Basic Math Examples

6 \frac{3}{7} \cdot 21

$6 \frac{3}{7} \cdot 21$

Step 1

Convert

6 \frac{3}{7}

$6 \frac{3}{7}$ to an improper fraction.

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Step 1.1

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

(6 + \frac{3}{7}) \cdot 21

$(6 + \frac{3}{7}) \cdot 21$

Step 1.2

Add

6

$6$ and

\frac{3}{7}

$\frac{3}{7}$ .

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Step 1.2.1

To write

6

$6$ as a fraction with a common denominator, multiply by

\frac{7}{7}

$\frac{7}{7}$ .

(6 \cdot \frac{7}{7} + \frac{3}{7}) \cdot 21

$(6 \cdot \frac{7}{7} + \frac{3}{7}) \cdot 21$

Step 1.2.2

Combine

6

$6$ and

\frac{7}{7}

$\frac{7}{7}$ .

(\frac{6 \cdot 7}{7} + \frac{3}{7}) \cdot 21

$(\frac{6 \cdot 7}{7} + \frac{3}{7}) \cdot 21$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{6 \cdot 7 + 3}{7} \cdot 21

$\frac{6 \cdot 7 + 3}{7} \cdot 21$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

6

$6$ by

7

$7$ .

\frac{42 + 3}{7} \cdot 21

$\frac{42 + 3}{7} \cdot 21$

Step 1.2.4.2

Add

42

$42$ and

3

$3$ .

\frac{45}{7} \cdot 21

$\frac{45}{7} \cdot 21$

\frac{45}{7} \cdot 21

$\frac{45}{7} \cdot 21$

\frac{45}{7} \cdot 21

$\frac{45}{7} \cdot 21$

\frac{45}{7} \cdot 21

$\frac{45}{7} \cdot 21$

Step 2

Cancel the common factor of

7

$7$ .

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Step 2.1

Factor

7

$7$ out of

21

$21$ .

\frac{45}{7} \cdot (7 (3))

$\frac{45}{7} \cdot (7 (3))$

Step 2.2

Cancel the common factor.

$\frac{45}{7} \cdot (7 \cdot 3)$

Step 2.3

Rewrite the expression.

$45 \cdot 3$

Step 3

Multiply

$45$ by

$3$ .

$135$