Let's solve each problem step by step, following the
order of operations (PEMDAS/BODMAS): Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). We must be especially careful with
signs and
negative numbers.
---
1.) 144 ÷ (-9) - 4 + 20
- First: Division → 144 ÷ (-9) =
-16
- Then: -16 - 4 =
-20
- Then: -20 + 20 =
0
✔ Answer: 0
---
2.) -11 - (-23) + (-6) - (+2) - 5 + 1
- Simplify signs:
- -(-23) =
+23
- +(-6) =
-6
- -(+2) =
-2
So expression becomes:
-11 + 23 - 6 - 2 - 5 + 1
Now compute left to right:
- -11 + 23 =
12
- 12 - 6 =
6
- 6 - 2 =
4
- 4 - 5 =
-1
- -1 + 1 =
0
✔ Answer: 0
---
3.) 4 × 5 ÷ (-10) + 1
- Left to right for × and ÷:
- 4 × 5 =
20
- 20 ÷ (-10) =
-2
- Then: -2 + 1 =
-1
✔ Answer: -1
---
4.) 15 - 37 + 2 × (-4 + 10) - 1
- Parentheses first: (-4 + 10) =
6
- Then multiplication: 2 × 6 =
12
- Now expression: 15 - 37 + 12 - 1
Left to right:
- 15 - 37 =
-22
- -22 + 12 =
-10
- -10 - 1 =
-11
✔ Answer: -11
---
5.) -18 × 6 + (-7) + (-5)³
- Exponent first: (-5)³ =
-125 (since odd power preserves sign)
- Multiplication: -18 × 6 =
-108
- Now: -108 + (-7) + (-125)
Which is: -108 - 7 - 125 =
-240
✔ Answer: -240
---
6.) 6 - (-13 + 20) - 3 × (-5)
- Parentheses: (-13 + 20) =
7
- Multiplication: 3 × (-5) =
-15
- Now: 6 - 7 - (-15)
Simplify: 6 - 7 =
-1, then -1 - (-15) = -1 + 15 =
14
✔ Answer: 14
---
7.) -78 ÷ [ -98 - (-132) - 21 ] + 14
- Inside brackets: -98 - (-132) - 21
- -(-132) = +132
- So: -98 + 132 - 21
- -98 + 132 =
34
- 34 - 21 =
13
Now: -78 ÷ 13 + 14
- -78 ÷ 13 =
-6
- -6 + 14 =
8
✔ Answer: 8
---
8.) [12 - (1 - 7) + 1] × [42 - 53 - (-6)]
First bracket: [12 - (1 - 7) + 1]
- (1 - 7) =
-6
- So: 12 - (-6) + 1 = 12 + 6 + 1 =
19
Second bracket: [42 - 53 - (-6)]
- -(-6) = +6
- So: 42 - 53 + 6 = (42 + 6) - 53 = 48 - 53 =
-5
Now multiply: 19 × (-5) =
-95
✔ Answer: -95
---
9.) [7 - (1 - 32) + 18] ÷ (1 - 16 + 13) × [-48 - (-53) + 2]
Break into parts:
Part A: [7 - (1 - 32) + 18]
- (1 - 32) =
-31
- 7 - (-31) + 18 = 7 + 31 + 18 =
56
Part B: (1 - 16 + 13)
- 1 - 16 = -15; -15 + 13 =
-2
Part C: [-48 - (-53) + 2]
- -(-53) = +53
- -48 + 53 + 2 = 5 + 2 =
7
Now entire expression:
56 ÷ (-2) × 7
Left to right:
- 56 ÷ (-2) =
-28
- -28 × 7 =
-196
✔ Answer: -196
---
##
✔ Final Answers:
1.
0
2.
0
3.
-1
4.
-11
5.
-240
6.
14
7.
8
8.
-95
9.
-196
All are integers as required!
Parent Tip: Review the logic above to help your child master the concept of operations of integers worksheet.
