Precalculus Examples

$\frac{3}{1 \cdot 2} + \frac{4}{2 \cdot 3} + \frac{5}{3 \cdot 4} + \frac{6}{4 \cdot 5} + \frac{7}{5 \cdot 6}$

Step 1

Find the common denominator.

Tap for more steps...

Step 1.1

Multiply $2$ by $1$ .

$\frac{3}{2} + \frac{4}{2 \cdot 3} + \frac{5}{3 \cdot 4} + \frac{6}{4 \cdot 5} + \frac{7}{5 \cdot 6}$

Step 1.2

Multiply $2$ by $3$ .

$\frac{3}{2} + \frac{4}{6} + \frac{5}{3 \cdot 4} + \frac{6}{4 \cdot 5} + \frac{7}{5 \cdot 6}$

Step 1.3

Multiply $3$ by $4$ .

$\frac{3}{2} + \frac{4}{6} + \frac{5}{12} + \frac{6}{4 \cdot 5} + \frac{7}{5 \cdot 6}$

Step 1.4

Multiply $4$ by $5$ .

$\frac{3}{2} + \frac{4}{6} + \frac{5}{12} + \frac{6}{20} + \frac{7}{5 \cdot 6}$

Step 1.5

Multiply $5$ by $6$ .

$\frac{3}{2} + \frac{4}{6} + \frac{5}{12} + \frac{6}{20} + \frac{7}{30}$

Step 1.6

Multiply $\frac{3}{2}$ by $\frac{30}{30}$ .

$\frac{3}{2} \cdot \frac{30}{30} + \frac{4}{6} + \frac{5}{12} + \frac{6}{20} + \frac{7}{30}$

Step 1.7

Multiply $\frac{3}{2}$ by $\frac{30}{30}$ .

$\frac{3 \cdot 30}{2 \cdot 30} + \frac{4}{6} + \frac{5}{12} + \frac{6}{20} + \frac{7}{30}$

Step 1.8

Multiply $\frac{4}{6}$ by $\frac{10}{10}$ .

$\frac{3 \cdot 30}{2 \cdot 30} + \frac{4}{6} \cdot \frac{10}{10} + \frac{5}{12} + \frac{6}{20} + \frac{7}{30}$

Step 1.9

Multiply $\frac{4}{6}$ by $\frac{10}{10}$ .

$\frac{3 \cdot 30}{2 \cdot 30} + \frac{4 \cdot 10}{6 \cdot 10} + \frac{5}{12} + \frac{6}{20} + \frac{7}{30}$

Step 1.10

Multiply $\frac{5}{12}$ by $\frac{5}{5}$ .

$\frac{3 \cdot 30}{2 \cdot 30} + \frac{4 \cdot 10}{6 \cdot 10} + \frac{5}{12} \cdot \frac{5}{5} + \frac{6}{20} + \frac{7}{30}$

Step 1.11

Multiply $\frac{5}{12}$ by $\frac{5}{5}$ .

$\frac{3 \cdot 30}{2 \cdot 30} + \frac{4 \cdot 10}{6 \cdot 10} + \frac{5 \cdot 5}{12 \cdot 5} + \frac{6}{20} + \frac{7}{30}$

Step 1.12

Multiply $\frac{6}{20}$ by $\frac{3}{3}$ .

$\frac{3 \cdot 30}{2 \cdot 30} + \frac{4 \cdot 10}{6 \cdot 10} + \frac{5 \cdot 5}{12 \cdot 5} + \frac{6}{20} \cdot \frac{3}{3} + \frac{7}{30}$

Step 1.13

Multiply $\frac{6}{20}$ by $\frac{3}{3}$ .

$\frac{3 \cdot 30}{2 \cdot 30} + \frac{4 \cdot 10}{6 \cdot 10} + \frac{5 \cdot 5}{12 \cdot 5} + \frac{6 \cdot 3}{20 \cdot 3} + \frac{7}{30}$

Step 1.14

Multiply $\frac{7}{30}$ by $\frac{2}{2}$ .

$\frac{3 \cdot 30}{2 \cdot 30} + \frac{4 \cdot 10}{6 \cdot 10} + \frac{5 \cdot 5}{12 \cdot 5} + \frac{6 \cdot 3}{20 \cdot 3} + \frac{7}{30} \cdot \frac{2}{2}$

Step 1.15

Multiply $\frac{7}{30}$ by $\frac{2}{2}$ .

