Basic Math Examples

$\frac{1}{4} + \frac{13}{120} + \frac{13}{120} + \frac{13}{240} + \frac{1}{24} + \frac{1}{20} + \frac{1}{20} + \frac{1}{20} + \frac{13}{480} + \frac{13}{480} + \frac{13}{480} + \frac{13}{480} + \frac{1}{32} + \frac{1}{72} + \frac{1}{72} + \frac{1}{72} + \frac{1}{144} + \frac{1}{144} + \frac{1}{144} + \frac{1}{144} + \frac{1}{144} + \frac{1}{192} + \frac{1}{192} + \frac{1}{432} + \frac{1}{432} + \frac{1}{432} + \frac{13}{240}$

Step 1

Combine the numerators over the common denominator.

$\frac{1}{4} + \frac{13 + 13}{120} + \frac{13 + 13}{240} + \frac{1}{24} + \frac{1 + 1 + 1}{20} + \frac{13 + 13 + 13 + 13}{480} + \frac{1}{32} + \frac{1 + 1 + 1}{72} + \frac{1 + 1 + 1 + 1 + 1}{144} + \frac{1 + 1}{192} + \frac{1 + 1 + 1}{432}$

Step 2

Simplify by adding numbers.

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Step 2.1

Add $13$ and $13$ .

$\frac{1}{4} + \frac{26}{120} + \frac{13 + 13}{240} + \frac{1}{24} + \frac{1 + 1 + 1}{20} + \frac{13 + 13 + 13 + 13}{480} + \frac{1}{32} + \frac{1 + 1 + 1}{72} + \frac{1 + 1 + 1 + 1 + 1}{144} + \frac{1 + 1}{192} + \frac{1 + 1 + 1}{432}$

Step 2.2

Add $13$ and $13$ .

$\frac{1}{4} + \frac{26}{120} + \frac{26}{240} + \frac{1}{24} + \frac{1 + 1 + 1}{20} + \frac{13 + 13 + 13 + 13}{480} + \frac{1}{32} + \frac{1 + 1 + 1}{72} + \frac{1 + 1 + 1 + 1 + 1}{144} + \frac{1 + 1}{192} + \frac{1 + 1 + 1}{432}$

Step 2.3

Add $1$ and $1$ .

$\frac{1}{4} + \frac{26}{120} + \frac{26}{240} + \frac{1}{24} + \frac{2 + 1}{20} + \frac{13 + 13 + 13 + 13}{480} + \frac{1}{32} + \frac{1 + 1 + 1}{72} + \frac{1 + 1 + 1 + 1 + 1}{144} + \frac{1 + 1}{192} + \frac{1 + 1 + 1}{432}$

Step 2.4

Add $2$ and $1$ .

$\frac{1}{4} + \frac{26}{120} + \frac{26}{240} + \frac{1}{24} + \frac{3}{20} + \frac{13 + 13 + 13 + 13}{480} + \frac{1}{32} + \frac{1 + 1 + 1}{72} + \frac{1 + 1 + 1 + 1 + 1}{144} + \frac{1 + 1}{192} + \frac{1 + 1 + 1}{432}$

Step 2.5

Add $13$ and $13$ .

$\frac{1}{4} + \frac{26}{120} + \frac{26}{240} + \frac{1}{24} + \frac{3}{20} + \frac{26 + 13 + 13}{480} + \frac{1}{32} + \frac{1 + 1 + 1}{72} + \frac{1 + 1 + 1 + 1 + 1}{144} + \frac{1 + 1}{192} + \frac{1 + 1 + 1}{432}$

Step 2.6

Add $26$ and $13$ .

$\frac{1}{4} + \frac{26}{120} + \frac{26}{240} + \frac{1}{24} + \frac{3}{20} + \frac{39 + 13}{480} + \frac{1}{32} + \frac{1 + 1 + 1}{72} + \frac{1 + 1 + 1 + 1 + 1}{144} + \frac{1 + 1}{192} + \frac{1 + 1 + 1}{432}$

Step 2.7

Add $39$ and $13$ .

