Basic Math Examples

$4 \frac{1}{2} + 12 \frac{3}{4} + 7 \frac{3}{4} + 9 \frac{3}{4} + 9 \frac{3}{4} + 15$

Step 1

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

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Step 1.1

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

$4 + \frac{1}{2} + 12 \frac{3}{4} + 7 \frac{3}{4} + 9 \frac{3}{4} + 9 \frac{3}{4} + 15$

Step 1.2

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

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Step 1.2.1

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

$4 \cdot \frac{2}{2} + \frac{1}{2} + 12 \frac{3}{4} + 7 \frac{3}{4} + 9 \frac{3}{4} + 9 \frac{3}{4} + 15$

Step 1.2.2

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

$\frac{4 \cdot 2}{2} + \frac{1}{2} + 12 \frac{3}{4} + 7 \frac{3}{4} + 9 \frac{3}{4} + 9 \frac{3}{4} + 15$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{4 \cdot 2 + 1}{2} + 12 \frac{3}{4} + 7 \frac{3}{4} + 9 \frac{3}{4} + 9 \frac{3}{4} + 15$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $4$ by $2$ .

$\frac{8 + 1}{2} + 12 \frac{3}{4} + 7 \frac{3}{4} + 9 \frac{3}{4} + 9 \frac{3}{4} + 15$

Step 1.2.4.2

Add $8$ and $1$ .

$\frac{9}{2} + 12 \frac{3}{4} + 7 \frac{3}{4} + 9 \frac{3}{4} + 9 \frac{3}{4} + 15$

Step 2

Convert $12 \frac{3}{4}$ to an improper fraction.

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Step 2.1

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

$\frac{9}{2} + 12 + \frac{3}{4} + 7 \frac{3}{4} + 9 \frac{3}{4} + 9 \frac{3}{4} + 15$

Step 2.2

Add $12$ and $\frac{3}{4}$ .

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Step 2.2.1

To write $12$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{9}{2} + 12 \cdot \frac{4}{4} + \frac{3}{4} + 7 \frac{3}{4} + 9 \frac{3}{4} + 9 \frac{3}{4} + 15$

Step 2.2.2

Combine $12$ and $\frac{4}{4}$ .

$\frac{9}{2} + \frac{12 \cdot 4}{4} + \frac{3}{4} + 7 \frac{3}{4} + 9 \frac{3}{4} + 9 \frac{3}{4} + 15$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{9}{2} + \frac{12 \cdot 4 + 3}{4} + 7 \frac{3}{4} + 9 \frac{3}{4} + 9 \frac{3}{4} + 15$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $12$ by $4$ .

$\frac{9}{2} + \frac{48 + 3}{4} + 7 \frac{3}{4} + 9 \frac{3}{4} + 9 \frac{3}{4} + 15$

Step 2.2.4.2

Add $48$ and $3$ .

$\frac{9}{2} + \frac{51}{4} + 7 \frac{3}{4} + 9 \frac{3}{4} + 9 \frac{3}{4} + 15$

Step 3

Convert $7 \frac{3}{4}$ to an improper fraction.

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Step 3.1

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

$\frac{9}{2} + \frac{51}{4} + 7 + \frac{3}{4} + 9 \frac{3}{4} + 9 \frac{3}{4} + 15$

Step 3.2

Add $7$ and $\frac{3}{4}$ .

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Step 3.2.1

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

$\frac{9}{2} + \frac{51}{4} + 7 \cdot \frac{4}{4} + \frac{3}{4} + 9 \frac{3}{4} + 9 \frac{3}{4} + 15$

Step 3.2.2

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

$\frac{9}{2} + \frac{51}{4} + \frac{7 \cdot 4}{4} + \frac{3}{4} + 9 \frac{3}{4} + 9 \frac{3}{4} + 15$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{9}{2} + \frac{51}{4} + \frac{7 \cdot 4 + 3}{4} + 9 \frac{3}{4} + 9 \frac{3}{4} + 15$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $7$ by $4$ .

$\frac{9}{2} + \frac{51}{4} + \frac{28 + 3}{4} + 9 \frac{3}{4} + 9 \frac{3}{4} + 15$

Step 3.2.4.2

Add $28$ and $3$ .

$\frac{9}{2} + \frac{51}{4} + \frac{31}{4} + 9 \frac{3}{4} + 9 \frac{3}{4} + 15$

Step 4

Convert $9 \frac{3}{4}$ to an improper fraction.

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Step 4.1

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

$\frac{9}{2} + \frac{51}{4} + \frac{31}{4} + 9 + \frac{3}{4} + 9 \frac{3}{4} + 15$

Step 4.2

Add $9$ and $\frac{3}{4}$ .

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Step 4.2.1

To write $9$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{9}{2} + \frac{51}{4} + \frac{31}{4} + 9 \cdot \frac{4}{4} + \frac{3}{4} + 9 \frac{3}{4} + 15$

Step 4.2.2

Combine $9$ and $\frac{4}{4}$ .

$\frac{9}{2} + \frac{51}{4} + \frac{31}{4} + \frac{9 \cdot 4}{4} + \frac{3}{4} + 9 \frac{3}{4} + 15$

Step 4.2.3

Combine the numerators over the common denominator.

