๐ KEY TO ENJOY LEARNING MATHS
Class 6 Ganita Prakash · Chapter 10
Class 6 Ganita Prakash · Chapter 10
The Other Side of Zero
Page-wise textbook solutions (pages 242–271) · Every step · Figures · Common mistakes · Tips
p.242p.243p.244p.245p.246p.247p.248p.249p.250p.251p.252p.253p.254p.255p.256p.257p.258p.259p.260p.261p.262p.263p.264p.265p.266p.268
✔ Understood 0/62
๐️ Key ideas of this chapter
- Integers: … −3, −2, −1, 0, 1, 2, 3 … Zero is neither positive nor negative.
- Starting position + movement = target; target − start = movement.
- Inverse: a number + its inverse = 0 (5 and −5).
- Subtracting a number = adding its inverse: 4 − (−6) = 4 + 6 = 10.
- On the number line smaller numbers are on the left: −5 < −3 < 0 < 2.
- Tokens: a + and a − make a zero pair.
- Brahmagupta (628 CE) gave the first full rules for positive, negative numbers and zero.
๐ Textbook Page 242
๐ Page 242Less than zero?
Can there be a number less than 0? Can you think of ways to have less than 0 of something?
1Temperature below freezing: −5°C.
2Floors below the ground floor (basements).
3Money owed: a balance of −₹50 means you owe ₹50.
4Depth below sea level.
✅ Answer: Yes — numbers less than 0 are called negative numbers.
๐ Textbook Page 243
๐ Page 243Lift buttons
What do you press to go four floors up? Three floors down?Bela’s Building of Fun (redrawn): floor numbers on the right.
1Up = ‘+’ button; down = ‘−’ button.
✅ Answer: + + + + (+4) and − − − (−3)
๐ Textbook Page 244
๐ Page 244Number the floors
Number all the floors of the Building of Fun.
1Ground floor (Welcome Hall) = 0.
2Above: Food Court +1, Art Centre +2, Book Store +3, Ice Cream +4, Sports +5, Space +6.
3Below: Toy Store −1, Video Games −2, Cinema −3, Ghost House −4, Dinosaur Park −5.
✅ Answer: See the numbered building.
๐ Textbook Page 245
๐ Page 245Food Court + 2
Start at the Food Court and press +2. Where do you reach?
1Starting floor + movement = target floor.
2(+1) + (+2) = +3.
✅ Answer: Book Store (Floor +3)
๐ Page 245Figure it Out · Q1
Start at Floor +2 and press −3. Where do you reach? Write the expression.
1(+2) + (−3) = −1.
✅ Answer: Floor −1 (Toy Store): (+2) + (−3) = −1
๐ Page 245Figure it Out · Q2
Evaluate: (a) (+1) + (+4); (b) (+4) + (+1); (c) (+4) + (−3); (d) (−1) + (+2); (e) (−1) + (+1); (f) 0 + (+2); (g) 0 + (−2)
1(a) (+1) + (+4) = +5
2(b) (+4) + (+1) = +5
3(c) (+4) + (−3) = +1
4(d) (−1) + (+2) = +1
5(e) (−1) + (+1) = 0
6(f) 0 + (+2) = +2
7(g) 0 + (−2) = −2
✅ Answer: (a) +5 · (b) +5 · (c) +1 · (d) +1 · (e) 0 · (f) +2 · (g) −2
๐ก Tip: Start at the first floor, then move up (+) or down (−).
๐ Page 245Figure it Out · Q3
Find starting floors and movements needed to reach Floor −5. Write the expressions.
1Movement = −5 − (start).
2(+6) + (−11) = −5; (+4) + (−9) = −5; (+1) + (−6) = −5; 0 + (−5) = −5; (−2) + (−3) = −5; (−4) + (−1) = −5.
✅ Answer: e.g. (+6) + (−11) = −5, 0 + (−5) = −5, (−2) + (−3) = −5
๐ Page 245Gurmit’s mistake
Gurmit in the Toy Store pressed + twice and then − three times. Where is he?
1(+2) + (−3) = −1: one floor down from the Toy Store.