$\frac{1}{4} + \frac{26}{120} + \frac{26}{240} + \frac{1}{24} + \frac{3}{20} + \frac{52}{480} + \frac{1}{32} + \frac{1 + 1 + 1}{72} + \frac{1 + 1 + 1 + 1 + 1}{144} + \frac{1 + 1}{192} + \frac{1 + 1 + 1}{432}$

Step 2.8

Add $1$ and $1$ .

$\frac{1}{4} + \frac{26}{120} + \frac{26}{240} + \frac{1}{24} + \frac{3}{20} + \frac{52}{480} + \frac{1}{32} + \frac{2 + 1}{72} + \frac{1 + 1 + 1 + 1 + 1}{144} + \frac{1 + 1}{192} + \frac{1 + 1 + 1}{432}$

Step 2.9

Add $2$ and $1$ .

$\frac{1}{4} + \frac{26}{120} + \frac{26}{240} + \frac{1}{24} + \frac{3}{20} + \frac{52}{480} + \frac{1}{32} + \frac{3}{72} + \frac{1 + 1 + 1 + 1 + 1}{144} + \frac{1 + 1}{192} + \frac{1 + 1 + 1}{432}$

Step 2.10

Add $1$ and $1$ .

$\frac{1}{4} + \frac{26}{120} + \frac{26}{240} + \frac{1}{24} + \frac{3}{20} + \frac{52}{480} + \frac{1}{32} + \frac{3}{72} + \frac{2 + 1 + 1 + 1}{144} + \frac{1 + 1}{192} + \frac{1 + 1 + 1}{432}$

Step 2.11

Add $2$ and $1$ .

$\frac{1}{4} + \frac{26}{120} + \frac{26}{240} + \frac{1}{24} + \frac{3}{20} + \frac{52}{480} + \frac{1}{32} + \frac{3}{72} + \frac{3 + 1 + 1}{144} + \frac{1 + 1}{192} + \frac{1 + 1 + 1}{432}$

Step 2.12

Add $3$ and $1$ .

$\frac{1}{4} + \frac{26}{120} + \frac{26}{240} + \frac{1}{24} + \frac{3}{20} + \frac{52}{480} + \frac{1}{32} + \frac{3}{72} + \frac{4 + 1}{144} + \frac{1 + 1}{192} + \frac{1 + 1 + 1}{432}$

Step 2.13

Add $4$ and $1$ .

$\frac{1}{4} + \frac{26}{120} + \frac{26}{240} + \frac{1}{24} + \frac{3}{20} + \frac{52}{480} + \frac{1}{32} + \frac{3}{72} + \frac{5}{144} + \frac{1 + 1}{192} + \frac{1 + 1 + 1}{432}$

Step 2.14

Add $1$ and $1$ .

$\frac{1}{4} + \frac{26}{120} + \frac{26}{240} + \frac{1}{24} + \frac{3}{20} + \frac{52}{480} + \frac{1}{32} + \frac{3}{72} + \frac{5}{144} + \frac{2}{192} + \frac{1 + 1 + 1}{432}$

Step 2.15

Add $1$ and $1$ .

$\frac{1}{4} + \frac{26}{120} + \frac{26}{240} + \frac{1}{24} + \frac{3}{20} + \frac{52}{480} + \frac{1}{32} + \frac{3}{72} + \frac{5}{144} + \frac{2}{192} + \frac{2 + 1}{432}$

Step 2.16

Add $2$ and $1$ .

$\frac{1}{4} + \frac{26}{120} + \frac{26}{240} + \frac{1}{24} + \frac{3}{20} + \frac{52}{480} + \frac{1}{32} + \frac{3}{72} + \frac{5}{144} + \frac{2}{192} + \frac{3}{432}$

Step 3

Find the common denominator.

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Step 3.1

Multiply $\frac{1}{4}$ by $\frac{2160}{2160}$ .

$\frac{1}{4} \cdot \frac{2160}{2160} + \frac{26}{120} + \frac{26}{240} + \frac{1}{24} + \frac{3}{20} + \frac{52}{480} + \frac{1}{32} + \frac{3}{72} + \frac{5}{144} + \frac{2}{192} + \frac{3}{432}$

Step 3.2

Multiply $\frac{1}{4}$ by $\frac{2160}{2160}$ .

