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