2(−1) + (−1) = −2.
✅ Answer: One floor below the Toy Store — Video Games (Floor −2).
๐ Textbook Page 246
๐ Page 246Figure it Out · Combining presses
Evaluate: (a) (+1) + (+4); (b) (+4) + (+1); (c) (+4) + (−3) + (−2); (d) (−1) + (+2) + (−3)
1(a) (+1) + (+4) = +5
2(b) (+4) + (+1) = +5
3(c) (+4) + (−3) + (−2) = −1
4(d) (−1) + (+2) + (−3) = −2
✅ Answer: (a) +5 · (b) +5 · (c) −1 · (d) −2
๐ Page 246Back to zero
Basant presses +4 and then −4. Where will he reach?
1(+4) + (−4) = 0.
✅ Answer: Back on the ground floor (0).
๐ Page 246Inverses
Write the inverses of +4, −4, −3, 0, +2, −1. Connect the inverses: +5, −7, −8, +9 with −9, +8, −5, +7.
1The inverse of a number added to it gives 0.
2+4 → −4, −4 → +4, −3 → +3, 0 → 0, +2 → −2, −1 → +1.
3Pairs: +5 ↔ −5, −7 ↔ +7, −8 ↔ +8, +9 ↔ −9.
✅ Answer: −4, +4, +3, 0, −2, +1; pairs (+5, −5), (−7, +7), (−8, +8), (+9, −9)
๐ Page 246Who is on the lowest floor?
Jay is in the Art Centre (+2). Asin in the Sports Centre, Binnu in the Cinema, Aman in the Toy Store. Fill the floors. Who is lowest?
1Asin: +5. Binnu: −3. Aman: −1.
2−3 is the lowest floor.
✅ Answer: Asin +5, Binnu −3, Aman −1; Binnu is lowest.
๐ Textbook Page 247
๐ Page 247Figure it Out · Q1
Fill in < or >: (a) −2, +5 (b) −5, +4 (c) −5, −3 (d) +6, −6 (e) 0, −4 (f) 0, +4
1The lower floor is the smaller number.
2(a) −2 < +5
3(b) −5 < +4
4(c) −5 < −3
5(d) +6 > −6
6(e) 0 > −4
7(f) 0 < +4
✅ Answer: (a) −2 < +5 · (b) −5 < +4 · (c) −5 < −3 · (d) +6 > −6 · (e) 0 > −4 · (f) 0 < +4
⚠️ Common mistake: Thinking −5 > −3 because 5 > 3. Floor −5 is BELOW Floor −3.
๐ Page 247Figure it Out · Q2
Fill in < or >: (a) −10, −12 (b) +17, −10 (c) 0, −20 (d) +9, −9 (e) −25, −7 (f) +15, −17
1(a) −10 > −12
2(b) +17 > −10
3(c) 0 > −20
4(d) +9 > −9
5(e) −25 < −7
6(f) +15 > −17
✅ Answer: (a) −10 > −12 · (b) +17 > −10 · (c) 0 > −20 · (d) +9 > −9 · (e) −25 < −7 · (f) +15 > −17
๐ Page 247Figure it Out · Q3
On the building drawn as a line, A = −12, D = −1, E = +1. Find B, C, F, G and H.
1Each tick is one floor; 0 lies between D and E.
2Count ticks from 0: B is 9 below → −9; C is 6 below → −6.
3F is 2 above → +2; G is 6 above → +6; H is 11 above → +11.
✅ Answer: B = −9, C = −6, F = +2, G = +6, H = +11
๐ Page 247Figure it Out · Q4
Mark the floors −7, −4, +3 and −10 on the building line.
1Count from 0: down 7, down 4, up 3, down 10.
✅ Answer: See the marks.
๐ Textbook Page 248
๐ Page 248Subtraction as ‘making equal’
Evaluate 15 − 5, 100 − 10 and 74 − 34 as ‘what must be added?’
15 + ? = 15 → 10.
210 + ? = 100 → 90.
334 + ? = 74 → 40.
✅ Answer: 10, 90, 40
๐ Page 248Art Centre to Sports Centre
Start at the Art Centre; the target is the Sports Centre. Which button press?