$\frac{2160}{4 \cdot 2160} + \frac{26}{120} + \frac{26}{240} + \frac{1}{24} + \frac{3}{20} + \frac{52}{480} + \frac{1}{32} + \frac{3}{72} + \frac{5}{144} + \frac{2}{192} + \frac{3}{432}$

Step 3.3

Multiply $\frac{26}{120}$ by $\frac{72}{72}$ .

$\frac{2160}{4 \cdot 2160} + \frac{26}{120} \cdot \frac{72}{72} + \frac{26}{240} + \frac{1}{24} + \frac{3}{20} + \frac{52}{480} + \frac{1}{32} + \frac{3}{72} + \frac{5}{144} + \frac{2}{192} + \frac{3}{432}$

Step 3.4

Multiply $\frac{26}{120}$ by $\frac{72}{72}$ .

$\frac{2160}{4 \cdot 2160} + \frac{26 \cdot 72}{120 \cdot 72} + \frac{26}{240} + \frac{1}{24} + \frac{3}{20} + \frac{52}{480} + \frac{1}{32} + \frac{3}{72} + \frac{5}{144} + \frac{2}{192} + \frac{3}{432}$

Step 3.5

Multiply $\frac{26}{240}$ by $\frac{36}{36}$ .

$\frac{2160}{4 \cdot 2160} + \frac{26 \cdot 72}{120 \cdot 72} + \frac{26}{240} \cdot \frac{36}{36} + \frac{1}{24} + \frac{3}{20} + \frac{52}{480} + \frac{1}{32} + \frac{3}{72} + \frac{5}{144} + \frac{2}{192} + \frac{3}{432}$

Step 3.6

Multiply $\frac{26}{240}$ by $\frac{36}{36}$ .

$\frac{2160}{4 \cdot 2160} + \frac{26 \cdot 72}{120 \cdot 72} + \frac{26 \cdot 36}{240 \cdot 36} + \frac{1}{24} + \frac{3}{20} + \frac{52}{480} + \frac{1}{32} + \frac{3}{72} + \frac{5}{144} + \frac{2}{192} + \frac{3}{432}$

Step 3.7

Multiply $\frac{1}{24}$ by $\frac{360}{360}$ .

$\frac{2160}{4 \cdot 2160} + \frac{26 \cdot 72}{120 \cdot 72} + \frac{26 \cdot 36}{240 \cdot 36} + \frac{1}{24} \cdot \frac{360}{360} + \frac{3}{20} + \frac{52}{480} + \frac{1}{32} + \frac{3}{72} + \frac{5}{144} + \frac{2}{192} + \frac{3}{432}$

Step 3.8

Multiply $\frac{1}{24}$ by $\frac{360}{360}$ .

$\frac{2160}{4 \cdot 2160} + \frac{26 \cdot 72}{120 \cdot 72} + \frac{26 \cdot 36}{240 \cdot 36} + \frac{360}{24 \cdot 360} + \frac{3}{20} + \frac{52}{480} + \frac{1}{32} + \frac{3}{72} + \frac{5}{144} + \frac{2}{192} + \frac{3}{432}$

Step 3.9

Multiply $\frac{3}{20}$ by $\frac{432}{432}$ .

$\frac{2160}{4 \cdot 2160} + \frac{26 \cdot 72}{120 \cdot 72} + \frac{26 \cdot 36}{240 \cdot 36} + \frac{360}{24 \cdot 360} + \frac{3}{20} \cdot \frac{432}{432} + \frac{52}{480} + \frac{1}{32} + \frac{3}{72} + \frac{5}{144} + \frac{2}{192} + \frac{3}{432}$

Step 3.10

Multiply $\frac{3}{20}$ by $\frac{432}{432}$ .

$\frac{2160}{4 \cdot 2160} + \frac{26 \cdot 72}{120 \cdot 72} + \frac{26 \cdot 36}{240 \cdot 36} + \frac{360}{24 \cdot 360} + \frac{3 \cdot 432}{20 \cdot 432} + \frac{52}{480} + \frac{1}{32} + \frac{3}{72} + \frac{5}{144} + \frac{2}{192} + \frac{3}{432}$

Step 3.11

Multiply $\frac{52}{480}$ by $\frac{18}{18}$ .

