Basic Math Examples

$\frac{1}{3} + \frac{1}{15} + \frac{1}{35} + \frac{1}{63} + \frac{1}{99} + \frac{1}{143} + \frac{1}{195}$

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{1}{3}$ by $\frac{15015}{15015}$ .

$\frac{1}{3} \cdot \frac{15015}{15015} + \frac{1}{15} + \frac{1}{35} + \frac{1}{63} + \frac{1}{99} + \frac{1}{143} + \frac{1}{195}$

Step 1.2

Multiply $\frac{1}{3}$ by $\frac{15015}{15015}$ .

$\frac{15015}{3 \cdot 15015} + \frac{1}{15} + \frac{1}{35} + \frac{1}{63} + \frac{1}{99} + \frac{1}{143} + \frac{1}{195}$

Step 1.3

Multiply $\frac{1}{15}$ by $\frac{3003}{3003}$ .

$\frac{15015}{3 \cdot 15015} + \frac{1}{15} \cdot \frac{3003}{3003} + \frac{1}{35} + \frac{1}{63} + \frac{1}{99} + \frac{1}{143} + \frac{1}{195}$

Step 1.4

Multiply $\frac{1}{15}$ by $\frac{3003}{3003}$ .

$\frac{15015}{3 \cdot 15015} + \frac{3003}{15 \cdot 3003} + \frac{1}{35} + \frac{1}{63} + \frac{1}{99} + \frac{1}{143} + \frac{1}{195}$

Step 1.5

Multiply $\frac{1}{35}$ by $\frac{1287}{1287}$ .

$\frac{15015}{3 \cdot 15015} + \frac{3003}{15 \cdot 3003} + \frac{1}{35} \cdot \frac{1287}{1287} + \frac{1}{63} + \frac{1}{99} + \frac{1}{143} + \frac{1}{195}$

Step 1.6

Multiply $\frac{1}{35}$ by $\frac{1287}{1287}$ .

$\frac{15015}{3 \cdot 15015} + \frac{3003}{15 \cdot 3003} + \frac{1287}{35 \cdot 1287} + \frac{1}{63} + \frac{1}{99} + \frac{1}{143} + \frac{1}{195}$

Step 1.7

Multiply $\frac{1}{63}$ by $\frac{715}{715}$ .

$\frac{15015}{3 \cdot 15015} + \frac{3003}{15 \cdot 3003} + \frac{1287}{35 \cdot 1287} + \frac{1}{63} \cdot \frac{715}{715} + \frac{1}{99} + \frac{1}{143} + \frac{1}{195}$

Step 1.8

Multiply $\frac{1}{63}$ by $\frac{715}{715}$ .

$\frac{15015}{3 \cdot 15015} + \frac{3003}{15 \cdot 3003} + \frac{1287}{35 \cdot 1287} + \frac{715}{63 \cdot 715} + \frac{1}{99} + \frac{1}{143} + \frac{1}{195}$

Step 1.9

Multiply $\frac{1}{99}$ by $\frac{455}{455}$ .

$\frac{15015}{3 \cdot 15015} + \frac{3003}{15 \cdot 3003} + \frac{1287}{35 \cdot 1287} + \frac{715}{63 \cdot 715} + \frac{1}{99} \cdot \frac{455}{455} + \frac{1}{143} + \frac{1}{195}$

Step 1.10

Multiply $\frac{1}{99}$ by $\frac{455}{455}$ .

$\frac{15015}{3 \cdot 15015} + \frac{3003}{15 \cdot 3003} + \frac{1287}{35 \cdot 1287} + \frac{715}{63 \cdot 715} + \frac{455}{99 \cdot 455} + \frac{1}{143} + \frac{1}{195}$

Step 1.11

Multiply $\frac{1}{143}$ by $\frac{315}{315}$ .

$\frac{15015}{3 \cdot 15015} + \frac{3003}{15 \cdot 3003} + \frac{1287}{35 \cdot 1287} + \frac{715}{63 \cdot 715} + \frac{455}{99 \cdot 455} + \frac{1}{143} \cdot \frac{315}{315} + \frac{1}{195}$

Step 1.12

Multiply $\frac{1}{143}$ by $\frac{315}{315}$ .

$\frac{15015}{3 \cdot 15015} + \frac{3003}{15 \cdot 3003} + \frac{1287}{35 \cdot 1287} + \frac{715}{63 \cdot 715} + \frac{455}{99 \cdot 455} + \frac{315}{143 \cdot 315} + \frac{1}{195}$

Step 1.13

Multiply $\frac{1}{195}$ by $\frac{231}{231}$ .

