Basic Math Examples

$\frac{3}{7} - m a t r i \cdot (- \frac{7}{3} - \frac{6}{7})$

Step 1

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

$\frac{3}{7} - m a t r i \cdot (- \frac{7}{3} \cdot \frac{7}{7} - \frac{6}{7})$

Step 2

To write $- \frac{6}{7}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{3}{7} - m a t r i \cdot (- \frac{7}{3} \cdot \frac{7}{7} - \frac{6}{7} \cdot \frac{3}{3})$

Step 3

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

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Step 3.1

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

$\frac{3}{7} - m a t r i \cdot (- \frac{7 \cdot 7}{3 \cdot 7} - \frac{6}{7} \cdot \frac{3}{3})$

Step 3.2

Multiply $3$ by $7$ .

$\frac{3}{7} - m a t r i \cdot (- \frac{7 \cdot 7}{21} - \frac{6}{7} \cdot \frac{3}{3})$

Step 3.3

Multiply $\frac{6}{7}$ by $\frac{3}{3}$ .

$\frac{3}{7} - m a t r i \cdot (- \frac{7 \cdot 7}{21} - \frac{6 \cdot 3}{7 \cdot 3})$

Step 3.4

Multiply $7$ by $3$ .

$\frac{3}{7} - m a t r i \cdot (- \frac{7 \cdot 7}{21} - \frac{6 \cdot 3}{21})$

Step 4

Combine the numerators over the common denominator.

$\frac{3}{7} - m a t r i \cdot \frac{- 7 \cdot 7 - 6 \cdot 3}{21}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $- 7$ by $7$ .

$\frac{3}{7} - m a t r i \cdot \frac{- 49 - 6 \cdot 3}{21}$

Step 5.2

Multiply $- 6$ by $3$ .

$\frac{3}{7} - m a t r i \cdot \frac{- 49 - 18}{21}$

Step 5.3

Subtract $18$ from $- 49$ .

$\frac{3}{7} - m a t r i \cdot \frac{- 67}{21}$

Step 6

Move the negative in front of the fraction.

$\frac{3}{7} - m a t r i (- \frac{67}{21})$

Step 7

Multiply $- m a t r i (- \frac{67}{21})$ .

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Step 7.1

Multiply $- 1$ by $- 1$ .

$\frac{3}{7} + 1 m a t r i \frac{67}{21}$

Step 7.2

Multiply $m$ by $1$ .

$\frac{3}{7} + m a t r i \frac{67}{21}$

Step 7.3

Combine $m$ and $\frac{67}{21}$ .

$\frac{3}{7} + a t r i \frac{m \cdot 67}{21}$

Step 7.4

Combine $a$ and $\frac{m \cdot 67}{21}$ .

$\frac{3}{7} + t r i \frac{a (m \cdot 67)}{21}$

Step 7.5

Combine $t$ and $\frac{a (m \cdot 67)}{21}$ .

$\frac{3}{7} + r i \frac{t (a (m \cdot 67))}{21}$

Step 7.6

Combine $\frac{t (a (m \cdot 67))}{21}$ and $r$ .

$\frac{3}{7} + \frac{t (a (m \cdot 67)) r}{21} i$

Step 7.7

Combine $\frac{t (a (m \cdot 67)) r}{21}$ and $i$ .

$\frac{3}{7} + \frac{t (a (m \cdot 67)) r i}{21}$

Step 8

Remove parentheses.

$\frac{3}{7} + \frac{t (a m \cdot 67) r i}{21}$

Step 9

Remove parentheses.

$\frac{3}{7} + \frac{t (a m) \cdot 67 r i}{21}$

Step 10

Remove parentheses.

$\frac{3}{7} + \frac{t a m \cdot 67 r i}{21}$

Step 11

Move $67$ to the left of $t a m$ .

$\frac{3}{7} + \frac{67 \cdot (t a m) r i}{21}$

Step 12

Remove parentheses.

$\frac{3}{7} + \frac{67 \cdot (t a) m r i}{21}$

Step 13

Remove parentheses.

$\frac{3}{7} + \frac{67 \cdot t a m r i}{21}$

Step 14

Multiply $67$ by $t$ .

$\frac{3}{7} + \frac{67 t a m r i}{21}$