Complex Fractions

Question 1

Simplify (1/x - 1/2)/(1/x + 1/2) to lowest terms.

Accepted Answer

(2 - x)/(2 + x)

Answer

(x - 2)/(x + 2)

Answer

(2 + x)/(2 - x)

Answer

(x + 2)/(x - 2)

Question 2

Simplify (9/x)/(18/x^2) to lowest terms.

Accepted Answer

x/2

Answer

9/x

Answer

162/x^3

Answer

2x

Question 3

Simplify (1/5 - 1/x)/(1/5 + 1/x) to lowest terms.

Accepted Answer

(x - 5)/(x + 5)

Answer

(5 - x)/(5 + x)

Answer

(x + 5)/(x - 5)

Answer

(5 + x)/(5 - x)

Question 4

For the complex fraction (1/x + 1/5)/(1/4 - 1/x), what is the most efficient first step?

Accepted Answer

multiply every term above and below the main bar by 20x

Answer

multiply only the terms above the main bar by 20x

Answer

cancel the 1/x that appears above and below the main bar

Answer

add 1/x to both sides

Question 5

Simplify (1/x + 1/6)/(3/x) to lowest terms.

Accepted Answer

(x + 6)/18

Answer

(x + 6)/(18x)

Answer

(x + 6)/3

Answer

18/(x + 6)

Question 6

Simplify (1/x - 1/5)/(1/x + 1/5) to lowest terms.

Accepted Answer

(5 - x)/(5 + x)

Answer

(x - 5)/(x + 5)

Answer

(5 + x)/(5 - x)

Answer

(x + 5)/(x - 5)

Question 7

Simplify (1/x + 1/4)/(7/x) to lowest terms.

Accepted Answer

(x + 4)/28

Answer

(x + 4)/(28x)

Answer

(x + 4)/7

Answer

28/(x + 4)

Question 8

Simplify (5/x)/(20/x^2) to lowest terms.

Accepted Answer

x/4

Answer

5/x

Answer

100/x^3

Answer

4x

Question 9

Simplify (1/6 - 1/x)/(1/6 + 1/x) to lowest terms.

Accepted Answer

(x - 6)/(x + 6)

Answer

(6 - x)/(6 + x)

Answer

(x + 6)/(x - 6)

Answer

(6 + x)/(6 - x)

Question 10

Simplify (1/7 - 1/x)/(1/7 + 1/x) to lowest terms.

Accepted Answer

(x - 7)/(x + 7)

Answer

(7 - x)/(7 + x)

Answer

(x + 7)/(x - 7)

Answer

(7 + x)/(7 - x)

Question 11

Simplify (1/x + 1/7)/(4/x) to lowest terms.

Accepted Answer

(x + 7)/28

Answer

(x + 7)/(28x)

Answer

(x + 7)/4

Answer

28/(x + 7)

Question 12

Simplify (1/x + 1/5)/(3/x) to lowest terms.

Accepted Answer

(x + 5)/15

Answer

(x + 5)/(15x)

Answer

(x + 5)/3

Answer

15/(x + 5)

Question 13

Simplify (1/x + 1/9)/(4/x) to lowest terms.

Accepted Answer

(x + 9)/36

Answer

(x + 9)/(36x)

Answer

(x + 9)/4

Answer

36/(x + 9)

Question 14

Simplify (1/2 - 1/x)/(1/2 + 1/x) to lowest terms.

Accepted Answer

(x - 2)/(x + 2)

Answer

(2 - x)/(2 + x)

Answer

(x + 2)/(x - 2)

Answer

(2 + x)/(2 - x)

Question 15

Simplify (4/(x^2 - 4))/(9/(x + 2)) to lowest terms.

Accepted Answer

4/(9(x - 2))

Answer

4/(x - 2)

Answer

4/(9(x + 2))

Answer

36/((x - 2)(x + 2))

Question 16

Simplify (6/x)/(4/x^2) to lowest terms.

Accepted Answer

3x/2

Answer

6/x

Answer

24/x^3

Answer

2x/3

Question 17

Simplify (6/x)/(12/x^2) to lowest terms.

Accepted Answer

x/2

Answer

6/x

Answer

72/x^3

Answer

2x

Question 18

Simplify (1/4 - 1/x)/(1/4 + 1/x) to lowest terms.

Accepted Answer

(x - 4)/(x + 4)

Answer

(4 - x)/(4 + x)

Answer

(x + 4)/(x - 4)

Answer

(4 + x)/(4 - x)

Question 19

For the complex fraction (1/x + 1/5)/(1/2 - 1/x), what is the most efficient first step?

Accepted Answer

multiply every term above and below the main bar by 10x

Answer

multiply only the terms above the main bar by 10x

Answer

cancel the 1/x that appears above and below the main bar

Answer

add 1/x to both sides

Question 20

Simplify (9/x)/(8/x^2) to lowest terms.

Accepted Answer

9x/8

Answer

9/x

Answer

72/x^3

Answer

8x/9

Question 21

For the complex fraction (1/x + 1/6)/(1/5 - 1/x), what is the most efficient first step?