$\frac{15015}{3 \cdot 15015} + \frac{3003}{15 \cdot 3003} + \frac{1287}{35 \cdot 1287} + \frac{715}{63 \cdot 715} + \frac{455}{99 \cdot 455} + \frac{315}{143 \cdot 315} + \frac{1}{195} \cdot \frac{231}{231}$

Step 1.14

Multiply $\frac{1}{195}$ by $\frac{231}{231}$ .

$\frac{15015}{3 \cdot 15015} + \frac{3003}{15 \cdot 3003} + \frac{1287}{35 \cdot 1287} + \frac{715}{63 \cdot 715} + \frac{455}{99 \cdot 455} + \frac{315}{143 \cdot 315} + \frac{231}{195 \cdot 231}$

Step 1.15

Multiply $3$ by $15015$ .

$\frac{15015}{45045} + \frac{3003}{15 \cdot 3003} + \frac{1287}{35 \cdot 1287} + \frac{715}{63 \cdot 715} + \frac{455}{99 \cdot 455} + \frac{315}{143 \cdot 315} + \frac{231}{195 \cdot 231}$

Step 1.16

Multiply $15$ by $3003$ .

$\frac{15015}{45045} + \frac{3003}{45045} + \frac{1287}{35 \cdot 1287} + \frac{715}{63 \cdot 715} + \frac{455}{99 \cdot 455} + \frac{315}{143 \cdot 315} + \frac{231}{195 \cdot 231}$

Step 1.17

Multiply $35$ by $1287$ .

$\frac{15015}{45045} + \frac{3003}{45045} + \frac{1287}{45045} + \frac{715}{63 \cdot 715} + \frac{455}{99 \cdot 455} + \frac{315}{143 \cdot 315} + \frac{231}{195 \cdot 231}$

Step 1.18

Multiply $63$ by $715$ .

$\frac{15015}{45045} + \frac{3003}{45045} + \frac{1287}{45045} + \frac{715}{45045} + \frac{455}{99 \cdot 455} + \frac{315}{143 \cdot 315} + \frac{231}{195 \cdot 231}$

Step 1.19

Multiply $99$ by $455$ .

$\frac{15015}{45045} + \frac{3003}{45045} + \frac{1287}{45045} + \frac{715}{45045} + \frac{455}{45045} + \frac{315}{143 \cdot 315} + \frac{231}{195 \cdot 231}$

Step 1.20

Multiply $143$ by $315$ .

$\frac{15015}{45045} + \frac{3003}{45045} + \frac{1287}{45045} + \frac{715}{45045} + \frac{455}{45045} + \frac{315}{45045} + \frac{231}{195 \cdot 231}$

Step 1.21

Multiply $195$ by $231$ .

$\frac{15015}{45045} + \frac{3003}{45045} + \frac{1287}{45045} + \frac{715}{45045} + \frac{455}{45045} + \frac{315}{45045} + \frac{231}{45045}$

Step 2

Combine the numerators over the common denominator.

$\frac{15015 + 3003 + 1287 + 715 + 455 + 315 + 231}{45045}$

Step 3

Simplify by adding numbers.

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Step 3.1

Add $15015$ and $3003$ .

$\frac{18018 + 1287 + 715 + 455 + 315 + 231}{45045}$

Step 3.2

Add $18018$ and $1287$ .

$\frac{19305 + 715 + 455 + 315 + 231}{45045}$

Step 3.3

Add $19305$ and $715$ .

$\frac{20020 + 455 + 315 + 231}{45045}$

Step 3.4

Add $20020$ and $455$ .

$\frac{20475 + 315 + 231}{45045}$

Step 3.5

Add $20475$ and $315$ .

$\frac{20790 + 231}{45045}$

Step 3.6

Add $20790$ and $231$ .

$\frac{21021}{45045}$

Step 4

Cancel the common factor of $21021$ and $45045$ .

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Step 4.1

Factor $3003$ out of $21021$ .

$\frac{3003 (7)}{45045}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $3003$ out of $45045$ .

$\frac{3003 \cdot 7}{3003 \cdot 15}$

Step 4.2.2

Cancel the common factor.

$\frac{3003 \cdot 7}{3003 \cdot 15}$

Step 4.2.3

Rewrite the expression.

$\frac{7}{15}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{7}{15}$

Decimal Form:

$0.4\overline{6}$