$\frac{2160}{4 \cdot 2160} + \frac{26 \cdot 72}{120 \cdot 72} + \frac{26 \cdot 36}{240 \cdot 36} + \frac{360}{24 \cdot 360} + \frac{3 \cdot 432}{20 \cdot 432} + \frac{52}{480} \cdot \frac{18}{18} + \frac{1}{32} + \frac{3}{72} + \frac{5}{144} + \frac{2}{192} + \frac{3}{432}$

Step 3.12

Multiply $\frac{52}{480}$ by $\frac{18}{18}$ .

$\frac{2160}{4 \cdot 2160} + \frac{26 \cdot 72}{120 \cdot 72} + \frac{26 \cdot 36}{240 \cdot 36} + \frac{360}{24 \cdot 360} + \frac{3 \cdot 432}{20 \cdot 432} + \frac{52 \cdot 18}{480 \cdot 18} + \frac{1}{32} + \frac{3}{72} + \frac{5}{144} + \frac{2}{192} + \frac{3}{432}$

Step 3.13

Multiply $\frac{1}{32}$ by $\frac{270}{270}$ .

$\frac{2160}{4 \cdot 2160} + \frac{26 \cdot 72}{120 \cdot 72} + \frac{26 \cdot 36}{240 \cdot 36} + \frac{360}{24 \cdot 360} + \frac{3 \cdot 432}{20 \cdot 432} + \frac{52 \cdot 18}{480 \cdot 18} + \frac{1}{32} \cdot \frac{270}{270} + \frac{3}{72} + \frac{5}{144} + \frac{2}{192} + \frac{3}{432}$

Step 3.14

Multiply $\frac{1}{32}$ by $\frac{270}{270}$ .

$\frac{2160}{4 \cdot 2160} + \frac{26 \cdot 72}{120 \cdot 72} + \frac{26 \cdot 36}{240 \cdot 36} + \frac{360}{24 \cdot 360} + \frac{3 \cdot 432}{20 \cdot 432} + \frac{52 \cdot 18}{480 \cdot 18} + \frac{270}{32 \cdot 270} + \frac{3}{72} + \frac{5}{144} + \frac{2}{192} + \frac{3}{432}$

Step 3.15

Multiply $\frac{3}{72}$ by $\frac{120}{120}$ .

$\frac{2160}{4 \cdot 2160} + \frac{26 \cdot 72}{120 \cdot 72} + \frac{26 \cdot 36}{240 \cdot 36} + \frac{360}{24 \cdot 360} + \frac{3 \cdot 432}{20 \cdot 432} + \frac{52 \cdot 18}{480 \cdot 18} + \frac{270}{32 \cdot 270} + \frac{3}{72} \cdot \frac{120}{120} + \frac{5}{144} + \frac{2}{192} + \frac{3}{432}$

Step 3.16

Multiply $\frac{3}{72}$ by $\frac{120}{120}$ .

$\frac{2160}{4 \cdot 2160} + \frac{26 \cdot 72}{120 \cdot 72} + \frac{26 \cdot 36}{240 \cdot 36} + \frac{360}{24 \cdot 360} + \frac{3 \cdot 432}{20 \cdot 432} + \frac{52 \cdot 18}{480 \cdot 18} + \frac{270}{32 \cdot 270} + \frac{3 \cdot 120}{72 \cdot 120} + \frac{5}{144} + \frac{2}{192} + \frac{3}{432}$

Step 3.17

Multiply $\frac{5}{144}$ by $\frac{60}{60}$ .

$\frac{2160}{4 \cdot 2160} + \frac{26 \cdot 72}{120 \cdot 72} + \frac{26 \cdot 36}{240 \cdot 36} + \frac{360}{24 \cdot 360} + \frac{3 \cdot 432}{20 \cdot 432} + \frac{52 \cdot 18}{480 \cdot 18} + \frac{270}{32 \cdot 270} + \frac{3 \cdot 120}{72 \cdot 120} + \frac{5}{144} \cdot \frac{60}{60} + \frac{2}{192} + \frac{3}{432}$

Step 3.18

Multiply $\frac{5}{144}$ by $\frac{60}{60}$ .

