Basic Math Examples

$2 \frac{13}{32} + 2 \frac{5}{8} + 2 \frac{9}{16} + 2 \frac{5}{16}$

Step 1

Convert $2 \frac{13}{32}$ to an improper fraction.

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Step 1.1

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

$2 + \frac{13}{32} + 2 \frac{5}{8} + 2 \frac{9}{16} + 2 \frac{5}{16}$

Step 1.2

Add $2$ and $\frac{13}{32}$ .

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Step 1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{32}{32}$ .

$2 \cdot \frac{32}{32} + \frac{13}{32} + 2 \frac{5}{8} + 2 \frac{9}{16} + 2 \frac{5}{16}$

Step 1.2.2

Combine $2$ and $\frac{32}{32}$ .

$\frac{2 \cdot 32}{32} + \frac{13}{32} + 2 \frac{5}{8} + 2 \frac{9}{16} + 2 \frac{5}{16}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{2 \cdot 32 + 13}{32} + 2 \frac{5}{8} + 2 \frac{9}{16} + 2 \frac{5}{16}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $32$ .

$\frac{64 + 13}{32} + 2 \frac{5}{8} + 2 \frac{9}{16} + 2 \frac{5}{16}$

Step 1.2.4.2

Add $64$ and $13$ .

$\frac{77}{32} + 2 \frac{5}{8} + 2 \frac{9}{16} + 2 \frac{5}{16}$

Step 2

Convert $2 \frac{5}{8}$ to an improper fraction.

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Step 2.1

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

$\frac{77}{32} + 2 + \frac{5}{8} + 2 \frac{9}{16} + 2 \frac{5}{16}$

Step 2.2

Add $2$ and $\frac{5}{8}$ .

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Step 2.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{77}{32} + 2 \cdot \frac{8}{8} + \frac{5}{8} + 2 \frac{9}{16} + 2 \frac{5}{16}$

Step 2.2.2

Combine $2$ and $\frac{8}{8}$ .

$\frac{77}{32} + \frac{2 \cdot 8}{8} + \frac{5}{8} + 2 \frac{9}{16} + 2 \frac{5}{16}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{77}{32} + \frac{2 \cdot 8 + 5}{8} + 2 \frac{9}{16} + 2 \frac{5}{16}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $2$ by $8$ .

$\frac{77}{32} + \frac{16 + 5}{8} + 2 \frac{9}{16} + 2 \frac{5}{16}$

Step 2.2.4.2

Add $16$ and $5$ .

$\frac{77}{32} + \frac{21}{8} + 2 \frac{9}{16} + 2 \frac{5}{16}$

Step 3

Convert $2 \frac{9}{16}$ to an improper fraction.

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Step 3.1

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

$\frac{77}{32} + \frac{21}{8} + 2 + \frac{9}{16} + 2 \frac{5}{16}$

Step 3.2

Add $2$ and $\frac{9}{16}$ .

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Step 3.2.1

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

$\frac{77}{32} + \frac{21}{8} + 2 \cdot \frac{16}{16} + \frac{9}{16} + 2 \frac{5}{16}$

Step 3.2.2

Combine $2$ and $\frac{16}{16}$ .

$\frac{77}{32} + \frac{21}{8} + \frac{2 \cdot 16}{16} + \frac{9}{16} + 2 \frac{5}{16}$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{77}{32} + \frac{21}{8} + \frac{2 \cdot 16 + 9}{16} + 2 \frac{5}{16}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $2$ by $16$ .

$\frac{77}{32} + \frac{21}{8} + \frac{32 + 9}{16} + 2 \frac{5}{16}$

Step 3.2.4.2

Add $32$ and $9$ .

$\frac{77}{32} + \frac{21}{8} + \frac{41}{16} + 2 \frac{5}{16}$

Step 4

Convert $2 \frac{5}{16}$ to an improper fraction.

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Step 4.1

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

$\frac{77}{32} + \frac{21}{8} + \frac{41}{16} + 2 + \frac{5}{16}$

Step 4.2

Add $2$ and $\frac{5}{16}$ .