1Target − start = movement: (+5) − (+2) = +3.
✅ Answer: +3
๐ Textbook Page 249
๐ Page 249Figure it Out
Complete: (a) (+1) − (+4); (b) (0) − (+2); (c) (+4) − (+1); (d) (0) − (−2); (e) (+4) − (−3); (f) (−4) − (−3); (g) (−1) − (+2); (h) (−2) − (−2); (i) (−1) − (+1); (j) (+3) − (−3)
1Target − Start = movement from floor ‘second number’ to floor ‘first number’.
2(a) from +4 to +1: −3
3(b) from +2 to 0: −2
4(c) from +1 to +4: +3
5(d) from −2 to 0: +2
6(e) from −3 to +4: +7
7(f) from −3 to −4: −1
8(g) from +2 to −1: −3
9(h) from −2 to −2: 0
10(i) from +1 to −1: −2
11(j) from −3 to +3: +6
✅ Answer: (a) −3 · (b) −2 · (c) +3 · (d) +2 · (e) +7 · (f) −1 · (g) −3 · (h) 0 · (i) −2 · (j) +6
๐ Textbook Page 250
๐ Page 250The mine
Use the mine levels: (+40) + (+60), (−90) + (−55), (+40) − (−50), (−90) − (+40).Mine levels (in metres): above ground positive, below ground negative.
1Start +40, go up 60 → +100.
2Start −90, go down 55 → −145.
3From −50 to +40 is 90 up → +90.
4From +40 to −90 is 130 down → −130.
✅ Answer: +100, −145, +90, −130
๐ Textbook Page 251
๐ Page 251Figure it Out · Mineshaft
Complete: (a) (+40) + ___ = +200; (b) (+40) + ___ = −200; (c) (−50) + ___ = +200; (d) (−50) + ___ = −200; (e) (−200) − (−40); (f) (+200) − (+40); (g) (−200) − (+40)
1Missing movement = target − start.
2(a) 200 − 40 = 160 up. (b) from +40 down to −200: 240 down.
3(c) from −50 up to +200: 250 up. (d) from −50 down to −200: 150 down.
4(e) from −40 to −200: 160 down. (f) from +40 to +200: 160 up. (g) from +40 to −200: 240 down.
✅ Answer: (a) +160 · (b) −240 · (c) +250 · (d) −150 · (e) −160 · (f) +160 · (g) −240
๐ Page 251Infinite lift
Evaluate: (a) −125 + (−30); (b) +105 − (−55); (c) +105 + (+55); (d) +80 − (−150); (e) +80 + (+150); (f) −99 − (−200); (g) −99 + (+200); (h) +1500 − (−1500)
1Subtracting a negative = adding the positive: (b) = (c), (d) = (e), (f) = (g).
2(a) −155
3(b) +160
4(c) +160
5(d) +230
6(e) +230
7(f) +101
8(g) +101
9(h) +3000
✅ Answer: (a) −155 · (b) +160 · (c) +160 · (d) +230 · (e) +230 · (f) +101 · (g) +101 · (h) +3000
๐ Textbook Page 252
๐ Page 252Math Talk
Did subtracting a negative number give the same as adding the positive? Does the infinite lift remind you of a number line?
1+105 − (−55) = 160 = +105 + (+55).
2Yes; the lift turned sideways is the number line: up = right, down = left.
✅ Answer: Yes and yes.
๐ Page 252Walking on the line
From 5 to 9? From 9 to 3? From 3 to −2? Write the statements.
15 + 4 = 9 and 9 − 5 = 4.
29 + (−6) = 3 and 3 − 9 = −6.
33 + (−5) = −2 and −2 − 3 = −5.
✅ Answer: +4, −6, −5
๐ Textbook Page 253
๐ Page 253Figure it Out · Q1–Q2
Mark 3 positive and 3 negative numbers on the number line; write the negative ones in the boxes.
1Positive numbers lie to the right of 0, negative ones to the left.
