Basic Math Examples

$5 \frac{1}{7} \div 3 \frac{3}{4}$

Step 1

Convert

$5 \frac{1}{7}$ to an improper fraction.

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Step 1.1

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

$(5 + \frac{1}{7}) \div 3 \frac{3}{4}$

Step 1.2

Add

$5$ and

$\frac{1}{7}$ .

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Step 1.2.1

To write

$5$ as a fraction with a common denominator, multiply by

$\frac{7}{7}$ .

$(5 \cdot \frac{7}{7} + \frac{1}{7}) \div 3 \frac{3}{4}$

Step 1.2.2

Combine

$5$ and

$\frac{7}{7}$ .

$(\frac{5 \cdot 7}{7} + \frac{1}{7}) \div 3 \frac{3}{4}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{5 \cdot 7 + 1}{7} \div 3 \frac{3}{4}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$5$ by

$7$ .

$\frac{35 + 1}{7} \div 3 \frac{3}{4}$

Step 1.2.4.2

Add

$35$ and

$1$ .

$\frac{36}{7} \div 3 \frac{3}{4}$

Step 2

Convert

$3 \frac{3}{4}$ to an improper fraction.

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Step 2.1

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

$\frac{36}{7} \div (3 + \frac{3}{4})$

Step 2.2

Add

$3$ and

$\frac{3}{4}$ .

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Step 2.2.1

To write

$3$ as a fraction with a common denominator, multiply by

$\frac{4}{4}$ .

$\frac{36}{7} \div (3 \cdot \frac{4}{4} + \frac{3}{4})$

Step 2.2.2

Combine

$3$ and

$\frac{4}{4}$ .

$\frac{36}{7} \div (\frac{3 \cdot 4}{4} + \frac{3}{4})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{36}{7} \div \frac{3 \cdot 4 + 3}{4}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

$3$ by

$4$ .

$\frac{36}{7} \div \frac{12 + 3}{4}$

Step 2.2.4.2

Add

$12$ and

$3$ .

$\frac{36}{7} \div \frac{15}{4}$

Step 3

To divide by a fraction, multiply by its reciprocal.

$\frac{36}{7} \cdot \frac{4}{15}$

Step 4

Cancel the common factor of

$3$ .

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Step 4.1

Factor

$3$ out of

$36$ .

$\frac{3 (12)}{7} \cdot \frac{4}{15}$

Step 4.2

Factor

$3$ out of

$15$ .

$\frac{3 \cdot 12}{7} \cdot \frac{4}{3 \cdot 5}$

Step 4.3

Cancel the common factor.

$\frac{3 \cdot 12}{7} \cdot \frac{4}{3 \cdot 5}$

Step 4.4

Rewrite the expression.

$\frac{12}{7} \cdot \frac{4}{5}$

Step 5

Multiply

$\frac{12}{7}$ by

$\frac{4}{5}$ .

$\frac{12 \cdot 4}{7 \cdot 5}$

Step 6

Multiply.

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Step 6.1

Multiply

$12$ by

$4$ .

$\frac{48}{7 \cdot 5}$

Step 6.2

Multiply

$7$ by

$5$ .

$\frac{48}{35}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{48}{35}$

Decimal Form:

$1.37142857 \dots$

Mixed Number Form:

$1 \frac{13}{35}$