$\frac{2160}{4 \cdot 2160} + \frac{26 \cdot 72}{120 \cdot 72} + \frac{26 \cdot 36}{240 \cdot 36} + \frac{360}{24 \cdot 360} + \frac{3 \cdot 432}{20 \cdot 432} + \frac{52 \cdot 18}{480 \cdot 18} + \frac{270}{32 \cdot 270} + \frac{3 \cdot 120}{72 \cdot 120} + \frac{5 \cdot 60}{144 \cdot 60} + \frac{2}{192} + \frac{3}{432}$

Step 3.19

Multiply $\frac{2}{192}$ by $\frac{45}{45}$ .

$\frac{2160}{4 \cdot 2160} + \frac{26 \cdot 72}{120 \cdot 72} + \frac{26 \cdot 36}{240 \cdot 36} + \frac{360}{24 \cdot 360} + \frac{3 \cdot 432}{20 \cdot 432} + \frac{52 \cdot 18}{480 \cdot 18} + \frac{270}{32 \cdot 270} + \frac{3 \cdot 120}{72 \cdot 120} + \frac{5 \cdot 60}{144 \cdot 60} + \frac{2}{192} \cdot \frac{45}{45} + \frac{3}{432}$

Step 3.20

Multiply $\frac{2}{192}$ by $\frac{45}{45}$ .

$\frac{2160}{4 \cdot 2160} + \frac{26 \cdot 72}{120 \cdot 72} + \frac{26 \cdot 36}{240 \cdot 36} + \frac{360}{24 \cdot 360} + \frac{3 \cdot 432}{20 \cdot 432} + \frac{52 \cdot 18}{480 \cdot 18} + \frac{270}{32 \cdot 270} + \frac{3 \cdot 120}{72 \cdot 120} + \frac{5 \cdot 60}{144 \cdot 60} + \frac{2 \cdot 45}{192 \cdot 45} + \frac{3}{432}$

Step 3.21

Multiply $\frac{3}{432}$ by $\frac{20}{20}$ .

$\frac{2160}{4 \cdot 2160} + \frac{26 \cdot 72}{120 \cdot 72} + \frac{26 \cdot 36}{240 \cdot 36} + \frac{360}{24 \cdot 360} + \frac{3 \cdot 432}{20 \cdot 432} + \frac{52 \cdot 18}{480 \cdot 18} + \frac{270}{32 \cdot 270} + \frac{3 \cdot 120}{72 \cdot 120} + \frac{5 \cdot 60}{144 \cdot 60} + \frac{2 \cdot 45}{192 \cdot 45} + \frac{3}{432} \cdot \frac{20}{20}$

Step 3.22

Multiply $\frac{3}{432}$ by $\frac{20}{20}$ .

$\frac{2160}{4 \cdot 2160} + \frac{26 \cdot 72}{120 \cdot 72} + \frac{26 \cdot 36}{240 \cdot 36} + \frac{360}{24 \cdot 360} + \frac{3 \cdot 432}{20 \cdot 432} + \frac{52 \cdot 18}{480 \cdot 18} + \frac{270}{32 \cdot 270} + \frac{3 \cdot 120}{72 \cdot 120} + \frac{5 \cdot 60}{144 \cdot 60} + \frac{2 \cdot 45}{192 \cdot 45} + \frac{3 \cdot 20}{432 \cdot 20}$

Step 3.23

Multiply $4$ by $2160$ .

$\frac{2160}{8640} + \frac{26 \cdot 72}{120 \cdot 72} + \frac{26 \cdot 36}{240 \cdot 36} + \frac{360}{24 \cdot 360} + \frac{3 \cdot 432}{20 \cdot 432} + \frac{52 \cdot 18}{480 \cdot 18} + \frac{270}{32 \cdot 270} + \frac{3 \cdot 120}{72 \cdot 120} + \frac{5 \cdot 60}{144 \cdot 60} + \frac{2 \cdot 45}{192 \cdot 45} + \frac{3 \cdot 20}{432 \cdot 20}$

Step 3.24

Reorder the factors of $120 \cdot 72$ .

$\frac{2160}{8640} + \frac{26 \cdot 72}{72 \cdot 120} + \frac{26 \cdot 36}{240 \cdot 36} + \frac{360}{24 \cdot 360} + \frac{3 \cdot 432}{20 \cdot 432} + \frac{52 \cdot 18}{480 \cdot 18} + \frac{270}{32 \cdot 270} + \frac{3 \cdot 120}{72 \cdot 120} + \frac{5 \cdot 60}{144 \cdot 60} + \frac{2 \cdot 45}{192 \cdot 45} + \frac{3 \cdot 20}{432 \cdot 20}$

Step 3.25

Multiply $72$ by $120$ .

