Basic Math Examples

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

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

Step 1

Find the common denominator.

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Step 1.1

Multiply

\frac{12}{52}

$\frac{12}{52}$ by

\frac{249900}{249900}

$\frac{249900}{249900}$ .

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

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

Step 1.2

Multiply

\frac{12}{52}

$\frac{12}{52}$ by

\frac{249900}{249900}

$\frac{249900}{249900}$ .

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

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

Step 1.3

Multiply

\frac{11}{51}

$\frac{11}{51}$ by

\frac{254800}{254800}

$\frac{254800}{254800}$ .

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

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

Step 1.4

Multiply

\frac{11}{51}

$\frac{11}{51}$ by

\frac{254800}{254800}

$\frac{254800}{254800}$ .

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

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

Step 1.5

Multiply

\frac{10}{50}

$\frac{10}{50}$ by

\frac{259896}{259896}

$\frac{259896}{259896}$ .

\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}

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

Step 1.6

Multiply

\frac{10}{50}

$\frac{10}{50}$ by

\frac{259896}{259896}

$\frac{259896}{259896}$ .

\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}

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

Step 1.7

Multiply

\frac{9}{49}

$\frac{9}{49}$ by

\frac{265200}{265200}

$\frac{265200}{265200}$ .

\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}

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

Step 1.8

Multiply

\frac{9}{49}

$\frac{9}{49}$ by

\frac{265200}{265200}

$\frac{265200}{265200}$ .

\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}

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

Step 1.9

Multiply

\frac{8}{48}

$\frac{8}{48}$ by

\frac{270725}{270725}

$\frac{270725}{270725}$ .

\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}

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

Step 1.10

Multiply

\frac{8}{48}

$\frac{8}{48}$ by

\frac{270725}{270725}

$\frac{270725}{270725}$ .

\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 \cdot 270725}{48 \cdot 270725}

Step 1.11

Multiply

52

$52$ by

249900

$249900$ .

\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}

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

Step 1.12

Multiply

51

$51$ by

254800

$254800$ .

\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}

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

Step 1.13

Multiply

50

$50$ by

259896

$259896$ .

\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}

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

Step 1.14

Multiply

49

$49$ by

265200

$265200$ .

\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}

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

Step 1.15

Multiply

48

$48$ by

270725

$270725$ .

\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}

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

\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}

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

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}

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

Step 3

Simplify each term.

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Step 3.1

Multiply

12

$12$ by

249900

$249900$ .

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

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

Step 3.2

Multiply

11

$11$ by

254800

$254800$ .

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

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

Step 3.3

Multiply

10

$10$ by

259896

$259896$ .

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

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

Step 3.4

Multiply

9

$9$ by

265200

$265200$ .

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

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

Step 3.5

Multiply

8

$8$ by

270725

$270725$ .

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

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

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

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

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Add

2998800

$2998800$ and

2802800

$2802800$ .

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

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

Step 4.2

Simplify by adding numbers.

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Step 4.2.1

Add

5801600

$5801600$ and

2598960

$2598960$ .

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

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

Step 4.2.2

Add

8400560

$8400560$ and

2386800

$2386800$ .

\frac{10787360 + 2165800}{12994800}

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

Step 4.2.3

Add

10787360

$10787360$ and

2165800

$2165800$ .

\frac{12953160}{12994800}

$\frac{12953160}{12994800}$

\frac{12953160}{12994800}

$\frac{12953160}{12994800}$

Step 4.3

Cancel the common factor of

12953160

$12953160$ and

12994800

$12994800$ .

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Step 4.3.1

Factor

120

$120$ out of

12953160

$12953160$ .

\frac{120 (107943)}{12994800}

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

Step 4.3.2

Cancel the common factors.

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Step 4.3.2.1

Factor

120

$120$ out of

12994800

$12994800$ .

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

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

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:

$0.99679564 \dots$