Basic Math Examples

$\frac{185}{12} + \frac{455}{36} + \frac{59}{6} + \frac{87}{8} + \frac{41}{4} + \frac{49}{6}$

Step 1

Combine the numerators over the common denominator.

$\frac{185}{12} + \frac{455}{36} + \frac{59 + 49}{6} + \frac{87}{8} + \frac{41}{4}$

Step 2

Add $59$ and $49$ .

$\frac{185}{12} + \frac{455}{36} + \frac{108}{6} + \frac{87}{8} + \frac{41}{4}$

Step 3

Find the common denominator.

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Step 3.1

Multiply $\frac{185}{12}$ by $\frac{6}{6}$ .

$\frac{185}{12} \cdot \frac{6}{6} + \frac{455}{36} + \frac{108}{6} + \frac{87}{8} + \frac{41}{4}$

Step 3.2

Multiply $\frac{185}{12}$ by $\frac{6}{6}$ .

$\frac{185 \cdot 6}{12 \cdot 6} + \frac{455}{36} + \frac{108}{6} + \frac{87}{8} + \frac{41}{4}$

Step 3.3

Multiply $\frac{455}{36}$ by $\frac{2}{2}$ .

$\frac{185 \cdot 6}{12 \cdot 6} + \frac{455}{36} \cdot \frac{2}{2} + \frac{108}{6} + \frac{87}{8} + \frac{41}{4}$

Step 3.4

Multiply $\frac{455}{36}$ by $\frac{2}{2}$ .

$\frac{185 \cdot 6}{12 \cdot 6} + \frac{455 \cdot 2}{36 \cdot 2} + \frac{108}{6} + \frac{87}{8} + \frac{41}{4}$

Step 3.5

Multiply $\frac{108}{6}$ by $\frac{12}{12}$ .

$\frac{185 \cdot 6}{12 \cdot 6} + \frac{455 \cdot 2}{36 \cdot 2} + \frac{108}{6} \cdot \frac{12}{12} + \frac{87}{8} + \frac{41}{4}$

Step 3.6

Multiply $\frac{108}{6}$ by $\frac{12}{12}$ .

$\frac{185 \cdot 6}{12 \cdot 6} + \frac{455 \cdot 2}{36 \cdot 2} + \frac{108 \cdot 12}{6 \cdot 12} + \frac{87}{8} + \frac{41}{4}$

Step 3.7

Multiply $\frac{87}{8}$ by $\frac{9}{9}$ .

$\frac{185 \cdot 6}{12 \cdot 6} + \frac{455 \cdot 2}{36 \cdot 2} + \frac{108 \cdot 12}{6 \cdot 12} + \frac{87}{8} \cdot \frac{9}{9} + \frac{41}{4}$

Step 3.8

Multiply $\frac{87}{8}$ by $\frac{9}{9}$ .

$\frac{185 \cdot 6}{12 \cdot 6} + \frac{455 \cdot 2}{36 \cdot 2} + \frac{108 \cdot 12}{6 \cdot 12} + \frac{87 \cdot 9}{8 \cdot 9} + \frac{41}{4}$

Step 3.9

Multiply $\frac{41}{4}$ by $\frac{18}{18}$ .

$\frac{185 \cdot 6}{12 \cdot 6} + \frac{455 \cdot 2}{36 \cdot 2} + \frac{108 \cdot 12}{6 \cdot 12} + \frac{87 \cdot 9}{8 \cdot 9} + \frac{41}{4} \cdot \frac{18}{18}$

Step 3.10

Multiply $\frac{41}{4}$ by $\frac{18}{18}$ .

$\frac{185 \cdot 6}{12 \cdot 6} + \frac{455 \cdot 2}{36 \cdot 2} + \frac{108 \cdot 12}{6 \cdot 12} + \frac{87 \cdot 9}{8 \cdot 9} + \frac{41 \cdot 18}{4 \cdot 18}$

Step 3.11

Reorder the factors of $12 \cdot 6$ .

