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

This is the full solutions for the problems and exercises about operations on integers, order of operations, and PEMDAS rules.

Practice Exercises 1

a.) 12 + (-4) = 8
b.) (-9) + 3 = – 6
c.) (-7) + (- 5) = -12
d.) 8 + 3 + (-11) = (8+3) + (-11) = (11) + (-11) = 0
e.) 6 + (-10) + (-2) = 6 + (-10 + -2) = 6 + (-12) = -6

Practice Exercises 2

a.) 3 – 5 = (3) + (-5) = -2
b.) -9 – 4 = (-9) + (-4) = -13
c.) (-7) – (- 8) = (-7) + (8) = 1
d.) – 2 – 6 = (-2) + (-6) = -8
e.) 1 – (-10) = (1) + (10) = 11

Practice Exercises 3

a.) 4 × (- 5) = -20
b.) (-2) × (- 4) = 8
c.) 6 × (- 3) = -18
d.) 8 × 2 × (-1) = -16
e.) (-3) × (2) × (-7) = 42

Practice Exercises 4
a.)-20 ÷ 4 = -5
b.) 18 ÷ (- 6) = -3
c.) (-16) ÷ (- 2) = 8
d.) 0 ÷ 8 = 0
e.) 9 ÷ 3 = 3

1.) 2 + 3 × 5

2 + 3 × 5
= 2 + 15
= 17

2.) (2 + 3) × 5

(2 + 3) × 5 = (5) × 5
= 25

3.) 3 × (-3) + 4 × (-2)

= 3× (-3) + 4× (-2)
= (-9) + (-8)
= -17

4.) 3(5^2 – 8)

3(5 × 5 – 8)
= 3(25 – 8)
= 3(17)
= 51

5.)  2(5 – 8)^2
= 2(-3)^2
= 2(-3 × -3)
= 2(9)
= 18

6.) 16 + (-4) + 12 + (-8 x 3)

= 16 + (-4) + 12 + (-24)
= (16 + 12) + (-4 + -24)
= (28) + (-28)
= 0

7.) (3^2 + 2^2)^2 = ?

= (3 × 3 +2× 2)^2
= (9 + 4)^2
= (13)^2
= 13 × 13
= 169

8.) 6 + 3 × 2 – 5 = ?

= 6 + (3 × 2) – 5
= 6 + 6 – 5
= 12 – 5
= 7

9.) 8 – 12(3 – 4) + (-5 × 2)

= 8 – 12(3 – 4) + (-5 × 2)
= 8 – 12(-1) + (-10)
= 8 – (-12) + (-10)
= 20 + (-10)
= 10

10.) 7 + 3 × (-5) – 9 / 3 = ?

= 7 + 3 × (-5) – 9/3
= 7 + (-15) – 3
= 7 + (-18)
= -11

PCSR REVIEW SERIES WEEK 5: Operations on Integers and PEMDAS

Below are the articles and videos that you should read and watch about operations on integers, order of operations, and PEMDAS. Exercises and problems will be posted soon.

PART 1: OPERATIONS ON INTEGERS

Articles

Videos

PART 2: PEMDAS

Articles

Videos

More video

Introduction to PEMDAS

MDAS Quiz with Solution

The order of operations namely multiplication, division, addition or subtraction or more popularly known as MDAS or PEMDAS is one of the most basic concepts in mathematics and yet many people are totally confused about it. Here is a 15-item quiz with solution to further your understanding about MDAS. Note that the rules are

1.) perform the operation inside the parenthesis
2.) perform the operation with exponent
3.) perform multiplication and division first before performing addition and subtraction
4.) if multiplication and division are adjacent operations, perform from left to right
5.) if addition and subtraction are adjacent operations, perform from left to right

Take note of rule 2 and 3 because this is the most common misconceptions of many. Many believes that since in MD, multiplication should be done first since M is before D. » Read more

PEMDAS Rules Practice 1 Solutions

Below are the solutions and answers to the problems in PEMDAS Rules Practice 1. Notice that I have color coded the solution to guide you which operation results to which answer. I have also varied the notations like / and ÷ to familiarize you with both of them. In addition, I have also included operations on fractions with expressions in the numerator and the denominator. In a fraction whose numerator and/or denominator contains one or more operations , you have to simplify first both the numerator and the denominator before dividing. The methods in calculating fractions are shown in numbers 7, 9 and 10.

PEMDAS Rules and Operations on Real Numbers

Now that you have already learned the four fundamental operations on real numbersaddition, subtraction, multiplication, division – it is time to combine these operations into a single problem. In the Philippine Civil Service Examination, most of the problems on operations on real numbers have at least two or more operations involved.  If you can recall, we call these operations MDAS in the elementary grades and later and PE making it PEMDAS. PEMDAS is the acronym for Parenthesis, Exponent, Multiplication, Division, Addition and Subtraction. This is basically the order of operations when you calculate an arithmetic problem involving two or more operations.

PEMDAS RULES

Calculate in the following order.

1. the expressions inside the Parentheses.
2. the expression with Exponents.
3. If no operation separates Multiplication and Division, perform from left hand side to right whichever comes first.
4. If no operation separates Addition and Subtraction, perform from left hand side to right whichever comes first.  » Read more