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Step 4.2.1

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

$\frac{77}{32} + \frac{21}{8} + \frac{41}{16} + 2 \cdot \frac{16}{16} + \frac{5}{16}$

Step 4.2.2

Combine $2$ and $\frac{16}{16}$ .

$\frac{77}{32} + \frac{21}{8} + \frac{41}{16} + \frac{2 \cdot 16}{16} + \frac{5}{16}$

Step 4.2.3

Combine the numerators over the common denominator.

$\frac{77}{32} + \frac{21}{8} + \frac{41}{16} + \frac{2 \cdot 16 + 5}{16}$

Step 4.2.4

Simplify the numerator.

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Step 4.2.4.1

Multiply $2$ by $16$ .

$\frac{77}{32} + \frac{21}{8} + \frac{41}{16} + \frac{32 + 5}{16}$

Step 4.2.4.2

Add $32$ and $5$ .

$\frac{77}{32} + \frac{21}{8} + \frac{41}{16} + \frac{37}{16}$

Step 5

To write $\frac{21}{8}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{77}{32} + \frac{21}{8} \cdot \frac{4}{4} + \frac{41}{16} + \frac{37}{16}$

Step 6

Write each expression with a common denominator of $32$ , by multiplying each by an appropriate factor of $1$ .

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Step 6.1

Multiply $\frac{21}{8}$ by $\frac{4}{4}$ .

$\frac{77}{32} + \frac{21 \cdot 4}{8 \cdot 4} + \frac{41}{16} + \frac{37}{16}$

Step 6.2

Multiply $8$ by $4$ .

$\frac{77}{32} + \frac{21 \cdot 4}{32} + \frac{41}{16} + \frac{37}{16}$

Step 7

Combine the numerators over the common denominator.

$\frac{77 + 21 \cdot 4}{32} + \frac{41}{16} + \frac{37}{16}$

Step 8

Simplify the numerator.

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Step 8.1

Multiply $21$ by $4$ .

$\frac{77 + 84}{32} + \frac{41}{16} + \frac{37}{16}$

Step 8.2

Add $77$ and $84$ .

$\frac{161}{32} + \frac{41}{16} + \frac{37}{16}$

Step 9

To write $\frac{41}{16}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{161}{32} + \frac{41}{16} \cdot \frac{2}{2} + \frac{37}{16}$

Step 10

Write each expression with a common denominator of $32$ , by multiplying each by an appropriate factor of $1$ .

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Step 10.1

Multiply $\frac{41}{16}$ by $\frac{2}{2}$ .

$\frac{161}{32} + \frac{41 \cdot 2}{16 \cdot 2} + \frac{37}{16}$

Step 10.2

Multiply $16$ by $2$ .

$\frac{161}{32} + \frac{41 \cdot 2}{32} + \frac{37}{16}$

Step 11

Combine the numerators over the common denominator.

$\frac{161 + 41 \cdot 2}{32} + \frac{37}{16}$

Step 12

Simplify the numerator.

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Step 12.1

Multiply $41$ by $2$ .

$\frac{161 + 82}{32} + \frac{37}{16}$

Step 12.2

Add $161$ and $82$ .

$\frac{243}{32} + \frac{37}{16}$

Step 13

To write $\frac{37}{16}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{243}{32} + \frac{37}{16} \cdot \frac{2}{2}$

Step 14

Write each expression with a common denominator of $32$ , by multiplying each by an appropriate factor of $1$ .

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Step 14.1

Multiply $\frac{37}{16}$ by $\frac{2}{2}$ .

$\frac{243}{32} + \frac{37 \cdot 2}{16 \cdot 2}$

Step 14.2

Multiply $16$ by $2$ .

$\frac{243}{32} + \frac{37 \cdot 2}{32}$

Step 15

Combine the numerators over the common denominator.

$\frac{243 + 37 \cdot 2}{32}$

Step 16

Simplify the numerator.

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Step 16.1

Multiply $37$ by $2$ .

$\frac{243 + 74}{32}$

Step 16.2

Add $243$ and $74$ .

$\frac{317}{32}$