$\frac{185 \cdot 6}{6 \cdot 12} + \frac{455 \cdot 2}{36 \cdot 2} + \frac{108 \cdot 12}{6 \cdot 12} + \frac{87 \cdot 9}{8 \cdot 9} + \frac{41 \cdot 18}{4 \cdot 18}$

Step 3.12

Multiply $6$ by $12$ .

$\frac{185 \cdot 6}{72} + \frac{455 \cdot 2}{36 \cdot 2} + \frac{108 \cdot 12}{6 \cdot 12} + \frac{87 \cdot 9}{8 \cdot 9} + \frac{41 \cdot 18}{4 \cdot 18}$

Step 3.13

Reorder the factors of $36 \cdot 2$ .

$\frac{185 \cdot 6}{72} + \frac{455 \cdot 2}{2 \cdot 36} + \frac{108 \cdot 12}{6 \cdot 12} + \frac{87 \cdot 9}{8 \cdot 9} + \frac{41 \cdot 18}{4 \cdot 18}$

Step 3.14

Multiply $2$ by $36$ .

$\frac{185 \cdot 6}{72} + \frac{455 \cdot 2}{72} + \frac{108 \cdot 12}{6 \cdot 12} + \frac{87 \cdot 9}{8 \cdot 9} + \frac{41 \cdot 18}{4 \cdot 18}$

Step 3.15

Multiply $6$ by $12$ .

$\frac{185 \cdot 6}{72} + \frac{455 \cdot 2}{72} + \frac{108 \cdot 12}{72} + \frac{87 \cdot 9}{8 \cdot 9} + \frac{41 \cdot 18}{4 \cdot 18}$

Step 3.16

Multiply $8$ by $9$ .

$\frac{185 \cdot 6}{72} + \frac{455 \cdot 2}{72} + \frac{108 \cdot 12}{72} + \frac{87 \cdot 9}{72} + \frac{41 \cdot 18}{4 \cdot 18}$

Step 3.17

Multiply $4$ by $18$ .

$\frac{185 \cdot 6}{72} + \frac{455 \cdot 2}{72} + \frac{108 \cdot 12}{72} + \frac{87 \cdot 9}{72} + \frac{41 \cdot 18}{72}$

Step 4

Combine the numerators over the common denominator.

$\frac{185 \cdot 6 + 455 \cdot 2 + 108 \cdot 12 + 87 \cdot 9 + 41 \cdot 18}{72}$

Step 5

Simplify each term.

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Step 5.1

Multiply $185$ by $6$ .

$\frac{1110 + 455 \cdot 2 + 108 \cdot 12 + 87 \cdot 9 + 41 \cdot 18}{72}$

Step 5.2

Multiply $455$ by $2$ .

$\frac{1110 + 910 + 108 \cdot 12 + 87 \cdot 9 + 41 \cdot 18}{72}$

Step 5.3

Multiply $108$ by $12$ .

$\frac{1110 + 910 + 1296 + 87 \cdot 9 + 41 \cdot 18}{72}$

Step 5.4

Multiply $87$ by $9$ .

$\frac{1110 + 910 + 1296 + 783 + 41 \cdot 18}{72}$

Step 5.5

Multiply $41$ by $18$ .

$\frac{1110 + 910 + 1296 + 783 + 738}{72}$

Step 6

Simplify by adding numbers.

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Step 6.1

Add $1110$ and $910$ .

$\frac{2020 + 1296 + 783 + 738}{72}$

Step 6.2

Add $2020$ and $1296$ .

$\frac{3316 + 783 + 738}{72}$

Step 6.3

Add $3316$ and $783$ .

$\frac{4099 + 738}{72}$

Step 6.4

Add $4099$ and $738$ .

$\frac{4837}{72}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{4837}{72}$

Decimal Form:

$67.180\overline{5}$

Mixed Number Form:

$67 \frac{13}{72}$