Basic Math Examples

$\frac{12}{52} + \frac{11}{51} + \frac{10}{50} + \frac{9}{49} + \frac{8}{48}$

Step 1

Find the common denominator.

Tap for more steps...

Step 1.1

Multiply $\frac{12}{52}$ by $\frac{249900}{249900}$ .

$\frac{12}{52} \cdot \frac{249900}{249900} + \frac{11}{51} + \frac{10}{50} + \frac{9}{49} + \frac{8}{48}$

Step 1.2

Multiply $\frac{12}{52}$ by $\frac{249900}{249900}$ .

$\frac{12 \cdot 249900}{52 \cdot 249900} + \frac{11}{51} + \frac{10}{50} + \frac{9}{49} + \frac{8}{48}$

Step 1.3

Multiply $\frac{11}{51}$ by $\frac{254800}{254800}$ .

$\frac{12 \cdot 249900}{52 \cdot 249900} + \frac{11}{51} \cdot \frac{254800}{254800} + \frac{10}{50} + \frac{9}{49} + \frac{8}{48}$

Step 1.4

Multiply $\frac{11}{51}$ by $\frac{254800}{254800}$ .

$\frac{12 \cdot 249900}{52 \cdot 249900} + \frac{11 \cdot 254800}{51 \cdot 254800} + \frac{10}{50} + \frac{9}{49} + \frac{8}{48}$

Step 1.5

Multiply $\frac{10}{50}$ by $\frac{259896}{259896}$ .

$\frac{12 \cdot 249900}{52 \cdot 249900} + \frac{11 \cdot 254800}{51 \cdot 254800} + \frac{10}{50} \cdot \frac{259896}{259896} + \frac{9}{49} + \frac{8}{48}$

Step 1.6

Multiply $\frac{10}{50}$ by $\frac{259896}{259896}$ .

$\frac{12 \cdot 249900}{52 \cdot 249900} + \frac{11 \cdot 254800}{51 \cdot 254800} + \frac{10 \cdot 259896}{50 \cdot 259896} + \frac{9}{49} + \frac{8}{48}$

Step 1.7

Multiply $\frac{9}{49}$ by $\frac{265200}{265200}$ .

$\frac{12 \cdot 249900}{52 \cdot 249900} + \frac{11 \cdot 254800}{51 \cdot 254800} + \frac{10 \cdot 259896}{50 \cdot 259896} + \frac{9}{49} \cdot \frac{265200}{265200} + \frac{8}{48}$

Step 1.8

Multiply $\frac{9}{49}$ by $\frac{265200}{265200}$ .

$\frac{12 \cdot 249900}{52 \cdot 249900} + \frac{11 \cdot 254800}{51 \cdot 254800} + \frac{10 \cdot 259896}{50 \cdot 259896} + \frac{9 \cdot 265200}{49 \cdot 265200} + \frac{8}{48}$

Step 1.9

Multiply $\frac{8}{48}$ by $\frac{270725}{270725}$ .

$\frac{12 \cdot 249900}{52 \cdot 249900} + \frac{11 \cdot 254800}{51 \cdot 254800} + \frac{10 \cdot 259896}{50 \cdot 259896} + \frac{9 \cdot 265200}{49 \cdot 265200} + \frac{8}{48} \cdot \frac{270725}{270725}$

Step 1.10

Multiply $\frac{8}{48}$ by $\frac{270725}{270725}$ .

Step 1.11

Multiply $52$ by $249900$ .

$\frac{12 \cdot 249900}{12994800} + \frac{11 \cdot 254800}{51 \cdot 254800} + \frac{10 \cdot 259896}{50 \cdot 259896} + \frac{9 \cdot 265200}{49 \cdot 265200} + \frac{8 \cdot 270725}{48 \cdot 270725}$

Step 1.12

Multiply $51$ by $254800$ .

$\frac{12 \cdot 249900}{12994800} + \frac{11 \cdot 254800}{12994800} + \frac{10 \cdot 259896}{50 \cdot 259896} + \frac{9 \cdot 265200}{49 \cdot 265200} + \frac{8 \cdot 270725}{48 \cdot 270725}$

Step 1.13

Multiply $50$ by $259896$ .

$\frac{12 \cdot 249900}{12994800} + \frac{11 \cdot 254800}{12994800} + \frac{10 \cdot 259896}{12994800} + \frac{9 \cdot 265200}{49 \cdot 265200} + \frac{8 \cdot 270725}{48 \cdot 270725}$

Step 1.14

Multiply $49$ by $265200$ .

$\frac{12 \cdot 249900}{12994800} + \frac{11 \cdot 254800}{12994800} + \frac{10 \cdot 259896}{12994800} + \frac{9 \cdot 265200}{12994800} + \frac{8 \cdot 270725}{48 \cdot 270725}$

Step 1.15

Multiply $48$ by $270725$ .

$\frac{12 \cdot 249900}{12994800} + \frac{11 \cdot 254800}{12994800} + \frac{10 \cdot 259896}{12994800} + \frac{9 \cdot 265200}{12994800} + \frac{8 \cdot 270725}{12994800}$

Step 2

Combine the numerators over the common denominator.

$\frac{12 \cdot 249900 + 11 \cdot 254800 + 10 \cdot 259896 + 9 \cdot 265200 + 8 \cdot 270725}{12994800}$

Step 3

Simplify each term.

Tap for more steps...

Step 3.1

Multiply $12$ by $249900$ .

$\frac{2998800 + 11 \cdot 254800 + 10 \cdot 259896 + 9 \cdot 265200 + 8 \cdot 270725}{12994800}$

Step 3.2

Multiply $11$ by $254800$ .

$\frac{2998800 + 2802800 + 10 \cdot 259896 + 9 \cdot 265200 + 8 \cdot 270725}{12994800}$

Step 3.3

Multiply $10$ by $259896$ .

$\frac{2998800 + 2802800 + 2598960 + 9 \cdot 265200 + 8 \cdot 270725}{12994800}$

Step 3.4

Multiply $9$ by $265200$ .

$\frac{2998800 + 2802800 + 2598960 + 2386800 + 8 \cdot 270725}{12994800}$

Step 3.5

Multiply $8$ by $270725$ .

$\frac{2998800 + 2802800 + 2598960 + 2386800 + 2165800}{12994800}$

Step 4

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 4.1

Add $2998800$ and $2802800$ .

$\frac{5801600 + 2598960 + 2386800 + 2165800}{12994800}$

Step 4.2

Simplify by adding numbers.

Tap for more steps...

Step 4.2.1

Add $5801600$ and $2598960$ .

$\frac{8400560 + 2386800 + 2165800}{12994800}$

Step 4.2.2

Add $8400560$ and $2386800$ .

$\frac{10787360 + 2165800}{12994800}$

Step 4.2.3

Add $10787360$ and $2165800$ .

$\frac{12953160}{12994800}$

Step 4.3

Cancel the common factor of $12953160$ and $12994800$ .

Tap for more steps...

Step 4.3.1

Factor $120$ out of $12953160$ .

$\frac{120 (107943)}{12994800}$

Step 4.3.2

Cancel the common factors.

Tap for more steps...

Step 4.3.2.1

Factor $120$ out of $12994800$ .

$\frac{120 \cdot 107943}{120 \cdot 108290}$

Step 4.3.2.2

Cancel the common factor.

$\frac{120 \cdot 107943}{120 \cdot 108290}$

Step 4.3.2.3

Rewrite the expression.

$\frac{107943}{108290}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{107943}{108290}$

Decimal Form:

$0.99679564 \dots$