Basic Math Examples

$6 \frac{5}{6} + 6 \frac{5}{6} + 2 \frac{6}{7} + 2 \frac{6}{7}$

Step 1

Convert $6 \frac{5}{6}$ to an improper fraction.

Tap for more steps...

Step 1.1

A mixed number is an addition of its whole and fractional parts.

$6 + \frac{5}{6} + 6 \frac{5}{6} + 2 \frac{6}{7} + 2 \frac{6}{7}$

Step 1.2

Add $6$ and $\frac{5}{6}$ .

Tap for more steps...

Step 1.2.1

To write $6$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

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

Step 1.2.2

Combine $6$ and $\frac{6}{6}$ .

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

Tap for more steps...

Step 1.2.4.1

Multiply $6$ by $6$ .

$\frac{36 + 5}{6} + 6 \frac{5}{6} + 2 \frac{6}{7} + 2 \frac{6}{7}$

Step 1.2.4.2

Add $36$ and $5$ .

$\frac{41}{6} + 6 \frac{5}{6} + 2 \frac{6}{7} + 2 \frac{6}{7}$

Step 2

Convert $6 \frac{5}{6}$ to an improper fraction.

Tap for more steps...

Step 2.1

A mixed number is an addition of its whole and fractional parts.

$\frac{41}{6} + 6 + \frac{5}{6} + 2 \frac{6}{7} + 2 \frac{6}{7}$

Step 2.2

Add $6$ and $\frac{5}{6}$ .

Tap for more steps...

Step 2.2.1

To write $6$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{41}{6} + 6 \cdot \frac{6}{6} + \frac{5}{6} + 2 \frac{6}{7} + 2 \frac{6}{7}$

Step 2.2.2

Combine $6$ and $\frac{6}{6}$ .

$\frac{41}{6} + \frac{6 \cdot 6}{6} + \frac{5}{6} + 2 \frac{6}{7} + 2 \frac{6}{7}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{41}{6} + \frac{6 \cdot 6 + 5}{6} + 2 \frac{6}{7} + 2 \frac{6}{7}$

Step 2.2.4

Simplify the numerator.

Tap for more steps...

Step 2.2.4.1

Multiply $6$ by $6$ .

$\frac{41}{6} + \frac{36 + 5}{6} + 2 \frac{6}{7} + 2 \frac{6}{7}$

Step 2.2.4.2

Add $36$ and $5$ .

$\frac{41}{6} + \frac{41}{6} + 2 \frac{6}{7} + 2 \frac{6}{7}$

Step 3

Convert $2 \frac{6}{7}$ to an improper fraction.

Tap for more steps...

Step 3.1

A mixed number is an addition of its whole and fractional parts.

$\frac{41}{6} + \frac{41}{6} + 2 + \frac{6}{7} + 2 \frac{6}{7}$

Step 3.2

Add $2$ and $\frac{6}{7}$ .

Tap for more steps...

Step 3.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{41}{6} + \frac{41}{6} + 2 \cdot \frac{7}{7} + \frac{6}{7} + 2 \frac{6}{7}$

Step 3.2.2

Combine $2$ and $\frac{7}{7}$ .

$\frac{41}{6} + \frac{41}{6} + \frac{2 \cdot 7}{7} + \frac{6}{7} + 2 \frac{6}{7}$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{41}{6} + \frac{41}{6} + \frac{2 \cdot 7 + 6}{7} + 2 \frac{6}{7}$

Step 3.2.4

Simplify the numerator.

Tap for more steps...

Step 3.2.4.1

Multiply $2$ by $7$ .

$\frac{41}{6} + \frac{41}{6} + \frac{14 + 6}{7} + 2 \frac{6}{7}$

Step 3.2.4.2

Add $14$ and $6$ .

$\frac{41}{6} + \frac{41}{6} + \frac{20}{7} + 2 \frac{6}{7}$

Step 4

Convert $2 \frac{6}{7}$ to an improper fraction.

Tap for more steps...

Step 4.1

A mixed number is an addition of its whole and fractional parts.

