## 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

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.

## Solving Equations Exercises – Set 1A

Below are exercises on solving equations.

Part I

1. $x + 2 = 10$

2. $x - 7 = -14$

3. $4x = 20$

4. $-3x = 18$

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

6. $\frac {x}{9} = -10$

7. $2x + 1 = 15$

8. $4x - 7 = 13$

9. $-6x + 2 = -14$

10. $3x - 1 = 8$

Part II

1. $9 - x = 17$

2. $4x - 7 = -15$

3. $7x + 36 = 4x$

4. $-2x - 11 = -x$

5. $7x = 5x - 6$

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

7. $9x + 6 = 7x - 8$

8. $9 - x = 2 + 6x$

9. $\frac {x}{2} = x + 7$

10. $-\frac {1}{4}x = 3x - 12$

Part III

1. $2(x - 5) = -8$

2. $6(2x - 1) = -8 + x$

3. $3(4 - 3x) = 3x$

4. $5(x- 7) - 2 = x - 1$

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

6. $7(4 - 2x) = x - 2$

7. $4 - 6(x - 7) = -x - 4$

8. $-\frac {x}{4} = x + 10$

9. $3x + \frac {1}{2} = 12$

10. $\frac {3x}{5} = 4x - 8$

## PEMDAS Exercises – Set 1

Below are exercises on division of signed numbers

Part I

1. $5 + 3 - 2$

2. $9 - 6 + 4$

3. $7 + 4 \times 3$

4. $6 \times (-2) + 3$

5. $2 \times (-9 + 4)$

6. $60 \div (-6 + 2)$

7. $(-3 - 11) \times (-7)$

8. $12 \div 3 \times 5$

9. $4 \times (-1 - 6)$

10. $-5 + (13 - 7) \div 3$

Part II

1. $4 \times (-3 - 5)$

2. $-2 \times (3 + 6)$

3. $(9 - 13) \div (-1)$

4. $(4 + 6)^2 - 7$

5. $(-4)^2 \times (-2)^3$

6. $-3 - 7 \times 2$

7. $3 - (-2) + 8$

8. –$12 - 8 \div 4$

9. $9 - (-4) \times (-4)$

10. $10 \div (-2) - (-3 \times 4)$

Part III

1. $3 - (-2) \times 5$

2. $-4 \times 3 + 6 \times 2$

3. $16 \div (-2) + 12 \div 4$

4. $36 \div (-13 + 4)$

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

6. $4 \times (-2) + (-3^2)$

7. $3 \times [-4 - (12 - 5)]$

8. $(-3)^2 + 2^3 \div (-4)$

9. $9 - (-4^2) \times (-2)$

10. $-2 \times (-3 \times 2)^2 - (-2)^2$

The solution can be found here.

## Division of Integers Exercises – Set 1

Below are exercises on division of signed numbers. Part I and II are exercises for divison of integers, while part III is an extension to fractions and decimals.

Part I

1.  $12 \div (-3)$

2. $-16 \div 4$

3. $-14 \div (-2)$

4. $15 \div (-3)$

5. $0 \div (-5)$

6. $-18 \div (-1)$

7. $-25 \div 5$

8. $6 \div (-3)$

9. $-8 \div (-4)$

10. $12 \div 2$

Part II

1.  $-34 \div 17$

2.  $45 \div -9$

3. $-56 \div (-8)$

4. $-63 \div 9$

5. $0 \div (-100)$

6. $-54 \div (-9)$

7. $72 \div (-8)$

8. $-50 \div 10$

9. $-17 \div (-17)$

10. $36 \div (-4)$

Part III

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

2. $-\frac {2}{5} \div(- \frac {3}{4})$

3. $-\frac {3}{4} \div \frac {3}{8}$

4. $\frac {4}{5} \div (-\frac {1}{5})$

5. $-\frac {5}{7} \div \frac {1}{2}$

6. $0.4 \div (-0.2)$

7. $-0.9 \div (-0.3)$

8. $-4.5 \div 0.9$

9. $-0.8 \div 0.2$

10. $0 \div 0.7$