✅ Answer: e.g. 2, 5, 8 and −3, −6, −9
๐ Textbook Page 254
๐ Page 254Figure it Out · Q3
Is 2 > −3? Why? Is −2 < 3? Why?
12 is to the right of −3 on the number line.
2−2 is to the left of 3.
✅ Answer: Yes and yes.
๐ Page 254Figure it Out · Q4
What are: (a) −5 + 0; (b) 7 + (−7); (c) −10 + 20; (d) 10 − 20; (e) 7 − (−7); (f) −8 − (−10)
1(a) −5 + 0 = −5
2(b) 7 + (−7) = 0
3(c) −10 + 20 = +10
4(d) 10 − 20 = −10
5(e) 7 − (−7) = +14
6(f) −8 − (−10) = +2
✅ Answer: (a) −5 · (b) 0 · (c) +10 · (d) −10 · (e) +14 · (f) +2
๐ Page 254Unmarked number line
Use an unmarked number line: 85 + (−60) and (−100) − (+250).
1From +85 go 60 left → +25.
2From +250 to −100 is 350 to the left → −350.
✅ Answer: +25 and −350
๐ Textbook Page 255
๐ Page 255Unmarked number lines
Evaluate: (a) −125 + (−30); (b) +105 − (−55); (c) +80 − (−150); (d) −99 − (−200)
1(a) from −125 go 30 left → −155.
2(b) = 105 + 55 → +160.
3(c) = 80 + 150 → +230.
4(d) = −99 + 200 → +101.
✅ Answer: (a) −155 · (b) +160 · (c) +230 · (d) +101
๐ Page 255Subtraction ↔ addition
From 2 to −3: what is the movement? Show it as subtraction and as addition.
1Subtraction: −3 − 2 = −5.
2In two parts: 2 → 0 is −2, 0 → −3 is −3; total (−3) + (−2) = −5.
✅ Answer: −5. Subtracting a number = adding its inverse.
๐ Textbook Page 256
๐ Page 256Tokens · lift attendant
5 positive and 3 negative tokens. Which floor?
1Cancel 3 zero pairs.
22 positive tokens are left: (+5) + (−3) = +2.
✅ Answer: Floor +2
๐ Page 256Example · +5 and −8
Add +5 and −8 with tokens.
1Cancel 5 zero pairs; 3 negatives remain.
✅ Answer: −3
๐ Textbook Page 257
๐ Page 257Figure it Out · Q1
Complete with tokens: (a) (+6) + (+4) (b) (−3) + (−2) (c) (+5) + (−7) (d) (−2) + (+6)
1Put down both sets, remove zero pairs, count what is left.
2(a) +10
3(b) −5
4(c) −2
5(d) +4
✅ Answer: (a) +10 · (b) −5 · (c) −2 · (d) +4
๐ Page 257Figure it Out · Q2
Cancel zero pairs: (a) 3 positives, 5 negatives (b) 6 positives, 3 negatives. Which floor? Write the statement.(a) (b)
1(a) 3 pairs cancel; 2 negatives left: (+3) + (−5) = −2.
2(b) 3 pairs cancel; 3 positives left: (+6) + (−3) = +3.
✅ Answer: (a) Floor −2 (b) Floor +3
๐ Page 257Tokens · subtraction
Using tokens: (+5) − (+4), (−7) − (−5), (+5) − (+6). Is (−7) − (−5) the same as (−7) + (+5)?
1(+5) − (+4): take 4 positives from 5 → +1.
2(−7) − (−5): take 5 negatives from 7 → −2; and (−7) + (+5) = −2 too.
3(+5) − (+6): add one zero pair, take 6 positives → −1.
✅ Answer: +1, −2 (yes, same), −1
๐ Textbook Page 258
๐ Page 258Figure it Out · Q1
Evaluate with tokens: (a) (+10) − (+7); (b) (−8) − (−4); (c) (−9) − (−4); (d) (+9) − (+12); (e) (−5) − (−7); (f) (−2) − (−6)
1Put down the first number; take away the second. If there are not enough, add zero pairs first.
