Basic Math Examples

$102 \frac{2}{3} + 130 \frac{3}{4} + 115 \frac{5}{8}$

Step 1

Convert $102 \frac{2}{3}$ to an improper fraction.

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Step 1.1

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

$102 + \frac{2}{3} + 130 \frac{3}{4} + 115 \frac{5}{8}$

Step 1.2

Add $102$ and $\frac{2}{3}$ .

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Step 1.2.1

To write $102$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$102 \cdot \frac{3}{3} + \frac{2}{3} + 130 \frac{3}{4} + 115 \frac{5}{8}$

Step 1.2.2

Combine $102$ and $\frac{3}{3}$ .

$\frac{102 \cdot 3}{3} + \frac{2}{3} + 130 \frac{3}{4} + 115 \frac{5}{8}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{102 \cdot 3 + 2}{3} + 130 \frac{3}{4} + 115 \frac{5}{8}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $102$ by $3$ .

$\frac{306 + 2}{3} + 130 \frac{3}{4} + 115 \frac{5}{8}$

Step 1.2.4.2

Add $306$ and $2$ .

$\frac{308}{3} + 130 \frac{3}{4} + 115 \frac{5}{8}$

Step 2

Convert $130 \frac{3}{4}$ to an improper fraction.

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Step 2.1

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

$\frac{308}{3} + 130 + \frac{3}{4} + 115 \frac{5}{8}$

Step 2.2

Add $130$ and $\frac{3}{4}$ .

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Step 2.2.1

To write $130$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{308}{3} + 130 \cdot \frac{4}{4} + \frac{3}{4} + 115 \frac{5}{8}$

Step 2.2.2

Combine $130$ and $\frac{4}{4}$ .

$\frac{308}{3} + \frac{130 \cdot 4}{4} + \frac{3}{4} + 115 \frac{5}{8}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{308}{3} + \frac{130 \cdot 4 + 3}{4} + 115 \frac{5}{8}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $130$ by $4$ .

$\frac{308}{3} + \frac{520 + 3}{4} + 115 \frac{5}{8}$

Step 2.2.4.2

Add $520$ and $3$ .

$\frac{308}{3} + \frac{523}{4} + 115 \frac{5}{8}$

Step 3

Convert $115 \frac{5}{8}$ to an improper fraction.

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Step 3.1

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

$\frac{308}{3} + \frac{523}{4} + 115 + \frac{5}{8}$

Step 3.2

Add $115$ and $\frac{5}{8}$ .

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Step 3.2.1

To write $115$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{308}{3} + \frac{523}{4} + 115 \cdot \frac{8}{8} + \frac{5}{8}$

Step 3.2.2

Combine $115$ and $\frac{8}{8}$ .

$\frac{308}{3} + \frac{523}{4} + \frac{115 \cdot 8}{8} + \frac{5}{8}$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{308}{3} + \frac{523}{4} + \frac{115 \cdot 8 + 5}{8}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $115$ by $8$ .

$\frac{308}{3} + \frac{523}{4} + \frac{920 + 5}{8}$

Step 3.2.4.2

Add $920$ and $5$ .

$\frac{308}{3} + \frac{523}{4} + \frac{925}{8}$

Step 4

Find the common denominator.

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Step 4.1

Multiply $\frac{308}{3}$ by $\frac{8}{8}$ .

$\frac{308}{3} \cdot \frac{8}{8} + \frac{523}{4} + \frac{925}{8}$

Step 4.2

Multiply $\frac{308}{3}$ by $\frac{8}{8}$ .

$\frac{308 \cdot 8}{3 \cdot 8} + \frac{523}{4} + \frac{925}{8}$

Step 4.3

Multiply $\frac{523}{4}$ by $\frac{6}{6}$ .

$\frac{308 \cdot 8}{3 \cdot 8} + \frac{523}{4} \cdot \frac{6}{6} + \frac{925}{8}$

Step 4.4

Multiply $\frac{523}{4}$ by $\frac{6}{6}$ .

$\frac{308 \cdot 8}{3 \cdot 8} + \frac{523 \cdot 6}{4 \cdot 6} + \frac{925}{8}$

Step 4.5

Multiply $\frac{925}{8}$ by $\frac{3}{3}$ .

$\frac{308 \cdot 8}{3 \cdot 8} + \frac{523 \cdot 6}{4 \cdot 6} + \frac{925}{8} \cdot \frac{3}{3}$

Step 4.6

Multiply $\frac{925}{8}$ by $\frac{3}{3}$ .

$\frac{308 \cdot 8}{3 \cdot 8} + \frac{523 \cdot 6}{4 \cdot 6} + \frac{925 \cdot 3}{8 \cdot 3}$

Step 4.7

Multiply $3$ by $8$ .

$\frac{308 \cdot 8}{24} + \frac{523 \cdot 6}{4 \cdot 6} + \frac{925 \cdot 3}{8 \cdot 3}$

Step 4.8

Multiply $4$ by $6$ .

$\frac{308 \cdot 8}{24} + \frac{523 \cdot 6}{24} + \frac{925 \cdot 3}{8 \cdot 3}$

Step 4.9

Reorder the factors of $8 \cdot 3$ .

$\frac{308 \cdot 8}{24} + \frac{523 \cdot 6}{24} + \frac{925 \cdot 3}{3 \cdot 8}$

Step 4.10

Multiply $3$ by $8$ .

$\frac{308 \cdot 8}{24} + \frac{523 \cdot 6}{24} + \frac{925 \cdot 3}{24}$

Step 5

Combine the numerators over the common denominator.

$\frac{308 \cdot 8 + 523 \cdot 6 + 925 \cdot 3}{24}$

Step 6

Simplify each term.

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Step 6.1

Multiply $308$ by $8$ .

$\frac{2464 + 523 \cdot 6 + 925 \cdot 3}{24}$

Step 6.2

Multiply $523$ by $6$ .

$\frac{2464 + 3138 + 925 \cdot 3}{24}$

Step 6.3

Multiply $925$ by $3$ .

$\frac{2464 + 3138 + 2775}{24}$

Step 7

Simplify by adding numbers.

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Step 7.1

Add $2464$ and $3138$ .

$\frac{5602 + 2775}{24}$

Step 7.2

Add $5602$ and $2775$ .

$\frac{8377}{24}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{8377}{24}$

Decimal Form:

$349.041\overline{6}$

Mixed Number Form:

$349 \frac{1}{24}$