Multiplication and Division of Fractions Exercises – Set 1

Week 4

1. 3/4 x 1/2

2. 2/7 x 7/10

3. 4 1/5 x 2/3

4. 8 x 3/4

5. 1 2/3 x 2 3/4 x 11/12

6. 2/5 ÷ 4/5

7. 3/4 ÷ 8

8. 9 ÷ 3/4

9. 5 1/6 ÷ 3/31

10. 2 5/6 ÷ 4 3/5

Answers:

1. 3/8 3/4 x 1/2 = 3/8

2. 1/5

Solution

2/7 x 7/10 = 14/70 = 1/5

3. 2 4/5

Solution

4 1/5 x 2/3
= 21/5 x 2/3 = 42/15
= 2 12/15 = 2 4/5

4. 6

Solution

8 x 3/4 = 8/1 x 3/4
= 24/4 = 6

5. 4 29/144

Solution
1 2/3 x 2 3/4 x 11/12
= 5/3 x 11/4 x 11/12
= 605/144
= 4 29/144

6. 1/2

Solution

2/5 x 5/4 = 10/20 = 1/2

7. 3/32

Solution
3/4 ÷ 8
= 3/4 x 1/8
= 3/32

8. 12

Solution

9 ÷ 3/4 = 9/1 x 4/3 = 36/3 = 12

9. 5 1/6 ÷ 31/3
= 31/6 x 3/31
= 961/18 = 53 7/18

10. 8/35

2 5/6 ÷ 4 3/5 = 17/6 ÷ 23/5
= 17/6 x 5/23 = 85/138

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LCM and GCD Exercises Set 1

After learning about LCM and GCD in our PCSR Review Guide 1, let’s practice what we have learned by answering the exercises below.

1.) What is the LCM of 6 and 8?

2.) What is the LCM of 3, 4, and 9?

3.) Consider the following sequences:
Sequence 1: 4, 8, 12, 16, 20, 24, 28, …
Sequence 2: 5, 10, 15, 20, 25, 30, …
As we can see, 20 is common to both sequences. What is the 10th common number?

4.) Gina goes to BODY SLIM gym every 3 days, while Sam goes to the same gym every 4 days. If they were in the same gym on a February 12, what’s the nearest date that they will be both in the gym?

5.) In a decoration LED light, the green lights blink every 400 milliseconds, the blue light every 500 milliseconds, and the red light every 750 milliseconds. If the three lights all blinked at the same time, in how many milliseconds will they again blink at the same time?

6.) What is the LCD of 1/3, 1/4, and 1/6?

7.) What is the GCD of 28 and 35?

8.) What is the GCD of 39, 65, and 91?

9.) A rectangular paper with dimensions 12 inches by 18 inches is to be cut into largest possible squares of equal sizes. If no paper is to be wasted, what should be the dimensions of the squares?

Q10.) A rectangular prism piece of wood with dimensions 16 inches by 20 inches by 32 is to be cut into cubes of the same size.

A. If we want to minimize the wasted wood while cutting, what should be the dimensions of the cubes?

B. How many cubes can we make given the above conditions?

Solutions and Answers

1.) 24

2.) 36

3.)  200

4.) LCM of 3 and 4 is 12. Twelve days after February 12 is February 24.

5.) 6000 milliseconds

6.) 12

7.) 7

8.) 13

9.) Side of the square should be GCD of 12 and 18 which is 6 inches.

10.) A. Side of the cube should be GCD of 16, 20, and 32 which is equal to 4 inches.

B. 16/4 × 20/4× 32/4 = 4 × 5 × 8 = 160 cubes

 

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Solving Equations Exercises Set 1A Answers

Below are the answers to Solving Equations Exercises Set 1A.

