Here's the step-by-step solution to each problem, 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
- Now: -16 - 4 + 20
→ -16 - 4 =
-20
→ -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
- 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 multiplication/division:
4 × 5 =
20
20 ÷ (-10) =
-2
- Then: -2 + 1 =
-1
✔ Answer: -1
---
4.) 15 - 37 + 2 × (-4 + 10) - 1
- Parentheses first:
(-4 + 10) =
6
- Now: 15 - 37 + 2 × 6 - 1
- Multiplication:
2 × 6 =
12
- Now: 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 = -5 × -5 × -5 =
-125
- Multiplication:
-18 × 6 =
-108
- Now: -108 + (-7) + (-125)
→ -108 - 7 - 125 =
-240
✔ Answer: -240
---
6.) 6 - (-13 + 20) - 3 × (-5)
- Parentheses:
(-13 + 20) =
7
- Multiplication:
3 × (-5) =
-15
- Now: 6 - 7 - (-15)
→ 6 - 7 =
-1
→ -1 - (-15) = -1 + 15 =
14
✔ Answer: 14
---
7.) -78 ÷ [ -98 - (-132) - 21 ] + 14
- Inside brackets:
-98 - (-132) = -98 + 132 =
34
34 - 21 =
13
- Now: -78 ÷ 13 + 14
→ -78 ÷ 13 =
-6
- Then: -6 + 14 =
8
✔ Answer: 8
---
8.) [12 - (1 - 7) + 1] × [42 - 53 - (-6)]
- First bracket:
(1 - 7) =
-6
12 - (-6) = 12 + 6 =
18
18 + 1 =
19
- Second bracket:
42 - 53 =
-11
-11 - (-6) = -11 + 6 =
-5
- Now: 19 × (-5) =
-95
✔ Answer: -95
---
9.) [7 - (1 - 32) + 18] ÷ (1 - 16 + 13) × [-48 - (-53) + 2]
- First group: [7 - (1 - 32) + 18]
(1 - 32) =
-31
7 - (-31) = 7 + 31 =
38
38 + 18 =
56
- Second group: (1 - 16 + 13)
1 - 16 =
-15
-15 + 13 =
-2
- Third group: [-48 - (-53) + 2]
-48 - (-53) = -48 + 53 =
5
5 + 2 =
7
- Now: 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 solutions are integers as required. Be sure to double-check signs — they’re the most common source of error!
Parent Tip: Review the logic above to help your child master the concept of all operations with integers worksheet.
