Deck 9: Fractions and Fractional Equations

Question 1

What values of $x$ , if any, are not permitted? $\frac{x-3}{x^{2}-16}$

Answer 1

$-4,4$

Question 2

What values of $x$ , if any, are not permitted? $\frac{a+3}{a^{2}+a-12}$

Answer 2

$3,-4$

Question 3

What values of $x$ , if any, are not permitted? $\frac{6}{-x-1}$

Answer 3

-1

Question 4

What values of $x$ , if any, are not permitted? $\frac{x^{2}-6}{2 x^{2}-3 x-9}$

Question 5

Change $\frac{11}{15}$ to a decimal. Work to four decimal places.

Question 6

Change $\frac{11}{17}$ to a decimal. Work to four decimal places.

Question 7

Change $\frac{15}{8}$ to a decimal. Work to four decimal places.

Question 8

Change 0.375 to a fraction.

Question 9

Change 0.035 to a fraction.

Question 10

Change 0.4178266 to a fraction.

Question 11

Change $0 . \overline{4}$ to a fraction.

Question 12

Change $0.\overline{71}$ to a fraction.

Question 13

Change $0 . \overline{565}$ to a fraction.

Question 14

Reduce $\frac{15}{12}$ to lowest terms. Write your answer without negative exponents.

Question 15

Reduce $\frac{36}{54}$ to lowest terms. Write your answer without negative exponents.

Question 16

Reduce $\frac{72}{108}$ to lowest terms. Write your answer without negative exponents.

Question 17

Simplify the fraction by manipulating the algebraic signs: $\frac{2(a-b-c)}{b-a+c}$

Question 18

Simplify the fraction by manipulating the algebraic signs: $\frac{2-x}{x^{2}-4}$

Question 19

Reduce to lowest terms. Write your answer without negative exponents: $\frac{42 a^{2} b^{3}}{14 a^{3} b^{2} c}$

Question 20

Reduce to lowest terms. Write your answer without negative exponents: $\frac{24 x^{4} y^{3} z^{2}}{32 x y^{4}}$

Question 21

Reduce to lowest terms. Write your answer without negative exponents: $\frac{a m^{2}-b c m^{2}}{b c n^{2}-a n^{2}}$

Question 22

Reduce to the lowest terms. Write your answers without negative exponents: $\frac{9 x^{2}-4 y^{2}}{3 x^{2}-2 x y}$

Question 23

Reduce to lowest terms. Write your answer without negative exponents: $\frac{16 x^{2}-16 x y+4 y^{2}}{4 y-8 x}$

Question 24

Reduce to the lowest terms. Write your answer without negative exponents: $\frac{2 a^{3}-54 b^{2}}{2 a^{2}+6 a b+18 b^{2}}$

Question 25

Reduce to lowest terms. Write your answer without negative exponents: $\frac{a^{6}-b^{2}}{b-a^{3}}$

Question 26

Reduce to lowest terms. Write your answer without negative exponents: $\frac{a-a^{5}}{a^{2}-a^{4}}$

Question 27

Reduce to lowest terms. Write your answer without negative exponents: $\frac{a^{2}-2 a x+x^{2}}{m^{2} n(a-x)}$

Question 28

Reduce to lowest terms. Write your answer without negative exponents: $\frac{3 a^{3}(1-2 b)}{a^{2} b\left(1-4 b+4 b^{2}\right)}$

Question 29

Reduce to lowest terms. Write your answer without negative exponents: $\frac{6 m^{2}+11 m-10}{6 m^{2}+5 m-6}$

Question 30

Reduce to lowest terms. Write your answer without negative exponents: $\frac{c^{3}+8}{c^{3}-4 c^{2}+8 c-8}$

Question 31

Multiply and reduce: $5 \times \frac{3}{11}$

Question 32

Multiply and reduce: $\frac{14}{3} \times \frac{6}{7}$

Question 33

Multiply and reduce: $3 \frac{2}{3} \times \frac{4}{9}$

Question 34

Multiply and reduce: $5 \frac{2}{5} \times 2 \frac{4}{9}$

Question 35

Multiply and reduce: $12 \times \frac{5}{9} \times \frac{11}{3}$

Question 36

Multiply and reduce: $\frac{6 a b}{5 x^{4}} \cdot \frac{2 x}{2 a^{2} b^{3}}$

Question 37

Multiply and reduce: $\frac{5 m^{2} n^{4}}{3 a^{2} b^{2} c^{2}} \cdot \frac{2 a^{5} b^{2} c^{3}}{10 m^{3}}$

Question 38

Multiply and reduce: $\frac{x-1}{y^{3}} \cdot \frac{x^{2} y}{x^{2}-1}$

Question 39

Multiply and reduce: $\frac{x-2}{y-3} \cdot \frac{x+3}{y+2}$

Question 40

Multiply and reduce: $\frac{a b-a c}{b-c} \cdot \frac{a c-c^{2}}{a^{2}-a c}$

Question 41

Multiply and reduce: $\frac{x^{2}+2 x y+y^{2}}{15 x} \cdot \frac{5 x^{2} y}{x^{2}-y^{2}}$

Question 42

Multiply and reduce: $\frac{x^{2}-x-6}{x^{2}+4 x+3} \cdot \frac{x^{2}-3 x-4}{x^{2}-4 x+3}$