Part I

1. x + 2 = 10
x = 10 - 2
x = 8

2. x - 7 = -14
x = -14 + 7
x = -7

3. 4x = 20
x = \frac{20}{4}
x = 5

4. -3x = 18
x = \frac{18}{-3}
x = -6

5. \frac {x}{4} = 20
x = 20(4)
x = 80

6. \frac {x}{9} = -10
x = -10(9)
x = -90

7. 2x + 1 = 15
2x = 15 - 1
2x = 14
x = \frac {14}{2}
x = 7

8. 4x - 7 = 13
4x = 13 + 7
4x = 20
x = \frac {20}{4}
x = 5

9. -6x + 2 = -14
-6x = -14 - 2
-6x = -16
x = \frac {-16}{-6}
x = \frac {8}{3} or 2 \frac {2}{3}

10. 3x - 1 = 8
3x = 8 + 1
3x = 9
x = \frac {9}{3}
x = 3

Part II

1. 9 - x = 17
-x = 17 - 9
-x = 12
x = \frac {12}{(-1)}
x = -12

2. 4x - 7 = -15
4x = -15 + 7
4x = -8
x = \frac {-8}{4}
x = -2

3. 7x + 36 = 4x
7x - 4x = -36
3x = -36
x = \frac {-36}{3}
x = -12

4. -2x - 11 = -x
-2x + x = 11
-x = 11
x = \frac {11}{-1}
x = -11

5. 7x = 5x - 6
7x - 5x = -6
2x = -6
x = \frac {-6}{2}
x = -3

6. 2x - 5 = x + 4
2x -x = 4 + 5
x = 9

7. 9x + 6 = 7x - 8
9x - 7x = -8 - 6
2x = -14
x = \frac {-14}{2}
x = -7

8. 9 - x = 2 + 6x
-x - 6x = 2 - 9
-7x = -7
x = \frac {-7}{-7}
x = 1

9. \frac {x}{2} = x + 7
x = 2(x + 7)
x = 2x + 14
x - 2x = 14
-x = 14
x = \frac {14}{-1}
x = -14

10. -\frac {1}{4}x = 3x - 12
-x = 4(3x - 12)
-x = 12x - 48
-x - 12x = - 48
-13x = -48
x = \frac {-48}{-13}
x = \frac {48}{13} or 3 \frac {9}{13}

Part III

1. 2(x - 5) = -8
2x - 10 = -8
2x = -8 + 10
2x = 2
x = 1

2. 6(2x - 1) = -8 + x
12x - 6 = -8 + x
12x - x = -8 + 6
11x = -2
x = \frac {-2}{11}

3. 3(4 - 3x) = 3x
12 - 9x = 3x
-9x - 3x = -12
-12x = -12
x = 1

4. 5(x- 7) - 2 = x - 1
5x - 35 - 2 = x - 1
5x - 37 = x - 1
5x - x = -1 + 37
4x = 36
x = \frac {36}{4}
x = 9

5. 4(x - 1) = 3(x + 1)
4x - 4 = 3x + 3
4x - 3x = 3 + 4
x = 7

6. 7(4 - 2x) = x - 2
28 - 14x = x - 2
-14x - x = -2 - 28
-15x = -30
x = \frac {-30}{-15}
x = 2

7. 4 - 6(x - 7) = -x - 4
4 - 6x + 42 = -x - 4
-6x + 48 = -x - 4
-6x + x = -4 - 48
-5x = -52
x = \frac {-52}{-5}
x = \frac {52}{5} or 10 \frac {2}{5}

8. \frac {-x}{4} = x + 10
-x = 4(x + 10)
-x = 4x + 40
-x - 4x = 40
-5x = 40
x = \frac {40}{-5}
x = -8

9. 3x + \frac {1}{2} = 12
To eliminate the fractions, we multiply both sides by 2.

2(3x + \frac {1}{2}) = 2(12)
6x + 1 = 24
6x = 24 - 1
6x = 23
x = \frac {23}{6} or 3 \frac {5}{23}

10. \frac {3x}{5} = 4x - 8
3x = 5(4x - 8)
3x = 20x - 40
3x - 20x = -40
-17x = -40
x = \frac {-40}{-17}
x = \frac {40}{17} or x = 2 \frac {6}{17}

We will have more exercises soon.

PEMDAS Exercises Set 1 Answers

Below are the answers to PEMDAS Exercises Set 1.