$\frac{2160}{8640} + \frac{26 \cdot 72}{8640} + \frac{26 \cdot 36}{240 \cdot 36} + \frac{360}{24 \cdot 360} + \frac{3 \cdot 432}{20 \cdot 432} + \frac{52 \cdot 18}{480 \cdot 18} + \frac{270}{32 \cdot 270} + \frac{3 \cdot 120}{72 \cdot 120} + \frac{5 \cdot 60}{144 \cdot 60} + \frac{2 \cdot 45}{192 \cdot 45} + \frac{3 \cdot 20}{432 \cdot 20}$

Step 3.26

Reorder the factors of $240 \cdot 36$ .

$\frac{2160}{8640} + \frac{26 \cdot 72}{8640} + \frac{26 \cdot 36}{36 \cdot 240} + \frac{360}{24 \cdot 360} + \frac{3 \cdot 432}{20 \cdot 432} + \frac{52 \cdot 18}{480 \cdot 18} + \frac{270}{32 \cdot 270} + \frac{3 \cdot 120}{72 \cdot 120} + \frac{5 \cdot 60}{144 \cdot 60} + \frac{2 \cdot 45}{192 \cdot 45} + \frac{3 \cdot 20}{432 \cdot 20}$

Step 3.27

Multiply $36$ by $240$ .

$\frac{2160}{8640} + \frac{26 \cdot 72}{8640} + \frac{26 \cdot 36}{8640} + \frac{360}{24 \cdot 360} + \frac{3 \cdot 432}{20 \cdot 432} + \frac{52 \cdot 18}{480 \cdot 18} + \frac{270}{32 \cdot 270} + \frac{3 \cdot 120}{72 \cdot 120} + \frac{5 \cdot 60}{144 \cdot 60} + \frac{2 \cdot 45}{192 \cdot 45} + \frac{3 \cdot 20}{432 \cdot 20}$

Step 3.28

Multiply $24$ by $360$ .

$\frac{2160}{8640} + \frac{26 \cdot 72}{8640} + \frac{26 \cdot 36}{8640} + \frac{360}{8640} + \frac{3 \cdot 432}{20 \cdot 432} + \frac{52 \cdot 18}{480 \cdot 18} + \frac{270}{32 \cdot 270} + \frac{3 \cdot 120}{72 \cdot 120} + \frac{5 \cdot 60}{144 \cdot 60} + \frac{2 \cdot 45}{192 \cdot 45} + \frac{3 \cdot 20}{432 \cdot 20}$

Step 3.29

Multiply $20$ by $432$ .

$\frac{2160}{8640} + \frac{26 \cdot 72}{8640} + \frac{26 \cdot 36}{8640} + \frac{360}{8640} + \frac{3 \cdot 432}{8640} + \frac{52 \cdot 18}{480 \cdot 18} + \frac{270}{32 \cdot 270} + \frac{3 \cdot 120}{72 \cdot 120} + \frac{5 \cdot 60}{144 \cdot 60} + \frac{2 \cdot 45}{192 \cdot 45} + \frac{3 \cdot 20}{432 \cdot 20}$

Step 3.30

Reorder the factors of $480 \cdot 18$ .

$\frac{2160}{8640} + \frac{26 \cdot 72}{8640} + \frac{26 \cdot 36}{8640} + \frac{360}{8640} + \frac{3 \cdot 432}{8640} + \frac{52 \cdot 18}{18 \cdot 480} + \frac{270}{32 \cdot 270} + \frac{3 \cdot 120}{72 \cdot 120} + \frac{5 \cdot 60}{144 \cdot 60} + \frac{2 \cdot 45}{192 \cdot 45} + \frac{3 \cdot 20}{432 \cdot 20}$

Step 3.31

Multiply $18$ by $480$ .

