Basic Math Examples

$\frac{2 j - 1}{3} + \frac{3 j + 4}{4} + \frac{7 (j + 3)}{10}$

Step 1

Find the common denominator.

Tap for more steps...

Step 1.1

Multiply $\frac{2 j - 1}{3}$ by $\frac{20}{20}$ .

$\frac{2 j - 1}{3} \cdot \frac{20}{20} + \frac{3 j + 4}{4} + \frac{7 (j + 3)}{10}$

Step 1.2

Multiply $\frac{2 j - 1}{3}$ by $\frac{20}{20}$ .

$\frac{(2 j - 1) \cdot 20}{3 \cdot 20} + \frac{3 j + 4}{4} + \frac{7 (j + 3)}{10}$

Step 1.3

Multiply $\frac{3 j + 4}{4}$ by $\frac{15}{15}$ .

$\frac{(2 j - 1) \cdot 20}{3 \cdot 20} + \frac{3 j + 4}{4} \cdot \frac{15}{15} + \frac{7 (j + 3)}{10}$

Step 1.4

Multiply $\frac{3 j + 4}{4}$ by $\frac{15}{15}$ .

$\frac{(2 j - 1) \cdot 20}{3 \cdot 20} + \frac{(3 j + 4) \cdot 15}{4 \cdot 15} + \frac{7 (j + 3)}{10}$

Step 1.5

Multiply $\frac{7 (j + 3)}{10}$ by $\frac{6}{6}$ .

$\frac{(2 j - 1) \cdot 20}{3 \cdot 20} + \frac{(3 j + 4) \cdot 15}{4 \cdot 15} + \frac{7 (j + 3)}{10} \cdot \frac{6}{6}$

Step 1.6

Multiply $\frac{7 (j + 3)}{10}$ by $\frac{6}{6}$ .

$\frac{(2 j - 1) \cdot 20}{3 \cdot 20} + \frac{(3 j + 4) \cdot 15}{4 \cdot 15} + \frac{7 (j + 3) \cdot 6}{10 \cdot 6}$

Step 1.7

Multiply $3$ by $20$ .

$\frac{(2 j - 1) \cdot 20}{60} + \frac{(3 j + 4) \cdot 15}{4 \cdot 15} + \frac{7 (j + 3) \cdot 6}{10 \cdot 6}$

Step 1.8

Multiply $4$ by $15$ .

$\frac{(2 j - 1) \cdot 20}{60} + \frac{(3 j + 4) \cdot 15}{60} + \frac{7 (j + 3) \cdot 6}{10 \cdot 6}$

Step 1.9

Reorder the factors of $10 \cdot 6$ .

$\frac{(2 j - 1) \cdot 20}{60} + \frac{(3 j + 4) \cdot 15}{60} + \frac{7 (j + 3) \cdot 6}{6 \cdot 10}$

Step 1.10

Multiply $6$ by $10$ .

$\frac{(2 j - 1) \cdot 20}{60} + \frac{(3 j + 4) \cdot 15}{60} + \frac{7 (j + 3) \cdot 6}{60}$

Step 2

Combine the numerators over the common denominator.

$\frac{(2 j - 1) \cdot 20 + (3 j + 4) \cdot 15 + 7 (j + 3) \cdot 6}{60}$

Step 3

Simplify each term.

Tap for more steps...

Step 3.1

Apply the distributive property.

$\frac{2 j \cdot 20 - 1 \cdot 20 + (3 j + 4) \cdot 15 + 7 (j + 3) \cdot 6}{60}$

Step 3.2

Multiply $20$ by $2$ .

$\frac{40 j - 1 \cdot 20 + (3 j + 4) \cdot 15 + 7 (j + 3) \cdot 6}{60}$

Step 3.3

Multiply $- 1$ by $20$ .

$\frac{40 j - 20 + (3 j + 4) \cdot 15 + 7 (j + 3) \cdot 6}{60}$

Step 3.4

Apply the distributive property.

$\frac{40 j - 20 + 3 j \cdot 15 + 4 \cdot 15 + 7 (j + 3) \cdot 6}{60}$

Step 3.5

Multiply $15$ by $3$ .

$\frac{40 j - 20 + 45 j + 4 \cdot 15 + 7 (j + 3) \cdot 6}{60}$

Step 3.6

Multiply $4$ by $15$ .

$\frac{40 j - 20 + 45 j + 60 + 7 (j + 3) \cdot 6}{60}$

Step 3.7

Apply the distributive property.

$\frac{40 j - 20 + 45 j + 60 + (7 j + 7 \cdot 3) \cdot 6}{60}$

Step 3.8

Multiply $7$ by $3$ .

$\frac{40 j - 20 + 45 j + 60 + (7 j + 21) \cdot 6}{60}$

Step 3.9

Apply the distributive property.

$\frac{40 j - 20 + 45 j + 60 + 7 j \cdot 6 + 21 \cdot 6}{60}$

Step 3.10

Multiply $6$ by $7$ .

$\frac{40 j - 20 + 45 j + 60 + 42 j + 21 \cdot 6}{60}$

Step 3.11

Multiply $21$ by $6$ .

$\frac{40 j - 20 + 45 j + 60 + 42 j + 126}{60}$

Step 4

Simplify by adding terms.

Tap for more steps...

Step 4.1

Add $40 j$ and $45 j$ .

$\frac{85 j - 20 + 60 + 42 j + 126}{60}$

Step 4.2

Add $85 j$ and $42 j$ .

$\frac{127 j - 20 + 60 + 126}{60}$

Step 4.3

Simplify by adding numbers.

Tap for more steps...

Step 4.3.1

Add $- 20$ and $60$ .

$\frac{127 j + 40 + 126}{60}$

Step 4.3.2

Add $40$ and $126$ .

$\frac{127 j + 166}{60}$