Part I

1. 5 + 3 - 2
= 8 - 2
= 6

2. 9 - 6 + 4
= 3 + 4
= 7

Note: Be careful! A lot of people make mistakes in number 2. If no other operation is between addition and subtraction, you operate from left to right. Here, we must subtract first before we add.

3. 7 + 4 \times 3
= 7 + 12
= 19

4. 6 \times (-2) + 3
= -12 + 3
= -9

5. 2 \times (-9 + 4)
= 2 \times (-5)
= -10

6. 60 \div (-6 + 2)
= 60 \div (-4)
= -15

7. (-3 - 11) \times (-7)
= (-14) \times (-7)
= 98

8. 12 \div 3 \times 5
= 4 \times 5
= 20

Note: Be careful! Just like in number 2, if no other operation is between multiplication and division, you operate from left to right. Here, we must divide first before we multiply.

9. 4 \times (-1 - 6)
= 4 \times (-7)
= -28

10. -5 + (13 - 7) \div 3
= -5 + (6) \div 3
= -5 + 2
= -3

Part II
1. 4 \times (-3 - 5)
= 4 \times (-8)
= -32

2. -2 \times (3 + 6)
= -2 \times (9)
= -18

3. (9 - 13) \div (-1)
= (-4) \div (-1)
= 4

4. (4 + 6)^2 - 7
= (10)^2 - 7
= (100) - 7
= 93

5. (-4)^2 \times (-2)^3
= (16) \times (-8)
= -128

6. -3 - 7 \times 2
= -3 - 14
= -17

7. = 3 - (-2) + 8
= 3 + 2 + 8
= 13

8. -12 - 8 \div 4
= -12 - 2
= -14

9. 9 - (-4^2) \times (-2)
= 9 - (-16) \times (-2)
= 9 - 32
= -23

Note the difference: $latex -4^2 = -16$ and (-4)^2 = 16.

10. 10 \div (-2) - (-3 \times 4)
= 10 \div (-2) - (-3 \times 4)
= (-5) - (-12)
= -5 + 12
= 7

Part III
1. 3 - (-2) \times 5
= 3 - (-10)
= 3 + 10
= 13

2. -4 \times 3 + 6 \times 2
= -12 + 12
= 0

3. 16 \div (-2) + 12 \div 4
= -8 + 3
= -5

4. 36 \div (-13 + 4)
= 36 \div (-9)
= -4

5. 18 \div (-3)^2 + (-4)
= 18 \div (9) + (-4)
= 2 + (-4)
= -2

6. 4 \times (-2) + (-3^2)
= 4 \times (-2) + (-9)
(-8) + (-9)
= -17

Note: Be careful! Please note that -3^2 = -9 and  (-3)^2 = 9.

7. 3 \times [-4 - (12 - 5)]
= 3 \times [-4 - (7)]
= 3 \times [-11]
= -33

8. (-3)^2 + 2^3 \div (-4)
= 9 + 8 \div (-4)
= 9 + (-2)
= 7

9. 9 - (-4^2) \times (-2)
= 9 - 16 \times (-2)
= 9 - (32)
= -23

Note: Again, -4^2) = -16, not 16.

10. -2 \times (-3 \times 2)^2 - (-2)^2
= -2 \times (-6)^2 - (4)
= -2 \times (36) - (4)
= -72 - (4)
= -76

Division of Integers Exercises Set 1 Answers

Below are the answers to Division of Integers Exercises (Set 1).
Part I

1. -4

2. -4

3. 7

4. -5

5. 0

6. 18

7. -5

8. -2

9. 2

10. 6

Part II

1. -2

2. -5

3. 7

4. -7

5. 0

6. 6

7. -9

8. -5

9. 1

10. -9

Part III

1. \frac {1}{2} \div (-\frac {1}{4}) =  \frac {1}{2} \times (-\frac {4}{1}) = \frac {4}{2} = -2

2. -\frac {2}{5} \div (-\frac {3}{4}) =  -\frac {2}{5} \times (-\frac {4}{3}) =  \frac {8}{15}

3. -\frac {3}{4} \div \frac {3}{8} =  -\frac {3}{4} \times \frac {8}{3} = (-\frac {24}{12}) =  -2

4. \frac {4}{5} \div (-\frac {1}{5}) = \frac {4}{5} \times (-\frac {5}{1}) = -\frac {20}{5} = -4

5. -\frac {5}{7} \div \frac {1}{2} = -\frac {5}{7} \times \frac {2}{1} = -\frac {10}{7} = -1 \frac {3}{7}

6. -2

7. 3

8. -5

9. -4

10. 0

Now, that you have compelted the four fundamental operations, you might want to learn about the PEMDAS Rules and answer PEMDAS exercises.