$\frac{3 \cdot 30}{2 \cdot 30} + \frac{4 \cdot 10}{6 \cdot 10} + \frac{5 \cdot 5}{12 \cdot 5} + \frac{6 \cdot 3}{20 \cdot 3} + \frac{7 \cdot 2}{30 \cdot 2}$

Step 1.16

Multiply $2$ by $30$ .

$\frac{3 \cdot 30}{60} + \frac{4 \cdot 10}{6 \cdot 10} + \frac{5 \cdot 5}{12 \cdot 5} + \frac{6 \cdot 3}{20 \cdot 3} + \frac{7 \cdot 2}{30 \cdot 2}$

Step 1.17

Multiply $6$ by $10$ .

$\frac{3 \cdot 30}{60} + \frac{4 \cdot 10}{60} + \frac{5 \cdot 5}{12 \cdot 5} + \frac{6 \cdot 3}{20 \cdot 3} + \frac{7 \cdot 2}{30 \cdot 2}$

Step 1.18

Reorder the factors of $12 \cdot 5$ .

$\frac{3 \cdot 30}{60} + \frac{4 \cdot 10}{60} + \frac{5 \cdot 5}{5 \cdot 12} + \frac{6 \cdot 3}{20 \cdot 3} + \frac{7 \cdot 2}{30 \cdot 2}$

Step 1.19

Multiply $5$ by $12$ .

$\frac{3 \cdot 30}{60} + \frac{4 \cdot 10}{60} + \frac{5 \cdot 5}{60} + \frac{6 \cdot 3}{20 \cdot 3} + \frac{7 \cdot 2}{30 \cdot 2}$

Step 1.20

Reorder the factors of $20 \cdot 3$ .

$\frac{3 \cdot 30}{60} + \frac{4 \cdot 10}{60} + \frac{5 \cdot 5}{60} + \frac{6 \cdot 3}{3 \cdot 20} + \frac{7 \cdot 2}{30 \cdot 2}$

Step 1.21

Multiply $3$ by $20$ .

$\frac{3 \cdot 30}{60} + \frac{4 \cdot 10}{60} + \frac{5 \cdot 5}{60} + \frac{6 \cdot 3}{60} + \frac{7 \cdot 2}{30 \cdot 2}$

Step 1.22

Reorder the factors of $30 \cdot 2$ .

$\frac{3 \cdot 30}{60} + \frac{4 \cdot 10}{60} + \frac{5 \cdot 5}{60} + \frac{6 \cdot 3}{60} + \frac{7 \cdot 2}{2 \cdot 30}$

Step 1.23

Multiply $2$ by $30$ .

$\frac{3 \cdot 30}{60} + \frac{4 \cdot 10}{60} + \frac{5 \cdot 5}{60} + \frac{6 \cdot 3}{60} + \frac{7 \cdot 2}{60}$

Step 2

Combine the numerators over the common denominator.

$\frac{3 \cdot 30 + 4 \cdot 10 + 5 \cdot 5 + 6 \cdot 3 + 7 \cdot 2}{60}$

Step 3

Simplify each term.

Tap for more steps...

Step 3.1

Multiply $3$ by $30$ .

$\frac{90 + 4 \cdot 10 + 5 \cdot 5 + 6 \cdot 3 + 7 \cdot 2}{60}$

Step 3.2

Multiply $4$ by $10$ .

$\frac{90 + 40 + 5 \cdot 5 + 6 \cdot 3 + 7 \cdot 2}{60}$

Step 3.3

Multiply $5$ by $5$ .

$\frac{90 + 40 + 25 + 6 \cdot 3 + 7 \cdot 2}{60}$

Step 3.4

Multiply $6$ by $3$ .

$\frac{90 + 40 + 25 + 18 + 7 \cdot 2}{60}$

Step 3.5

Multiply $7$ by $2$ .

$\frac{90 + 40 + 25 + 18 + 14}{60}$

Step 4

Simplify by adding numbers.

Tap for more steps...

Step 4.1

Add $90$ and $40$ .

$\frac{130 + 25 + 18 + 14}{60}$

Step 4.2

Add $130$ and $25$ .

$\frac{155 + 18 + 14}{60}$

Step 4.3

Add $155$ and $18$ .

$\frac{173 + 14}{60}$

Step 4.4

Add $173$ and $14$ .

$\frac{187}{60}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{187}{60}$

Decimal Form:

$3.11\overline{6}$

Mixed Number Form:

$3 \frac{7}{60}$