Basic Operations Set A

A. $\dfrac{5}{8}$

To find the sum of fractions with common denominators (bottoms), you simply add the two numerators (tops) and keep the same denominator.

$$\dfrac{2}{8} + \dfrac{3}{8} = \dfrac{2 + 3}{8} = \dfrac{5}{8}$$

B. $\dfrac{7}{10}$

$$\dfrac{3}{10} + \dfrac{4}{10} = \dfrac{3 + 4}{10} = \dfrac{7}{10}$$

A. $\dfrac{4}{7}$

To find the difference of fractions with common denominators (bottoms), you simply subtract the two numerators (tops) and keep the same denominator.

$$\dfrac{6}{7} - \dfrac{2}{7} = \dfrac{6 - 2}{7} = \dfrac{4}{7}$$

A. $\dfrac{5}{9}$

$$\dfrac{8}{9} - \dfrac{3}{9} = \dfrac{8 - 3}{9} = \dfrac{5}{9}$$

A. $6\dfrac{3}{5}$

$33 \div 5 = 6$ with a remainder of $3$. Since the original value was represented in fifths, you put the remainder over $5$.

$$33 \div 5 = 6 \text{ remainder } 3 = $$ $$6\dfrac{3}{5}$$

C. $\dfrac{12}{63}$

When multiplying fractions, just multiply numerator × numerator and denominator × denominator.

$$\dfrac{4}{9} \times \dfrac{3}{7} = \dfrac{4 \times 3}{9 \times 7} = \dfrac{12}{63}$$

A. $\dfrac{25}{7}$

Multiply the whole number, $3$, by the denominator, $7$, and add the numerator, $4$. Then, write the result over $7$ (the initial denominator).

$$3\dfrac{4}{7} = \dfrac{(3 \times 7) + 4}{7} = $$ $$\dfrac{21 + 4}{7} = \dfrac{25}{7}$$

A. $\dfrac{21}{8}$

$$2\dfrac{5}{8} = \dfrac{(2 \times 8) + 5}{8} = $$ $$\dfrac{16 + 5}{8} = \dfrac{21}{8}$$

B. $18$

To change the improper fraction $\dfrac{216}{12}$ to a whole number, divide $216$ by $12$.

$$216 \div 12 = 18$$

C. $5$

$$30 \div 6 = 5$$