Basic Math Examples

$\frac{23}{10} a - \frac{56}{5} \div \frac{7}{10} = (\frac{19}{10} - \frac{94}{10}) \div (- \frac{21}{10})$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Combine $\frac{23}{10}$ and $a$ .

$\frac{23 a}{10} - \frac{56}{5} \div \frac{7}{10} = (\frac{19}{10} - \frac{94}{10}) \div (- \frac{21}{10})$

Step 1.2

To divide by a fraction, multiply by its reciprocal.

$\frac{23 a}{10} - (\frac{56}{5} \cdot \frac{10}{7}) = (\frac{19}{10} - \frac{94}{10}) \div (- \frac{21}{10})$

Step 1.3

Cancel the common factor of $7$ .

Tap for more steps...

Step 1.3.1

Factor $7$ out of $56$ .

$\frac{23 a}{10} - (\frac{7 (8)}{5} \cdot \frac{10}{7}) = (\frac{19}{10} - \frac{94}{10}) \div (- \frac{21}{10})$

Step 1.3.2

Cancel the common factor.

$\frac{23 a}{10} - (\frac{7 \cdot 8}{5} \cdot \frac{10}{7}) = (\frac{19}{10} - \frac{94}{10}) \div (- \frac{21}{10})$

Step 1.3.3

Rewrite the expression.

$\frac{23 a}{10} - (\frac{8}{5} \cdot 10) = (\frac{19}{10} - \frac{94}{10}) \div (- \frac{21}{10})$

Step 1.4

Cancel the common factor of $5$ .

Tap for more steps...

Step 1.4.1

Factor $5$ out of $10$ .

$\frac{23 a}{10} - (\frac{8}{5} \cdot (5 (2))) = (\frac{19}{10} - \frac{94}{10}) \div (- \frac{21}{10})$

Step 1.4.2

Cancel the common factor.

$\frac{23 a}{10} - (\frac{8}{5} \cdot (5 \cdot 2)) = (\frac{19}{10} - \frac{94}{10}) \div (- \frac{21}{10})$

Step 1.4.3

Rewrite the expression.

$\frac{23 a}{10} - (8 \cdot 2) = (\frac{19}{10} - \frac{94}{10}) \div (- \frac{21}{10})$

Step 1.5

Multiply $8$ by $2$ .

$\frac{23 a}{10} - 1 \cdot 16 = (\frac{19}{10} - \frac{94}{10}) \div (- \frac{21}{10})$

Step 1.6

Multiply $- 1$ by $16$ .

$\frac{23 a}{10} - 16 = (\frac{19}{10} - \frac{94}{10}) \div (- \frac{21}{10})$

Step 2

Simplify $(\frac{19}{10} - \frac{94}{10}) \div (- \frac{21}{10})$ .

Tap for more steps...

Step 2.1

To divide by a fraction, multiply by its reciprocal.

$\frac{23 a}{10} - 16 = (\frac{19}{10} - \frac{94}{10}) (- \frac{10}{21})$

Step 2.2

Combine the numerators over the common denominator.

$\frac{23 a}{10} - 16 = \frac{19 - 94}{10} (- \frac{10}{21})$

Step 2.3

Subtract $94$ from $19$ .

$\frac{23 a}{10} - 16 = \frac{- 75}{10} (- \frac{10}{21})$

Step 2.4

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.4.1

Move the leading negative in $- \frac{10}{21}$ into the numerator.

$\frac{23 a}{10} - 16 = \frac{- 75}{10} \cdot \frac{- 10}{21}$

Step 2.4.2

Factor $3$ out of $- 75$ .

$\frac{23 a}{10} - 16 = \frac{3 (- 25)}{10} \cdot \frac{- 10}{21}$

Step 2.4.3

Factor $3$ out of $21$ .

$\frac{23 a}{10} - 16 = \frac{3 \cdot - 25}{10} \cdot \frac{- 10}{3 \cdot 7}$

Step 2.4.4

Cancel the common factor.