Multiplication of Integers Exercises Set 1 Answers

Below are the answers to Multiplication of Integers Exercises (Set 1).

Part I

1. -6

2. 28

3. -27

4. 49

5. -33

6. -48

7. 18

8. 0

9. -15

10. 39

Part II

1. -24

2. -32

3. 36

4. 60

5. 0

6. 12

7. -120

8. -21

9. -88

10. 42

Part III

1. -\frac {1}{6}

2. \frac {1}{8}.

3. -\frac {1}{8}

4. \frac {1}{14}

5. -\frac {4}{11}

6. -1.5

7. -0.08

8. 0.3

9. 0.24

10. 0

Subtraction of Integers Exercises Set 1 Answers

Below are the answers to Subtraction of Integers Exercises (Set 1).

Part I

1.) 8 – (-7) = 8 + (7) = 15

2.) -4 – (-10) = -4 + (10) = 6

3. -6 – 8 = -6 + (-8) = -14

4. 0 – (-5) = 0 + (5) = 5

5. -17 – (-13) = -17 + (13) = -4

6. 0 – 18 = 0 + (-18) =-18

7. 12 – 19 = 12 + (-19) = -7

8. -11 – 18 = -11 + (-18) = -29

9. 21 – (-22) = 21 + (22) = 43

10. -14 – (-14) = -14 + (14) = 0

Part II

1. 31 – (-14) = 31 + (14) = 45

2. -17 – (-11) = -17 + (11) =-6

3. -19 – 12 = -19 + (-12) = -31

4. 0 – (-17) = 0 + (17) = 17

5. -34 – (-21) = -34 + (21) = -13

6. 0 + (-47) = -47

7. 36 – 42 = 36 + (-42) = -6

8. -25 – 35 = -25 + (-35) = -60

9. 28 – (-30) = 28 + (30) = 58

10. -45 – (-45) = -45 + (45) = 0

Part III

1. \frac {1}{7} - (-\frac {3}{7}) = \frac {1}{7} + (\frac {3}{7}) = \frac {4}{7}

2. -\frac {3}{5} - (-\frac {4}{5}) = -\frac {3}{5} + (\frac {4}{5})= \frac {1}{5}

3. -\frac {3}{4} - \frac {1}{4} = -\frac {3}{4} +(-\frac {1}{4}) = -\frac {4}{4} = -1

4. \frac {7}{11} - \frac {9}{11} = \frac {7}{11} + (-\frac {9}{11}) = -\frac {2}{11}

5. -\frac {5}{12} - (-\frac {5}{12}) = -\frac {5}{12} + (\frac {5}{12}) = 0

6. 0.4 – (-0.3) = 0.4 + (0.3) = 0.7

7. -0.8 – (-0.7) = -0.8 + (0.7) = -0.1

8. -1.2 – 0.4 = -1.2 + (-0.4) = -1.6

9. 0.3 – 0.9 = 0.3 + (-0.9) = -0.6

10. -0.6 – (-0.6) = -0.6 + (0.6) = 0

Addition of Integers Exercises Set 1 Answers

Below are the answers to Addition of Integers Exercises (Set 1).

1. 6
2. -17
3. -13
4. -4
5. 0
6. -25
7. 23
8. -26
9. 0
10. 34

Part II
1. 10
2. -6
3. 8
4. 0
5. -9
6. -3
7. -6
8. 11
9. 0
10. 11

Part III
1. -2/2 or -1
2. -1/4
3. 0
4. 1/4
5. -7/11
6. 0.4
7. 3.6
8. -1.5
9. 1.5
10. -1.45

You might also want to answer the exercises on subtraction of integers.

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