} + \frac{9 \cdot 8 + 1}{8} + 7 \frac{1}{4} + 8 \frac{3}{4}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $9$ by $8$ .

$\frac{35}{4} + \frac{21}{2} + \frac{72 + 1}{8} + 7 \frac{1}{4} + 8 \frac{3}{4}$

Step 3.2.4.2

Add $72$ and $1$ .

$\frac{35}{4} + \frac{21}{2} + \frac{73}{8} + 7 \frac{1}{4} + 8 \frac{3}{4}$

Step 4

Convert $7 \frac{1}{4}$ to an improper fraction.

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Step 4.1

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

$\frac{35}{4} + \frac{21}{2} + \frac{73}{8} + 7 + \frac{1}{4} + 8 \frac{3}{4}$

Step 4.2

Add $7$ and $\frac{1}{4}$ .

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Step 4.2.1

To write $7$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{35}{4} + \frac{21}{2} + \frac{73}{8} + 7 \cdot \frac{4}{4} + \frac{1}{4} + 8 \frac{3}{4}$

Step 4.2.2

Combine $7$ and $\frac{4}{4}$ .

$\frac{35}{4} + \frac{21}{2} + \frac{73}{8} + \frac{7 \cdot 4}{4} + \frac{1}{4} + 8 \frac{3}{4}$

Step 4.2.3

Combine the numerators over the common denominator.

$\frac{35}{4} + \frac{21}{2} + \frac{73}{8} + \frac{7 \cdot 4 + 1}{4} + 8 \frac{3}{4}$

Step 4.2.4

Simplify the numerator.

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Step 4.2.4.1

Multiply $7$ by $4$ .

$\frac{35}{4} + \frac{21}{2} + \frac{73}{8} + \frac{28 + 1}{4} + 8 \frac{3}{4}$

Step 4.2.4.2

Add $28$ and $1$ .

$\frac{35}{4} + \frac{21}{2} + \frac{73}{8} + \frac{29}{4} + 8 \frac{3}{4}$

Step 5

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

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Step 5.1

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

$\frac{35}{4} + \frac{21}{2} + \frac{73}{8} + \frac{29}{4} + 8 + \frac{3}{4}$

Step 5.2

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

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Step 5.2.1

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

$\frac{35}{4} + \frac{21}{2} + \frac{73}{8} + \frac{29}{4} + 8 \cdot \frac{4}{4} + \frac{3}{4}$

Step 5.2.2

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

$\frac{35}{4} + \frac{21}{2} + \frac{73}{8} + \frac{29}{4} + \frac{8 \cdot 4}{4} + \frac{3}{4}$

Step 5.2.3

Combine the numerators over the common denominator.

$\frac{35}{4} + \frac{21}{2} + \frac{73}{8} + \frac{29}{4} + \frac{8 \cdot 4 + 3}{4}$

Step 5.2.4

Simplify the numerator.

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Step 5.2.4.1

Multiply $8$ by $4$ .

$\frac{35}{4} + \frac{21}{2} + \frac{73}{8} + \frac{29}{4} + \frac{32 + 3}{4}$

Step 5.2.4.2

Add $32$ and $3$ .

$\frac{35}{4} + \frac{21}{2} + \frac{73}{8} + \frac{29}{4} + \frac{35}{4}$

Step 6

Combine the numerators over the common denominator.

$\frac{35 + 29 + 35}{4} + \frac{21}{2} + \frac{73}{8}$

Step 7

Simplify by adding numbers.

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Step 7.1

Add $35$ and $29$ .

$\frac{64 + 35}{4} + \frac{21}{2} + \frac{73}{8}$

Step 7.2

Add $64$ and $35$ .

$\frac{99}{4} + \frac{21}{2} + \frac{73}{8}$

Step 8

Find the common denominator.

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Step 8.1

Multiply $\frac{99}{4}$ by $\frac{2}{2}$ .

$\frac{99}{4} \cdot \frac{2}{2} + \frac{21}{2} + \frac{73}{8}$

Step 8.2

Multiply $\frac{99}{4}$ by $\frac{2}{2}$ .

$\frac{99 \cdot 2}{4 \cdot 2} + \frac{21}{2} + \frac{73}{8}$

Step 8.3

Multiply $\frac{21}{2}$ by $\frac{4}{4}$ .

$\frac{99 \cdot 2}{4 \cdot 2} + \frac{21}{2} \cdot \frac{4}{4} + \frac{73}{8}$

Step 8.4

Multiply $\frac{21}{2}$ by $\frac{4}{4}$ .

$\frac{99 \cdot 2}{4 \cdot 2} + \frac{21 \cdot 4}{2 \cdot 4} + \frac{73}{8}$

Step 8.5

Reorder the factors of $4 \cdot 2$ .

$\frac{99 \cdot 2}{2 \cdot 4} + \frac{21 \cdot 4}{2 \cdot 4} + \frac{73}{8}$

Step 8.6

Multiply $2$ by $4$ .

$\frac{99 \cdot 2}{8} + \frac{21 \cdot 4}{2 \cdot 4} + \frac{73}{8}$

Step 8.7

Multiply $2$ by $4$ .

$\frac{99 \cdot 2}{8} + \frac{21 \cdot 4}{8} + \frac{73}{8}$

Step 9

Combine the numerators over the common denominator.

$\frac{99 \cdot 2 + 21 \cdot 4 + 73}{8}$

Step 10

Simplify each term.

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Step 10.1

Multiply $99$ by $2$ .

$\frac{198 + 21 \cdot 4 + 73}{8}$

Step 10.2

Multiply $21$ by $4$ .

$\frac{198 + 84 + 73}{8}$

Step 11

Simplify by adding numbers.

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Step 11.1

Add $198$ and $84$ .

$\frac{282 + 73}{8}$

Step 11.2

Add $282$ and $73$ .

$\frac{355}{8}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$\frac{355}{8}$

Decimal Form:

$44.375$

Mixed Number Form:

$44 \frac{3}{8}$