$\frac{2160}{8640} + \frac{26 \cdot 72}{8640} + \frac{26 \cdot 36}{8640} + \frac{360}{8640} + \frac{3 \cdot 432}{8640} + \frac{52 \cdot 18}{8640} + \frac{270}{32 \cdot 270} + \frac{3 \cdot 120}{72 \cdot 120} + \frac{5 \cdot 60}{144 \cdot 60} + \frac{2 \cdot 45}{192 \cdot 45} + \frac{3 \cdot 20}{432 \cdot 20}$

Step 3.32

Multiply $32$ by $270$ .

$\frac{2160}{8640} + \frac{26 \cdot 72}{8640} + \frac{26 \cdot 36}{8640} + \frac{360}{8640} + \frac{3 \cdot 432}{8640} + \frac{52 \cdot 18}{8640} + \frac{270}{8640} + \frac{3 \cdot 120}{72 \cdot 120} + \frac{5 \cdot 60}{144 \cdot 60} + \frac{2 \cdot 45}{192 \cdot 45} + \frac{3 \cdot 20}{432 \cdot 20}$

Step 3.33

Multiply $72$ by $120$ .

$\frac{2160}{8640} + \frac{26 \cdot 72}{8640} + \frac{26 \cdot 36}{8640} + \frac{360}{8640} + \frac{3 \cdot 432}{8640} + \frac{52 \cdot 18}{8640} + \frac{270}{8640} + \frac{3 \cdot 120}{8640} + \frac{5 \cdot 60}{144 \cdot 60} + \frac{2 \cdot 45}{192 \cdot 45} + \frac{3 \cdot 20}{432 \cdot 20}$

Step 3.34

Reorder the factors of $144 \cdot 60$ .

$\frac{2160}{8640} + \frac{26 \cdot 72}{8640} + \frac{26 \cdot 36}{8640} + \frac{360}{8640} + \frac{3 \cdot 432}{8640} + \frac{52 \cdot 18}{8640} + \frac{270}{8640} + \frac{3 \cdot 120}{8640} + \frac{5 \cdot 60}{60 \cdot 144} + \frac{2 \cdot 45}{192 \cdot 45} + \frac{3 \cdot 20}{432 \cdot 20}$

Step 3.35

Multiply $60$ by $144$ .

$\frac{2160}{8640} + \frac{26 \cdot 72}{8640} + \frac{26 \cdot 36}{8640} + \frac{360}{8640} + \frac{3 \cdot 432}{8640} + \frac{52 \cdot 18}{8640} + \frac{270}{8640} + \frac{3 \cdot 120}{8640} + \frac{5 \cdot 60}{8640} + \frac{2 \cdot 45}{192 \cdot 45} + \frac{3 \cdot 20}{432 \cdot 20}$

Step 3.36

Reorder the factors of $192 \cdot 45$ .

$\frac{2160}{8640} + \frac{26 \cdot 72}{8640} + \frac{26 \cdot 36}{8640} + \frac{360}{8640} + \frac{3 \cdot 432}{8640} + \frac{52 \cdot 18}{8640} + \frac{270}{8640} + \frac{3 \cdot 120}{8640} + \frac{5 \cdot 60}{8640} + \frac{2 \cdot 45}{45 \cdot 192} + \frac{3 \cdot 20}{432 \cdot 20}$

Step 3.37

Multiply $45$ by $192$ .

$\frac{2160}{8640} + \frac{26 \cdot 72}{8640} + \frac{26 \cdot 36}{8640} + \frac{360}{8640} + \frac{3 \cdot 432}{8640} + \frac{52 \cdot 18}{8640} + \frac{270}{8640} + \frac{3 \cdot 120}{8640} + \frac{5 \cdot 60}{8640} + \frac{2 \cdot 45}{8640} + \frac{3 \cdot 20}{432 \cdot 20}$

Step 3.38

Reorder the factors of $432 \cdot 20$ .

$\frac{2160}{8640} + \frac{26 \cdot 72}{8640} + \frac{26 \cdot 36}{8640} + \frac{360}{8640} + \frac{3 \cdot 432}{8640} + \frac{52 \cdot 18}{8640} + \frac{270}{8640} + \frac{3 \cdot 120}{8640} + \frac{5 \cdot 60}{8640} + \frac{2 \cdot 45}{8640} + \frac{3 \cdot 20}{20 \cdot 432}$

Step 3.39

Multiply $20$ by $432$ .