$\frac{41}{6} + \frac{41}{6} + \frac{20}{7} + 2 + \frac{6}{7}$

Step 4.2

Add $2$ and $\frac{6}{7}$ .

Tap for more steps...

Step 4.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{41}{6} + \frac{41}{6} + \frac{20}{7} + 2 \cdot \frac{7}{7} + \frac{6}{7}$

Step 4.2.2

Combine $2$ and $\frac{7}{7}$ .

$\frac{41}{6} + \frac{41}{6} + \frac{20}{7} + \frac{2 \cdot 7}{7} + \frac{6}{7}$

Step 4.2.3

Combine the numerators over the common denominator.

$\frac{41}{6} + \frac{41}{6} + \frac{20}{7} + \frac{2 \cdot 7 + 6}{7}$

Step 4.2.4

Simplify the numerator.

Tap for more steps...

Step 4.2.4.1

Multiply $2$ by $7$ .

$\frac{41}{6} + \frac{41}{6} + \frac{20}{7} + \frac{14 + 6}{7}$

Step 4.2.4.2

Add $14$ and $6$ .

$\frac{41}{6} + \frac{41}{6} + \frac{20}{7} + \frac{20}{7}$

Step 5

Combine the numerators over the common denominator.

$\frac{41 + 41}{6} + \frac{20 + 20}{7}$

Step 6

Simplify by adding numbers.

Tap for more steps...

Step 6.1

Add $41$ and $41$ .

$\frac{82}{6} + \frac{20 + 20}{7}$

Step 6.2

Add $20$ and $20$ .

$\frac{82}{6} + \frac{40}{7}$

Step 7

Cancel the common factor of $82$ and $6$ .

Tap for more steps...

Step 7.1

Factor $2$ out of $82$ .

$\frac{2 (41)}{6} + \frac{40}{7}$

Step 7.2

Cancel the common factors.

Tap for more steps...

Step 7.2.1

Factor $2$ out of $6$ .

$\frac{2 \cdot 41}{2 \cdot 3} + \frac{40}{7}$

Step 7.2.2

Cancel the common factor.

$\frac{2 \cdot 41}{2 \cdot 3} + \frac{40}{7}$

Step 7.2.3

Rewrite the expression.

$\frac{41}{3} + \frac{40}{7}$

Step 8

To write $\frac{41}{3}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{41}{3} \cdot \frac{7}{7} + \frac{40}{7}$

Step 9

To write $\frac{40}{7}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{41}{3} \cdot \frac{7}{7} + \frac{40}{7} \cdot \frac{3}{3}$

Step 10

Write each expression with a common denominator of $21$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 10.1

Multiply $\frac{41}{3}$ by $\frac{7}{7}$ .

$\frac{41 \cdot 7}{3 \cdot 7} + \frac{40}{7} \cdot \frac{3}{3}$

Step 10.2

Multiply $3$ by $7$ .

$\frac{41 \cdot 7}{21} + \frac{40}{7} \cdot \frac{3}{3}$

Step 10.3

Multiply $\frac{40}{7}$ by $\frac{3}{3}$ .

$\frac{41 \cdot 7}{21} + \frac{40 \cdot 3}{7 \cdot 3}$

Step 10.4

Multiply $7$ by $3$ .

$\frac{41 \cdot 7}{21} + \frac{40 \cdot 3}{21}$

Step 11

Combine the numerators over the common denominator.

$\frac{41 \cdot 7 + 40 \cdot 3}{21}$

Step 12

Simplify the numerator.

Tap for more steps...

Step 12.1

Multiply $41$ by $7$ .

$\frac{287 + 40 \cdot 3}{21}$

Step 12.2

Multiply $40$ by $3$ .

$\frac{287 + 120}{21}$

Step 12.3

Add $287$ and $120$ .

$\frac{407}{21}$

Step 13

The result can be shown in multiple forms.

Exact Form:

$\frac{407}{21}$

Decimal Form:

$19.38095238 \dots$

Mixed Number Form:

$19 \frac{8}{21}$