$\frac{23 a}{10} - 16 = \frac{3 \cdot - 25}{10} \cdot \frac{- 10}{3 \cdot 7}$

Step 2.4.5

Rewrite the expression.

$\frac{23 a}{10} - 16 = \frac{- 25}{10} \cdot \frac{- 10}{7}$

Step 2.5

Cancel the common factor of $10$ .

Tap for more steps...

Step 2.5.1

Factor $10$ out of $- 10$ .

$\frac{23 a}{10} - 16 = \frac{- 25}{10} \cdot \frac{10 (- 1)}{7}$

Step 2.5.2

Cancel the common factor.

$\frac{23 a}{10} - 16 = \frac{- 25}{10} \cdot \frac{10 \cdot - 1}{7}$

Step 2.5.3

Rewrite the expression.

$\frac{23 a}{10} - 16 = - 25 (\frac{- 1}{7})$

Step 2.6

Combine $- 25$ and $\frac{- 1}{7}$ .

$\frac{23 a}{10} - 16 = \frac{- 25 \cdot - 1}{7}$

Step 2.7

Multiply $- 25$ by $- 1$ .

$\frac{23 a}{10} - 16 = \frac{25}{7}$

Step 3

Move all terms not containing $a$ to the right side of the equation.

Tap for more steps...

Step 3.1

Add $16$ to both sides of the equation.

$\frac{23 a}{10} = \frac{25}{7} + 16$

Step 3.2

To write $16$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{23 a}{10} = \frac{25}{7} + 16 \cdot \frac{7}{7}$

Step 3.3

Combine $16$ and $\frac{7}{7}$ .

$\frac{23 a}{10} = \frac{25}{7} + \frac{16 \cdot 7}{7}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{23 a}{10} = \frac{25 + 16 \cdot 7}{7}$

Step 3.5

Simplify the numerator.

Tap for more steps...

Step 3.5.1

Multiply $16$ by $7$ .

$\frac{23 a}{10} = \frac{25 + 112}{7}$

Step 3.5.2

Add $25$ and $112$ .

$\frac{23 a}{10} = \frac{137}{7}$

Step 4

Multiply both sides of the equation by $\frac{10}{23}$ .

$\frac{10}{23} \cdot \frac{23 a}{10} = \frac{10}{23} \cdot \frac{137}{7}$

Step 5

Simplify both sides of the equation.

Tap for more steps...

Step 5.1

Simplify the left side.

Tap for more steps...

Step 5.1.1

Simplify $\frac{10}{23} \cdot \frac{23 a}{10}$ .

Tap for more steps...

Step 5.1.1.1

Cancel the common factor of $10$ .

Tap for more steps...

Step 5.1.1.1.1

Cancel the common factor.

$\frac{10}{23} \cdot \frac{23 a}{10} = \frac{10}{23} \cdot \frac{137}{7}$

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{23} (23 a) = \frac{10}{23} \cdot \frac{137}{7}$

Step 5.1.1.2

Cancel the common factor of $23$ .

Tap for more steps...

Step 5.1.1.2.1

Factor $23$ out of $23 a$ .

$\frac{1}{23} (23 (a)) = \frac{10}{23} \cdot \frac{137}{7}$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{23} (23 a) = \frac{10}{23} \cdot \frac{137}{7}$

Step 5.1.1.2.3

Rewrite the expression.

$a = \frac{10}{23} \cdot \frac{137}{7}$

Step 5.2

Simplify the right side.

Tap for more steps...

Step 5.2.1

Multiply $\frac{10}{23} \cdot \frac{137}{7}$ .

Tap for more steps...

Step 5.2.1.1

Multiply $\frac{10}{23}$ by $\frac{137}{7}$ .

$a = \frac{10 \cdot 137}{23 \cdot 7}$

Step 5.2.1.2

Multiply $10$ by $137$ .

$a = \frac{1370}{23 \cdot 7}$

Step 5.2.1.3

Multiply $23$ by $7$ .

$a = \frac{1370}{161}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$a = \frac{1370}{161}$

Decimal Form:

$a = 8.50931677 \dots$

Mixed Number Form:

$a = 8 \frac{82}{161}$