2(a) +3
3(b) −4
4(c) −5
5(d) −3
6(e) +2
7(f) +4
✅ Answer: (a) +3 · (b) −4 · (c) −5 · (d) −3 · (e) +2 · (f) +4
๐ Page 258Figure it Out · Q2
Complete: (a) (−5) − (−7); (b) (+10) − (+13); (c) (−7) − (−9); (d) (+3) − (+8); (e) (−2) − (−7); (f) (+3) − (+15)
1(a) −5 + (+7) = +2
2(b) +10 + (−13) = −3
3(c) −7 + (+9) = +2
4(d) +3 + (−8) = −5
5(e) −2 + (+7) = +5
6(f) +3 + (−15) = −12
✅ Answer: (a) +2 · (b) −3 · (c) +2 · (d) −5 · (e) +5 · (f) −12
๐ Page 258Example · +4 − (−6)
Find +4 − (−6) with tokens.
14 positives; we need 6 negatives to take away, so add 6 zero pairs.
2Take away 6 negatives: 10 positives remain.
✅ Answer: +10
๐ Textbook Page 259
๐ Page 259Figure it Out · Q1
Subtract −3 − (+5). How many zero pairs? What is the result?
13 negatives; no positives to take away 5.
2Add 5 zero pairs, take 5 positives: 8 negatives left.
✅ Answer: 5 zero pairs; −8
๐ Page 259Figure it Out · Q2
Evaluate with tokens: (a) (−3) − (+10); (b) (+8) − (−7); (c) (−5) − (+9); (d) (−9) − (+10); (e) (+6) − (−4); (f) (−2) − (+7)
1(a) −13
2(b) +15
3(c) −14
4(d) −19
5(e) +10
6(f) −9
✅ Answer: (a) −13 · (b) +15 · (c) −14 · (d) −19 · (e) +10 · (f) −9
๐ Page 259Credits and debits
Start ₹100; credit ₹60; debit ₹30; debit ₹150; credit ₹200. Find the balance after each step.
1100 + 60 = 160.
2160 − 30 = 130.
3130 − 150 = −20 (possible for a short time in some banks).
4−20 + 200 = 180.
✅ Answer: ₹160, ₹130, −₹20, ₹180
๐ Textbook Page 260
๐ Page 260Figure it Out · Q1
Start ₹0; credits ₹30, ₹40, ₹50; debits ₹40, ₹50, ₹60. Balance?
1Credits 120, debits 150.
2120 − 150 = −30.
✅ Answer: −₹30
๐ Page 260Figure it Out · Q2
Start ₹0; debits ₹1, 2, 4, 8, 16, 32, 64, 128; then a credit of ₹256. Balance?
1Debits add up to 255.
2−255 + 256 = +1.
✅ Answer: ₹1
๐ Page 260Figure it Out · Q3
Why keep a positive balance? When may a negative balance be worthwhile?
1A negative balance means you owe the bank and may pay interest or a fee.
2It can be worthwhile for a short time to buy something that soon earns more money (like the business purchase that earned ₹200).
✅ Answer: To avoid owing money and extra charges; short-term for a useful investment or an emergency.
๐ Textbook Page 261
๐ Page 261Cross section · Q1–Q3
Read the heights of A–G. Which is highest and lowest? Order them.Geographical cross section (redrawn; heights in metres).
1Approximate readings: A +1500, B −500, C +250, D −1250, E +1250, F −250, G +100 (metres).
2Highest A, lowest D.
3Decreasing: A, E, C, G, F, B, D. Increasing: D, B, F, G, C, E, A.
✅ Answer: A highest, D lowest.
๐ Page 261Cross section · Q4–Q5
Highest point on Earth above sea level? Lowest point (land or ocean floor)?
1Mount Everest: about +8849 m.
2Challenger Deep in the Mariana Trench (Pacific Ocean): about −10,900 m.
3On land: the shore of the Dead Sea, about −430 m.
✅ Answer: Everest ≈ +8849 m; Challenger Deep ≈ −10,900 m
๐ Textbook Page 262
๐ Page 262Temperature · Q1
Name places in India where the temperature can go below 0°C. What is common?Thermometers showing 40°C and 15°C
1Leh and Kargil (Ladakh), Drass, Gulmarg, Sikkim and Himachal hill towns (e.g. Keylong).
