Basic Math Examples

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

Step 1

Combine the numerators over the common denominator.

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

Step 2

Add $3$ and $1$ .

$\frac{2}{5} + \frac{4}{4} + \frac{5}{7}$

Step 3

Find the common denominator.

Tap for more steps...

Step 3.1

Multiply $\frac{2}{5}$ by $\frac{28}{28}$ .

$\frac{2}{5} \cdot \frac{28}{28} + \frac{4}{4} + \frac{5}{7}$

Step 3.2

Multiply $\frac{2}{5}$ by $\frac{28}{28}$ .

$\frac{2 \cdot 28}{5 \cdot 28} + \frac{4}{4} + \frac{5}{7}$

Step 3.3

Multiply $\frac{4}{4}$ by $\frac{35}{35}$ .

$\frac{2 \cdot 28}{5 \cdot 28} + \frac{4}{4} \cdot \frac{35}{35} + \frac{5}{7}$

Step 3.4

Multiply $\frac{4}{4}$ by $\frac{35}{35}$ .

$\frac{2 \cdot 28}{5 \cdot 28} + \frac{4 \cdot 35}{4 \cdot 35} + \frac{5}{7}$

Step 3.5

Multiply $\frac{5}{7}$ by $\frac{20}{20}$ .

$\frac{2 \cdot 28}{5 \cdot 28} + \frac{4 \cdot 35}{4 \cdot 35} + \frac{5}{7} \cdot \frac{20}{20}$

Step 3.6

Multiply $\frac{5}{7}$ by $\frac{20}{20}$ .

$\frac{2 \cdot 28}{5 \cdot 28} + \frac{4 \cdot 35}{4 \cdot 35} + \frac{5 \cdot 20}{7 \cdot 20}$

Step 3.7

Multiply $5$ by $28$ .

$\frac{2 \cdot 28}{140} + \frac{4 \cdot 35}{4 \cdot 35} + \frac{5 \cdot 20}{7 \cdot 20}$

Step 3.8

Multiply $4$ by $35$ .

$\frac{2 \cdot 28}{140} + \frac{4 \cdot 35}{140} + \frac{5 \cdot 20}{7 \cdot 20}$

Step 3.9

Multiply $7$ by $20$ .

$\frac{2 \cdot 28}{140} + \frac{4 \cdot 35}{140} + \frac{5 \cdot 20}{140}$

Step 4

Combine the numerators over the common denominator.

$\frac{2 \cdot 28 + 4 \cdot 35 + 5 \cdot 20}{140}$

Step 5

Simplify each term.

Tap for more steps...

Step 5.1

Multiply $2$ by $28$ .

$\frac{56 + 4 \cdot 35 + 5 \cdot 20}{140}$

Step 5.2

Multiply $4$ by $35$ .

$\frac{56 + 140 + 5 \cdot 20}{140}$

Step 5.3

Multiply $5$ by $20$ .

$\frac{56 + 140 + 100}{140}$

Step 6

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 6.1

Add $56$ and $140$ .

$\frac{196 + 100}{140}$

Step 6.2

Add $196$ and $100$ .

$\frac{296}{140}$

Step 6.3

Cancel the common factor of $296$ and $140$ .

Tap for more steps...

Step 6.3.1

Factor $4$ out of $296$ .

$\frac{4 (74)}{140}$

Step 6.3.2

Cancel the common factors.

Tap for more steps...

Step 6.3.2.1

Factor $4$ out of $140$ .

$\frac{4 \cdot 74}{4 \cdot 35}$

Step 6.3.2.2

Cancel the common factor.

$\frac{4 \cdot 74}{4 \cdot 35}$

Step 6.3.2.3

Rewrite the expression.

$\frac{74}{35}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{74}{35}$

Decimal Form:

$2.11428571 \dots$

Mixed Number Form:

$2 \frac{4}{35}$