Accepted Answer

multiply every term above and below the main bar by 30x

Answer

multiply only the terms above the main bar by 30x

Answer

cancel the 1/x that appears above and below the main bar

Answer

add 1/x to both sides

Question 22

Simplify (1/x - 1/3)/(1/x + 1/3) to lowest terms.

Accepted Answer

(3 - x)/(3 + x)

Answer

(x - 3)/(x + 3)

Answer

(3 + x)/(3 - x)

Answer

(x + 3)/(x - 3)

Question 23

Simplify (1/x - 1/4)/(1/x + 1/4) to lowest terms.

Accepted Answer

(4 - x)/(4 + x)

Answer

(x - 4)/(x + 4)

Answer

(4 + x)/(4 - x)

Answer

(x + 4)/(x - 4)

Question 24

Simplify (6/(x^2 - 1))/(4/(x + 1)) to lowest terms.

Accepted Answer

3/(2(x - 1))

Answer

6/(x - 1)

Answer

3/(2(x + 1))

Answer

24/((x - 1)(x + 1))

Question 25

Simplify (2/x)/(15/x^2) to lowest terms.

Accepted Answer

2x/15

Answer

2/x

Answer

30/x^3

Answer

15x/2

Question 26

Simplify (4/x)/(10/x^2) to lowest terms.

Accepted Answer

2x/5

Answer

4/x

Answer

40/x^3

Answer

5x/2

Question 27

Simplify (1/x + 1/4)/(3/x) to lowest terms.

Accepted Answer

(x + 4)/12

Answer

(x + 4)/(12x)

Answer

(x + 4)/3

Answer

12/(x + 4)

Question 28

Simplify (1/x + 1/3)/(2/x) to lowest terms.

Accepted Answer

(x + 3)/6

Answer

(x + 3)/(6x)

Answer

(x + 3)/2

Answer

6/(x + 3)

Question 29

Simplify (1/x + 1/6)/(5/x) to lowest terms.

Accepted Answer

(x + 6)/30

Answer

(x + 6)/(30x)

Answer

(x + 6)/5

Answer

30/(x + 6)

Question 30

Simplify (1/9 - 1/x)/(1/9 + 1/x) to lowest terms.

Accepted Answer

(x - 9)/(x + 9)

Answer

(9 - x)/(9 + x)

Answer

(x + 9)/(x - 9)

Answer

(9 + x)/(9 - x)

Question 31

Simplify (8/x)/(20/x^2) to lowest terms.

Accepted Answer

2x/5

Answer

8/x

Answer

160/x^3

Answer

5x/2

Question 32

For the complex fraction (1/x + 1/7)/(1/5 - 1/x), what is the most efficient first step?

Accepted Answer

multiply every term above and below the main bar by 35x

Answer

multiply only the terms above the main bar by 35x

Answer

cancel the 1/x that appears above and below the main bar

Answer

add 1/x to both sides

Question 33

Simplify (1/x + 1/5)/(5/x) to lowest terms.

Accepted Answer

(x + 5)/25

Answer

(x + 5)/(25x)

Answer

(x + 5)/5

Answer

25/(x + 5)

Question 34

Simplify (1/x + 1/6)/(7/x) to lowest terms.

Accepted Answer

(x + 6)/42

Answer

(x + 6)/(42x)

Answer

(x + 6)/7

Answer

42/(x + 6)

Question 35

Simplify (2/(x^2 - 16))/(6/(x + 4)) to lowest terms.

Accepted Answer

1/(3(x - 4))

Answer

2/(x - 4)

Answer

1/(3(x + 4))

Answer

12/((x - 4)(x + 4))

Question 36

Simplify (1/x + 1/4)/(5/x) to lowest terms.

Accepted Answer

(x + 4)/20

Answer

(x + 4)/(20x)

Answer

(x + 4)/5

Answer

20/(x + 4)

Question 37

Simplify (4/(x^2 - 25))/(8/(x + 5)) to lowest terms.

Accepted Answer

1/(2(x - 5))

Answer

4/(x - 5)

Answer

1/(2(x + 5))

Answer

32/((x - 5)(x + 5))

Question 38

Simplify (1/x + 1/7)/(6/x) to lowest terms.

Accepted Answer

(x + 7)/42

Answer

(x + 7)/(42x)

Answer

(x + 7)/6

Answer

42/(x + 7)

Question 39

Simplify (3/x)/(4/x^2) to lowest terms.

Accepted Answer

3x/4

Answer

3/x

Answer

12/x^3

Answer

4x/3

Question 40

Simplify (3/x)/(18/x^2) to lowest terms.

Accepted Answer

x/6

Answer

3/x

Answer

54/x^3

Answer

6x

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Complex Fractions

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Complex Fractions

Ways to Play

Device Games: Students play on their phones

Blast Go

Zombie Escape

Avalanche

Maze Blast

Cave Climb

Blast Out

Mystery Auction

Tour Guide

Food Truck Rush

Tug of War

Alien Blast

Glacier Rush

Board Games: Teacher-led, projected to the class

Like what you see?

More like this

Bug Blast

BlastRace

BlastQuiz

BlastBoard

Seek & Destroy

Mystery Blast

Checkers

Texas Hold 'Em

Da Bomb

Castle Siege

Hot Potato

Market Mayhem

King of the Hill

Bank Heist

Top Corner