Question 43

Multiply and reduce: $\frac{a^{6}-b^{6}}{a^{4}+2 a^{2} b^{2}+b^{4}} \cdot \frac{a^{2}+b^{2}}{a^{2}-a b+b^{2}} \cdot \frac{a^{2}+b^{2}}{a^{2}-b^{2}}$

Question 44

Multiply and reduce: $\frac{(a-3 b)^{2}}{a^{2}-9 a b} \cdot \frac{a b+9 b^{2}}{a^{2}-9 b^{2}} \cdot \frac{a^{2}+3 a b}{a b-3 b^{2}}$

Question 45

Multiply and reduce: $\frac{x^{2}-x-20}{4 x^{2}-12 x-40} \cdot \frac{2 x^{2}-2 x-12}{x^{2}+x-12}$

Question 46

Multiply and reduce: $\frac{2 a+2 b+a b+4}{a^{2}+2 a-a b-2 b} \cdot \frac{2 a-2 b+a c-b c}{2 b+2 c+b c+4}$

Question 47

Divide and reduce: $\frac{9}{10} \div \frac{1}{5}$

Question 48

Divide and reduce: $\frac{9}{2} \div 4$

Question 49

Divide and reduce: $2 \div \frac{4}{5}$

Question 50

Divide and reduce: $2 \frac{3}{7} \div \frac{2}{5}$

Question 51

Divide and reduce: $4 \frac{1}{2} \div 2 \frac{1}{3}$

Question 52

Divide and reduce: $\frac{27 a^{2} b^{3}}{8 x^{2} y^{3}} \div \frac{9 a b c}{16 x y z}$

Question 53

Divide and reduce: $\frac{27 x^{3} y^{3}}{y^{3}} \div \frac{18 x^{3} y}{6 y z^{3}}$

Question 54

Divide and reduce: $\frac{3 a+b}{4 a x} \div \frac{9 a^{2}-b^{2}}{12 x}$

Question 55

Divide and reduce: $\frac{a x-b x}{a+b} \div \frac{a y-b y}{a+b}$

Question 56

Divide and reduce: $\frac{4-x^{2}}{x^{2}-1} \div \frac{x-2}{x-1}$

Question 57

Divide and reduce: $\frac{x^{2}-3 x y-4 y^{2}}{4 x-y} \div(x-4 y)$

Question 58

Divide and reduce: $\frac{a^{2} b^{2} x-a^{2} c^{2} x}{y-z} \div(c+b)$

Question 59

Divide and reduce: $\left(x^{3}-27 y^{3}\right) \div\left(\frac{1}{y^{2}}+\frac{3}{x y}+\frac{9}{x^{2}}\right)$

Question 60

The acceleration of an object is equal to the force on the object divided by the object's mass. A cylinder of volume $\frac{\pi d^{2} h}{4}$ and density $\rho$ experiences an electrostatic force equal to $\frac{k q_{1} q_{2}}{r^{2}}$ . Write an expression for the acceleration and simplify it.

Question 61

In analyzing the change of a certain variable, the expression $\frac{a^{3}-8}{a^{4}-4 a^{3}+8 a^{2}-8}$ is used. Determine the reciprocal of this expression and then divide.

Question 62

Combine and simplify: $\frac{4}{5}+\frac{6}{11}$

Question 63

Combine and simplify: $\frac{1}{3}-\frac{3}{5}$

Question 64

Combine and simplify: $5-\frac{3}{4}+\frac{11}{6}+\frac{7}{8}$

Question 65

Combine and simplify: $\frac{6}{13}+\frac{2}{5}+\frac{3}{10}$

Question 66

Combine and simplify: $\frac{22}{9}-\frac{11}{3}+\frac{7}{6}$

Question 67

Combine and simplify: $\frac{3 x}{4}+\frac{2 x}{5}$

Question 68

Combine and simplify: $\frac{4}{a}+\frac{2}{b}$

Question 69

Combine and simplify: $\frac{16 x}{y}-\frac{16 y}{x}$

Question 70

Combine and simplify: $\frac{4 x}{3 a}+\frac{3 x}{5 a}$

Question 71

Combine and simplify: $\frac{2}{x}-\frac{2}{y}$

Question 72

Combine and simplify: $\frac{a^{2}}{x-1}-\frac{a^{2}}{x+1}$

Question 73

Combine and simplify: $\frac{y}{x}-\frac{x}{y}$

Question 74

Combine and simplify: $\frac{2}{x+1}-\frac{3}{x^{2}-1}+\frac{2}{x-1}$

Question 75

Combine and simplify: $\frac{2}{x-3}-\frac{x}{3-x}+\frac{3 x}{x+3}$

Question 76

Combine and simplify: $\frac{y^{2}+3}{y^{2}-1}-\frac{2 y+2}{y^{2}-1}$

Question 77

Combine and simplify: $\frac{p-k}{p+k}-\frac{4 p k}{k^{2}-p^{2}}$

Question 78

Combine and simplify: $\frac{2-x}{x^{3}+x^{2}-6 x}-\frac{1}{x+3}$

Question 79

Combine and simplify: $\frac{x}{x-1}+\frac{x+4}{x^{2}+3 x-4}$

Question 80

Combine and simplify: $\frac{3 m+1}{3 m-1}-\frac{9 m^{2}+3}{9 m^{2}-1}+\frac{3 m-1}{3 m+1}$