$\frac{9}{2} + \frac{51}{4} + \frac{31}{4} + \frac{9 \cdot 4 + 3}{4} + 9 \frac{3}{4} + 15$

Step 4.2.4

Simplify the numerator.

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Step 4.2.4.1

Multiply $9$ by $4$ .

$\frac{9}{2} + \frac{51}{4} + \frac{31}{4} + \frac{36 + 3}{4} + 9 \frac{3}{4} + 15$

Step 4.2.4.2

Add $36$ and $3$ .

$\frac{9}{2} + \frac{51}{4} + \frac{31}{4} + \frac{39}{4} + 9 \frac{3}{4} + 15$

Step 5

Convert $9 \frac{3}{4}$ to an improper fraction.

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Step 5.1

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

$\frac{9}{2} + \frac{51}{4} + \frac{31}{4} + \frac{39}{4} + 9 + \frac{3}{4} + 15$

Step 5.2

Add $9$ and $\frac{3}{4}$ .

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Step 5.2.1

To write $9$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{9}{2} + \frac{51}{4} + \frac{31}{4} + \frac{39}{4} + 9 \cdot \frac{4}{4} + \frac{3}{4} + 15$

Step 5.2.2

Combine $9$ and $\frac{4}{4}$ .

$\frac{9}{2} + \frac{51}{4} + \frac{31}{4} + \frac{39}{4} + \frac{9 \cdot 4}{4} + \frac{3}{4} + 15$

Step 5.2.3

Combine the numerators over the common denominator.

$\frac{9}{2} + \frac{51}{4} + \frac{31}{4} + \frac{39}{4} + \frac{9 \cdot 4 + 3}{4} + 15$

Step 5.2.4

Simplify the numerator.

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Step 5.2.4.1

Multiply $9$ by $4$ .

$\frac{9}{2} + \frac{51}{4} + \frac{31}{4} + \frac{39}{4} + \frac{36 + 3}{4} + 15$

Step 5.2.4.2

Add $36$ and $3$ .

$\frac{9}{2} + \frac{51}{4} + \frac{31}{4} + \frac{39}{4} + \frac{39}{4} + 15$

Step 6

Combine the numerators over the common denominator.

$15 + \frac{9}{2} + \frac{51 + 31 + 39 + 39}{4}$

Step 7

Simplify by adding numbers.

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Step 7.1

Add $51$ and $31$ .

$15 + \frac{9}{2} + \frac{82 + 39 + 39}{4}$

Step 7.2

Add $82$ and $39$ .

$15 + \frac{9}{2} + \frac{121 + 39}{4}$

Step 7.3

Add $121$ and $39$ .

$15 + \frac{9}{2} + \frac{160}{4}$

Step 8

Find the common denominator.

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Step 8.1

Write $15$ as a fraction with denominator $1$ .

$\frac{15}{1} + \frac{9}{2} + \frac{160}{4}$

Step 8.2

Multiply $\frac{15}{1}$ by $\frac{4}{4}$ .

$\frac{15}{1} \cdot \frac{4}{4} + \frac{9}{2} + \frac{160}{4}$

Step 8.3

Multiply $\frac{15}{1}$ by $\frac{4}{4}$ .

$\frac{15 \cdot 4}{4} + \frac{9}{2} + \frac{160}{4}$

Step 8.4

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

$\frac{15 \cdot 4}{4} + \frac{9}{2} \cdot \frac{2}{2} + \frac{160}{4}$

Step 8.5

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

$\frac{15 \cdot 4}{4} + \frac{9 \cdot 2}{2 \cdot 2} + \frac{160}{4}$

Step 8.6

Multiply $2$ by $2$ .

$\frac{15 \cdot 4}{4} + \frac{9 \cdot 2}{4} + \frac{160}{4}$

Step 9

Combine the numerators over the common denominator.

$\frac{15 \cdot 4 + 9 \cdot 2 + 160}{4}$

Step 10

Simplify each term.

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Step 10.1

Multiply $15$ by $4$ .

$\frac{60 + 9 \cdot 2 + 160}{4}$

Step 10.2

Multiply $9$ by $2$ .

$\frac{60 + 18 + 160}{4}$

Step 11

Reduce the expression by cancelling the common factors.

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Step 11.1

Add $60$ and $18$ .

$\frac{78 + 160}{4}$

Step 11.2

Add $78$ and $160$ .

$\frac{238}{4}$

Step 11.3

Cancel the common factor of $238$ and $4$ .

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Step 11.3.1

Factor $2$ out of $238$ .

$\frac{2 (119)}{4}$

Step 11.3.2

Cancel the common factors.

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Step 11.3.2.1

Factor $2$ out of $4$ .

$\frac{2 \cdot 119}{2 \cdot 2}$

Step 11.3.2.2

Cancel the common factor.

$\frac{2 \cdot 119}{2 \cdot 2}$

Step 11.3.2.3

Rewrite the expression.

$\frac{119}{2}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$\frac{119}{2}$

Decimal Form:

$59.5$

Mixed Number Form:

$59 \frac{1}{2}$