2They are high in the mountains; air is thinner and colder higher up, and snow falls in winter.
✅ Answer: High mountain places in the north and north-east.
๐ Page 262Temperature · Q2
Leh in November: match 14°C, 8°C, −2°C, −4°C with 02:00 a.m., 11:00 p.m., 02:00 p.m., 11:00 a.m.
1Warmest in the afternoon, coldest before dawn.
214°C → 02:00 p.m.; 8°C → 11:00 a.m.; −2°C → 11:00 p.m.; −4°C → 02:00 a.m.
✅ Answer: 14°C – 2 p.m., 8°C – 11 a.m., −2°C – 11 p.m., −4°C – 2 a.m.
๐ Textbook Page 263
๐ Page 263Hollow grid · Q1
Find the border sum of the second grid.
1Top: 5 + (−3) + (−5) = −3.
2Bottom: (−8) + (−2) + 7 = −3.
3Left: 5 + 0 + (−8) = −3.
4Right: (−5) + (−5) + 7 = −3.
✅ Answer: −3
๐ Textbook Page 264
๐ Page 264Hollow grid · Q2
Complete the grids for border sums +4, −2 and −4.Border sum +4 Border sum −2 Border sum −4
1Grid 1: left column −10 + ? + 9 = 4 → 5. Choose the top-right, e.g. 10; then the other boxes follow.
2Grid 2: top row 6 + 8 + ? = −2 → −16; right column → 19; bottom row → −19; left column → 11.
3Grid 3: choose the top-right, e.g. −8; the rest follows.
✅ Answer: See the completed grids (one answer each).
๐ Page 264Hollow grid · Q3–Q4
Find another way for the −4 grid. Which grids have many answers, and why?
1Another answer: 7, −11, 0 / −11, _, −5 / 0, −5, 1.
2Grids 1 and 3 have many answers because one corner is still free to choose.
3Grid 2 has only one answer: its top row already had two numbers, which fixed everything.
✅ Answer: Grids 1 and 3: many answers; grid 2: one answer.
๐ Textbook Page 265
๐ Page 265Amazing grid · Q1–Q3
Play the circle-and-strike game. What sum do you get each time? What is special about these grids?
1Each circled number comes from a different row and a different column.
2First grid: always −1, whatever you choose.
3Second grid: always −8 (each row goes up by 3, each row is 9 less than the row above). Note: the book prints −7 in the bottom row; the pattern needs −17 there, otherwise one choice gives +2.
4Third grid: always −14.
5Magic: every number = (row number) + (column number), so any choice adds all row numbers and all column numbers once.
✅ Answer: −1, −8, −14 — the sum never changes.
๐ Page 265Figure it Out · Q1
Write all integers between: (a) 0 and −7 (b) −4 and 4 (c) −8 and −15 (d) −30 and −23, in increasing order.
1(a) −6, −5, −4, −3, −2, −1
2(b) −3, −2, −1, 0, 1, 2, 3
3(c) −14, −13, −12, −11, −10, −9
4(d) −29, −28, −27, −26, −25, −24
✅ Answer: See the lists.
๐ Page 265Figure it Out · Q2
Give three numbers whose sum is −8.
1e.g. (−2) + (−3) + (−3) = −8; or 5 + (−10) + (−3) = −8.
✅ Answer: e.g. −2, −3, −3
๐ Page 265Figure it Out · Q3
Two dice have faces −1, 2, −3, 4, −5, 6. Which numbers between −10 and 12 cannot be the sum?
1Negative faces −1, −3, −5 are odd; positive faces 2, 4, 6 are even.
2Two negatives: −2, −4, −6, −8, −10. Two positives: 4, 6, 8, 10, 12.
3One of each: −1+2=1, −1+4=3, −1+6=5, −3+2=−1, −3+4=1, −3+6=3, −5+2=−3, −5+4=−1, −5+6=1.
4So possible sums: −10, −8, −6, −4, −3, −2, −1, 1, 3, 4, 5, 6, 8, 10, 12. The rest are impossible.
