**Integers: Numbers on Both Sides of Zero**
**Key Definitions:**
**Important Rules:**
All negative numbers < 0 < all positive numbers
Floor −4 is lower than Floor −3, so −4 < −3 (bigger negative = smaller value)
(+n) + (−n) = 0 (inverses cancel out)
**Addition with Integers:**
Starting Floor + Movement = Target Floor
(+2) + (+3) = +5 (up 2, then up 3 = up 5)
(+2) + (−5) = −3 (up 2, then down 5 = down 3)
(−1) + (+4) = +3 (down 1, then up 4 = up 3)
**Comparing Integers:**
Use < (less than) or > (greater than) by thinking: which floor is lower?
−5 < −3 (Floor −5 is lower)
+2 > −4 (Floor +2 is higher)
**Don't Confuse:** −5 is NOT greater than −2. Although 5 > 2, we have −5 < −2 because Floor −5 is lower than Floor −2. Negative comparison reverses!
Q1. Which of these is a positive number?
Answer: A — A positive number has a + sign in front, so +5 is positive; −5 is negative and 0 is neither.
Q2. What is the inverse of −8?
Answer: B — The inverse of −8 is +8 because (−8) + (+8) = 0, they cancel each other out.
Q3. You are at Floor +3 and press −4 in the lift. Which floor do you reach?
Answer: B — (+3) + (−4) = −1, so you go down 1 floor from +3 and reach Floor −1.
Q4. Which symbol should go in the box: −5 ___ −2?
Answer: B — Floor −5 is lower than Floor −2, so −5 < −2; the bigger negative number is the smaller value.
Q5. Which of these numbers is the smallest?
Answer: C — Floor −3 is the lowest, so −3 is the smallest; all negative numbers are less than 0 or positive numbers.
Q6. Gurmit presses +2 by mistake, then presses −3 to fix it. What is his total movement? (Think: (+2) + (−3) = ?)
Answer: B — (+2) + (−3) = −1 means he moves down 1 floor overall (up 2, then down 3 = net down 1).
Q7. Is 0 a positive number, negative number, or neither?
Answer: C — Zero is the starting point between positive and negative, so it is neither positive nor negative.
Q8. If you start at Floor −2 and want to reach Floor +3, what movement do you need? (−2) + ___ = +3
Answer: C — From Floor −2 to Floor +3 requires moving up 5 floors, so (−2) + (+5) = +3.
Q9. In the Building of Fun, which statement is true?
Answer: C — Floor −1 (below ground) is physically lower than Floor +2 (above ground), so −1 < +2 is true.
Q10. What is the result of combining these button presses: (+1) + (+2) + (−2)?
Answer: A — (+1) + (+2) + (−2) = (+1) + 0 = +1 because (+2) and (−2) are inverses that cancel to zero.
What is a positive number?
A number with a + sign in front that represents a position above zero or going up.
What is a negative number?
A number with a − sign in front that represents a position below zero or going down.
What floor is the ground floor called?
Floor 0, because it is the starting or reference point with neither + nor − sign.
If you press +4 in the lift, where do you go?
You go up 4 floors from your starting position.
What is the inverse of +7?
The inverse of +7 is −7, because (+7) + (−7) = 0.
If you start at Floor +2 and press −5, which floor do you reach?
You reach Floor −3, because (+2) + (−5) = −3.
Is −4 greater than or less than −2?
−4 is less than −2 because Floor −4 is lower than Floor −2, so −4 < −2.
Compare: 0 and −5. Which is greater?
0 is greater than −5 because zero is higher than all negative numbers, so 0 > −5.
What does the expression (+3) + (−1) mean in the Building?
Start at Floor +3 and press the − button once, reaching Floor +2.
Can you write a + or − sign in front of 0?
No, zero is neither positive nor negative, so we never write +0 or −0.
What is the ground floor called in the Building of Fun, and why? [1 mark]
It is the reference or starting point from which all other floors are measured; remember that 0 is neither + nor −.
Write the inverse of each number: +6, −3, 0. Explain what inverse means using one example. [2 marks]
Inverse of +n is −n. Example: (+6) + (−6) = 0 shows they cancel and bring you back to zero or ground floor.
Imagine you are in a lift in the Building of Fun. You start at Floor +1 (Food Court) and press −2. Using the expression (+1) + (−2), explain which floor you reach and why. (Use the building example to show your answer.) [3 marks]
Starting Floor is +1. You press − 2 times (go down 2). So (+1) + (−2) = −1, meaning you reach Floor −1 (Toy Store). Explain: up 1, then down 2 = net down 1.
In the Building of Fun, there are floors +4, −3, +1, 0, and −1. (a) Arrange these floors from lowest to highest. (b) Which floor is the reference point? (c) Explain why we write −3 < −1 using floor positions. (d) If you start at Floor +4 and need to reach Floor −3, what total movement (as an expression) do you need? [5 marks]
Arrange from lowest to highest: −3, −1, 0, +1, +4. Reference = Floor 0. Lowest floor is lowest number. For (c): Floor −3 is physically lower than Floor −1. For (d): (+4) + (−7) = −3 (need to go down 7 floors total).
True or False? −5 is greater than −2. Explain your answer using the Building of Fun example. [2 marks]
False. Floor −5 is below Floor −2, so −5 is lower and smaller. Think: which floor is deeper/lower in the building?
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