Basic Math Examples

$\frac{2}{5} + 4 \frac{2}{7} \div 1 \frac{11}{49}$

Step 1

Convert $4 \frac{2}{7}$ to an improper fraction.

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Step 1.1

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

$\frac{2}{5} + (4 + \frac{2}{7}) \div 1 \frac{11}{49}$

Step 1.2

Add $4$ and $\frac{2}{7}$ .

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Step 1.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{2}{5} + (4 \cdot \frac{7}{7} + \frac{2}{7}) \div 1 \frac{11}{49}$

Step 1.2.2

Combine $4$ and $\frac{7}{7}$ .

$\frac{2}{5} + (\frac{4 \cdot 7}{7} + \frac{2}{7}) \div 1 \frac{11}{49}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{2}{5} + \frac{4 \cdot 7 + 2}{7} \div 1 \frac{11}{49}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $4$ by $7$ .

$\frac{2}{5} + \frac{28 + 2}{7} \div 1 \frac{11}{49}$

Step 1.2.4.2

Add $28$ and $2$ .

$\frac{2}{5} + \frac{30}{7} \div 1 \frac{11}{49}$

Step 2

Convert $1 \frac{11}{49}$ to an improper fraction.

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Step 2.1

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

$\frac{2}{5} + \frac{30}{7} \div (1 + \frac{11}{49})$

Step 2.2

Add $1$ and $\frac{11}{49}$ .

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Step 2.2.1

Write $1$ as a fraction with a common denominator.

$\frac{2}{5} + \frac{30}{7} \div (\frac{49}{49} + \frac{11}{49})$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{2}{5} + \frac{30}{7} \div \frac{49 + 11}{49}$

Step 2.2.3

Add $49$ and $11$ .

$\frac{2}{5} + \frac{30}{7} \div \frac{60}{49}$

Step 3

Simplify each term.

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Step 3.1

To divide by a fraction, multiply by its reciprocal.

$\frac{2}{5} + \frac{30}{7} \cdot \frac{49}{60}$

Step 3.2

Cancel the common factor of $30$ .

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Step 3.2.1

Factor $30$ out of $60$ .

$\frac{2}{5} + \frac{30}{7} \cdot \frac{49}{30 (2)}$

Step 3.2.2

Cancel the common factor.

$\frac{2}{5} + \frac{30}{7} \cdot \frac{49}{30 \cdot 2}$

Step 3.2.3

Rewrite the expression.

$\frac{2}{5} + \frac{1}{7} \cdot \frac{49}{2}$

Step 3.3

Cancel the common factor of $7$ .

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Step 3.3.1

Factor $7$ out of $49$ .

$\frac{2}{5} + \frac{1}{7} \cdot \frac{7 (7)}{2}$

Step 3.3.2

Cancel the common factor.

$\frac{2}{5} + \frac{1}{7} \cdot \frac{7 \cdot 7}{2}$

Step 3.3.3

Rewrite the expression.

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

Step 4

To write $\frac{2}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 5

To write $\frac{7}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Step 6

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 6.1

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

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

Step 6.2

Multiply $5$ by $2$ .

$\frac{2 \cdot 2}{10} + \frac{7}{2} \cdot \frac{5}{5}$

Step 6.3

Multiply $\frac{7}{2}$ by $\frac{5}{5}$ .

$\frac{2 \cdot 2}{10} + \frac{7 \cdot 5}{2 \cdot 5}$

Step 6.4

Multiply $2$ by $5$ .

$\frac{2 \cdot 2}{10} + \frac{7 \cdot 5}{10}$

Step 7

Combine the numerators over the common denominator.

$\frac{2 \cdot 2 + 7 \cdot 5}{10}$

Step 8

Simplify the numerator.

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Step 8.1

Multiply $2$ by $2$ .

$\frac{4 + 7 \cdot 5}{10}$

Step 8.2

Multiply $7$ by $5$ .

$\frac{4 + 35}{10}$

Step 8.3

Add $4$ and $35$ .

$\frac{39}{10}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{39}{10}$

Decimal Form:

$3.9$

Mixed Number Form:

$3 \frac{9}{10}$