Year 5 Maths: Understanding Integers

What Are Integers?

Today, we are going to learn about integers. An integer is a whole number. This means it can be positive, negative, or zero. Let’s break it down:

• Positive integers: These are numbers like 1, 2, 3, 4, and so on.
• Negative integers: These are numbers like -1, -2, -3, -4, and so on.
• Zero: Zero is also an integer, and it is neither positive nor negative.

So, the set of integers looks like this:

…, -3, -2, -1, 0, 1, 2, 3, …

Why Do We Use Integers?

Integers help us in everyday life. For example:

• Temperature: When it’s cold outside, the temperature can be a negative number (like -5 degrees).
• Money: If you owe someone money, you can think of that as a negative amount.

Key Rules About Integers

1. Adding Integers:
   • If you add two positive integers, you get a positive integer.
     • Example: 2 + 3 = 5
   • If you add two negative integers, you get a negative integer.
     • Example: -2 + (-3) = -5
   • If you add a positive integer and a negative integer, you need to take away from the positive.
     • Example: 3 + (-2) = 1 (because you take away 2 from 3)
2. Subtracting Integers:
   • Subtracting a positive integer is like adding a negative integer.
     • Example: 4 – 2 = 4 + (-2) = 2
   • Subtracting a negative integer means you add the positive.
     • Example: 5 – (-3) = 5 + 3 = 8
3. Multiplying Integers:
   • A positive times a positive is positive.
     • Example: 2 × 3 = 6
   • A negative times a negative is also positive.
     • Example: -2 × -3 = 6
   • A positive times a negative is negative.
     • Example: 2 × -3 = -6
4. Dividing Integers:
   • A positive divided by a positive is positive.
     • Example: 6 ÷ 2 = 3
   • A negative divided by a negative is positive.
     • Example: -6 ÷ -2 = 3
   • A positive divided by a negative is negative.
     • Example: 6 ÷ -2 = -3

Tips and Tricks

• Number Line: Use a number line to help you visualize where the integers are. It makes it easier to add and subtract.
• Think of zero: Remember that zero is like a balance point. It helps you understand where positive and negative numbers go.
• Practice, practice, practice: The more you work with integers, the easier they will become!

Questions

Easy Level Questions

1. What is -3 + 5?
2. What is 4 – 2?
3. Is 0 an integer?
4. What is -1 – 1?
5. What is 6 + (-2)?
6. What is -4 + 4?
7. What is 3 – (-3)?
8. What is 5 – 3?
9. What is -5 + 2?
10. What is 7 + (-3)?
11. What is -2 × 4?
12. What is 0 × 5?
13. What is 2 ÷ 2?
14. What is -3 ÷ -1?
15. What is 8 + (-5)?
16. What is -1 + (-1)?
17. What is 10 – 10?
18. What is 1 + (-1)?
19. What is -6 + 3?
20. What is 4 + 0?

Medium Level Questions

1. What is -2 + 7?
2. What is 9 – (-4)?
3. What is 5 + (-8)?
4. What is -3 – 5?
5. What is 6 – 9?
6. What is -2 × -6?
7. What is -8 ÷ 4?
8. What is 10 – (-5)?
9. What is -1 + 6 + (-3)?
10. What is 15 + (-10) + (-5)?
11. What is -4 × 2?
12. What is 12 ÷ -3?
13. What is -6 + 9 – 4?
14. What is 3 × (-4)?
15. What is -5 + (-2) + 1?
16. What is -10 ÷ -2?
17. What is 4 – 6 + 10?
18. What is 5 + (-2) + (-3)?
19. What is 14 – 2 × 3?
20. What is 9 ÷ -3 + 5?

Hard Level Questions

1. What is (-7) + (-8) + 5?
2. What is 12 – (3 + 4)?
3. What is -3 × (2 – 5)?
4. What is 5 – 2 × (-3)?
5. What is 8 + (-2) + (-6)?
6. What is (-3) × (-3) + 5?
7. What is -10 + 15 – 20?
8. What is -2 × (-2) – 4?
9. What is 20 ÷ (-4) + 7?
10. What is (6 – 9) × (-2)?
11. What is 30 – (5 × 6) + (-2)?
12. What is (-5) + 3 × 4 – 10?
13. What is (-8) – (-4) + 7?
14. What is 1 – (-1) × 10?
15. What is (-5) × 2 + 8?
16. What is 15 ÷ (-3) + 4?
17. What is 25 – (9 + 7) ÷ 4?
18. What is (-4) + (2 × (-3)) + 8?
19. What is -9 + (-4) × 3 + 5?
20. What is 18 ÷ (-2) + (-6) × 3?

Answers

Easy Level Answers

1. 2
2. 2
3. Yes
4. -2
5. 4
6. 0
7. 6
8. 2
9. -3
10. 4
11. -8
12. 0
13. 1
14. 6
15. 3
16. -2
17. 0
18. 0
19. -3
20. 4

Medium Level Answers

1. 5
2. 13
3. -3
4. -8
5. -3
6. 12
7. -2
8. 15
9. 2
10. 0
11. -8
12. -4
13. -1
14. -12
15. -6
16. 5
17. 10
18. 0
19. 8
20. 0

Hard Level Answers

1. -10
2. 5
3. 9
4. 11
5. 0
6. 14
7. -15
8. 0
9. -2
10. 6
11. 0
12. -3
13. 3
14. 11
15. -10
16. -5
17. 3
18. 4
19. -10
20. -12

I hope this helps you understand integers better! Remember to practice and use your number line whenever you need. Happy learning!