$\frac{2160}{8640} + \frac{26 \cdot 72}{8640} + \frac{26 \cdot 36}{8640} + \frac{360}{8640} + \frac{3 \cdot 432}{8640} + \frac{52 \cdot 18}{8640} + \frac{270}{8640} + \frac{3 \cdot 120}{8640} + \frac{5 \cdot 60}{8640} + \frac{2 \cdot 45}{8640} + \frac{3 \cdot 20}{8640}$

Step 4

Combine the numerators over the common denominator.

$\frac{2160 + 26 \cdot 72 + 26 \cdot 36 + 360 + 3 \cdot 432 + 52 \cdot 18 + 270 + 3 \cdot 120 + 5 \cdot 60 + 2 \cdot 45 + 3 \cdot 20}{8640}$

Step 5

Simplify each term.

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Step 5.1

Multiply $26$ by $72$ .

$\frac{2160 + 1872 + 26 \cdot 36 + 360 + 3 \cdot 432 + 52 \cdot 18 + 270 + 3 \cdot 120 + 5 \cdot 60 + 2 \cdot 45 + 3 \cdot 20}{8640}$

Step 5.2

Multiply $26$ by $36$ .

$\frac{2160 + 1872 + 936 + 360 + 3 \cdot 432 + 52 \cdot 18 + 270 + 3 \cdot 120 + 5 \cdot 60 + 2 \cdot 45 + 3 \cdot 20}{8640}$

Step 5.3

Multiply $3$ by $432$ .

$\frac{2160 + 1872 + 936 + 360 + 1296 + 52 \cdot 18 + 270 + 3 \cdot 120 + 5 \cdot 60 + 2 \cdot 45 + 3 \cdot 20}{8640}$

Step 5.4

Multiply $52$ by $18$ .

$\frac{2160 + 1872 + 936 + 360 + 1296 + 936 + 270 + 3 \cdot 120 + 5 \cdot 60 + 2 \cdot 45 + 3 \cdot 20}{8640}$

Step 5.5

Multiply $3$ by $120$ .

$\frac{2160 + 1872 + 936 + 360 + 1296 + 936 + 270 + 360 + 5 \cdot 60 + 2 \cdot 45 + 3 \cdot 20}{8640}$

Step 5.6

Multiply $5$ by $60$ .

$\frac{2160 + 1872 + 936 + 360 + 1296 + 936 + 270 + 360 + 300 + 2 \cdot 45 + 3 \cdot 20}{8640}$

Step 5.7

Multiply $2$ by $45$ .

$\frac{2160 + 1872 + 936 + 360 + 1296 + 936 + 270 + 360 + 300 + 90 + 3 \cdot 20}{8640}$

Step 5.8

Multiply $3$ by $20$ .

$\frac{2160 + 1872 + 936 + 360 + 1296 + 936 + 270 + 360 + 300 + 90 + 60}{8640}$

Step 6

Simplify the expression.

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Step 6.1

Add $2160$ and $1872$ .

$\frac{4032 + 936 + 360 + 1296 + 936 + 270 + 360 + 300 + 90 + 60}{8640}$

Step 6.2

Add $4032$ and $936$ .

$\frac{4968 + 360 + 1296 + 936 + 270 + 360 + 300 + 90 + 60}{8640}$

Step 6.3

Add $4968$ and $360$ .

$\frac{5328 + 1296 + 936 + 270 + 360 + 300 + 90 + 60}{8640}$

Step 6.4

Add $5328$ and $1296$ .

$\frac{6624 + 936 + 270 + 360 + 300 + 90 + 60}{8640}$

Step 6.5

Add $6624$ and $936$ .

$\frac{7560 + 270 + 360 + 300 + 90 + 60}{8640}$

Step 6.6

Add $7560$ and $270$ .

$\frac{7830 + 360 + 300 + 90 + 60}{8640}$

Step 6.7

Add $7830$ and $360$ .

$\frac{8190 + 300 + 90 + 60}{8640}$

Step 6.8

Add $8190$ and $300$ .

$\frac{8490 + 90 + 60}{8640}$

Step 6.9

Add $8490$ and $90$ .

$\frac{8580 + 60}{8640}$

Step 6.10

Add $8580$ and $60$ .

$\frac{8640}{8640}$

Step 6.11

Divide $8640$ by $8640$ .

$1$