✅ Answer: −9, −7, −5, 0, +2, +7, +9, +11
๐ Page 265Figure it Out · Q4
Solve: 8 − 13; (−8) − (13); (−13) − (−8); (−13) + (−8); 8 + (−13); (−8) − (−13); (13) − 8; 13 − (−8)
18 − 13 = −5
2(−8) − (13) = −21
3(−13) − (−8) = −5
4(−13) + (−8) = −21
58 + (−13) = −5
6(−8) − (−13) = +5
7(13) − 8 = +5
813 − (−8) = +21
✅ Answer: −5 · −21 · −5 · −21 · −5 · +5 · +5 · +21
๐ Page 265Figure it Out · Q5
(a) Which year was 150 years ago? (b) 2200 years ago? (c) Which year is 320 years after 680 BCE?
1Taking the present year as 2026: (a) 2026 − 150 = 1876.
2(b) 2026 − 2200 = −174, but there is no year 0, so it is 175 BCE.
3(c) 680 BCE + 320 years = 360 BCE (we do not cross year 0).
✅ Answer: (a) 1876 (b) 175 BCE (c) 360 BCE
๐ก Tip: Going from 1 CE back one year gives 1 BCE — there is no year 0.
๐ Textbook Page 266
๐ Page 266Figure it Out · Q6
Complete the sequences: (a) −40, −34, −28, −22, … (b) 3, 4, 2, 5, 1, 6, 0, 7, … (c) __, __, 12, 6, 1, −3, −6, __, __, __
1(a) add 6: −16, −10, −4.
2(b) two patterns take turns: 3, 2, 1, 0, −1 … and 4, 5, 6, 7, 8 … → −1, 8, −2.
3(c) differences −6, −5, −4, −3, then −2, −1, 0; going back +7, +8: 27, 19, …, −8, −9, −9.
✅ Answer: (a) −16, −10, −4 (b) −1, 8, −2 (c) 27, 19 … −8, −9, −9
๐ Page 266Figure it Out · Q7
Cards (+1), (+7), (+18), (−5), (−2), (−9): make an expression with value close to −30.
1Add negatives and subtract positives to go down.
2(−2) + (−9) − (+18) − (+1) = −30.
✅ Answer: (−2) + (−9) − (+18) − (+1) = −30 exactly
๐ Page 266Figure it Out · Q8
Is the result always positive, always negative, or either: (a) pos − neg (b) pos + neg (c) neg + neg (d) neg − neg (e) neg − pos (f) neg + pos?
1(a) e.g. 3 − (−2) = 5 → always positive.
2(b) 3 + (−5) = −2, 5 + (−3) = 2 → either.
3(c) always negative.
4(d) −3 − (−5) = 2, −5 − (−3) = −2 → either.
5(e) always negative.
6(f) either.
✅ Answer: (a) positive (b) either (c) negative (d) either (e) negative (f) either
๐ Page 266Figure it Out · Q9
A string of 100 tokens repeats + + + − −. What is its value?Pattern + + + − − repeats: each block of 5 tokens is worth +1.
1Each block of 5 tokens = 3 − 2 = +1.
2100 ÷ 5 = 20 blocks → +20.
✅ Answer: +20
๐ Textbook Page 268
๐ Page 268Brahmagupta’s rules
Explain Brahmagupta’s rules with the Building of Fun or a number line, and give your own examples.
1Two positives: go up twice → higher (4 + 3 = 7).
2Two negatives: go down twice → lower (−4 + (−3) = −7).
3Positive + negative: the bigger movement wins (−6 + 2 = −4; 6 + (−2) = 4).
4Number + inverse: up and down the same → 0.
5Subtracting a negative: −(−3) is the same as +3 (5 − (−3) = 8).
✅ Answer: See the explanations and examples.
๐ Where do we use integers?
- Lifts and basements, temperatures, bank credits and debits, heights above and below sea level, years BCE/CE.
๐ Link to higher classes
- Class 7: multiplying and dividing integers. Class 8: rational numbers and algebra.
No comments:
Post a Comment