CLASS 6 · GANITA PRAKASH · CHAPTER 10
Understand negative numbers with number lines, tokens, temperatures, money and patterns.
56 worked answers · short steps first, explanations when you need them
Textbook pages 243–254
Question 1
Count upward with positive integers and downward with negative integers.
Above: +1, +2, +3. Welcome Hall: 0. Below: −1, −2, −3.
Question 2
Moving down three levels means add −3.
+2 + (−3) = −1.
Level −1.
Question 3(1)
Start at 1; move 4 right steps.
+5.
Question 3(2)
Start at 4; move 1 right step.
+5.
Question 3(3)
Start at 4; move 3 left steps.
+1.
Question 3(4)
Start at -1; move 2 right steps.
+1.
Question 3(5)
Start at -1; move 1 right step.
+0.
Question 3(6)
Start at 0; move 2 right steps.
+2.
Question 3(7)
Start at 0; move 2 left steps.
-2.
Question 3(iii)
Start at +4; move three left to +1, then two left to −1.
−1.
Question 4
The opposite is the same distance from zero on the other side.
−4, +3, 0, −2, +1.
Question 5
On a number line, the number farther right is greater.
−2 < +5; −5 < +4; −5 < −3; +6 > −6; 0 > −4; 0 < +4.
Question 6
Use left-to-right order on the number line.
−10 > −12; +17 > −10; 0 > −20; +9 > −9; −25 < −7; +15 > −17.
Question 7
For A−B, move from B back to A, or add the opposite of B.
−3, −2, +3, +2, +7, −1.
Question 8
Change = destination − starting level.
+200−(+40)=+160; −200−(+40)=−240.
Rise 160 m; descend 240 m.
Question 9
Subtract the starting level from each destination.
+200−(−50)=+250 m; −200−(−50)=−150 m.
Question 10
Adding a negative moves left. Subtracting a negative is adding its positive opposite.
−155; 160; 230; 101.
Question 11
Rewrite each subtraction as: subtracted number + missing amount = starting number.
5+?=15; 10+?=100; 34+?=74.
10, 90 and 40.
Question 12
Change = destination − starting point.
9−5=4; 3−9=−6; −2−3=−5.
Move +4, then −6, then −5 units.
Question 13
Compare examples such as 7−(−7)=14 and −8−(−10)=2.
Subtracting a negative changes to adding its positive opposite.
Subtracting −a is the same as adding +a: x−(−a)=x+a.
Question 14
Choose any three integers on each side of zero.
Read the negative marks from left to right.
Example: positives 2, 5, 8; negatives −1, −3, −7. Increasing order: −7<−3<−1.
Question 15
On a number line, 2 lies to the right of −3.
Likewise, −2 lies to the left of 3.
Yes: 2>−3 and −2<3.
Question 16
Zero does not change a number. Opposites cancel. Replace subtracting a negative with addition.
−5, 0, 10, −10, 14, 2.
Textbook pages 256–260
Question 1
Pair one positive token with one negative token; each pair has total zero.
Keep and count any unpaired tokens.
+10, −5, −2, +4.
Question 2
Cancel three positive-negative pairs.
Two negative tokens remain.
−2.
Question 3
Removing positive tokens reduces a positive count. To remove negatives, cancel matching negative tokens.
3, −4, −5, −3.
Question 4
Rewrite subtraction as addition of the opposite, then combine.
+2, −3, +2, −5, +5, −12.
Question 5
Start with three negative tokens.
Add five zero pairs so five positive tokens are available to remove.
Remove those five positives; eight negatives remain.
−3−(+5)=−8. Zero pairs let us remove tokens that are not initially present.
Question 6
Change subtraction to addition of the opposite.
−13, +15, −14, −19, +10, −9.
Textbook pages 260–262
Question 1
Represent deposits as positive and withdrawals or spending as negative.
100+60−30−150=−20.
−₹20: the account is overdrawn by ₹20.
Question 2
Add the deposit to the current balance: −20+200=180.
₹180.
Question 3
Add credits and debits: 30+40+50−40−50−60.
−30.
Question 4
Negative temperatures are below zero; compare the signed values.
−4°C, −2°C, 8°C, 14°C.
Question 5
Positive heights are above sea level; negative heights are below it.
Sort the signed values from greatest to least.
Highest: +1500 m; lowest: −1200 m. Order: +1500, +1200, +300, +100, −200, −500, −1200 m.
Question 6
A point above sea level has a positive height.
A point below sea level has a negative height.
Mount Everest: about +8,848 m; Challenger Deep: about −10,994 m, using the figures printed in the chapter.
Question 7
Use the daily temperature pattern: afternoon is warmest, late morning is next, and early morning is coldest.
Match each reading to the corresponding time in the data table.
14°C—2 pm; 8°C—11 am; −2°C—11 pm; −4°C—2 am.
Textbook pages 263–265
Question 1
Do not include either endpoint. List values from smallest to largest.
−6, −5, −4, −3, −2, −1; −3, −2, −1, 0, 1, 2, 3; −14, −13, −12, −11, −10, −9; −29, −28, −27, −26, −25, −24.
Question 2
Choose two numbers first, then find the third to make the total −8.
One answer: −5 + 7 + (−10) = −8. Many answers are possible.
Question 3
The least total is −5+(−5)=−10; greatest is 6+6=12.
Check sums of two listed face values.
Impossible totals: −9, −7, −5, 0, 2, 7, 9 and 11.
Question 4
Change each subtraction to adding the opposite.
The extracted answer grid gives −5, −21, −5, −21 / −5, +5, +5, +21 for the printed arrangement. The diagram’s exact cell layout should be checked against the book.
Question 5a
Subtract 150 from 2026.
1876 CE.
Question 5b
First calculate 2026−2200=−174 on a number line.
There is no year zero, so one year farther back is 175 BCE.
175 BCE.
Question 5c
Move 320 years toward the present: 680−320=360.
360 BCE.
Question 6a
Each term increases by 6.
−16, −10, −4.
Question 6b
Odd-position terms decrease by 1; even-position terms increase by 1.
−1, 8, −2.
Question 6c
The changes are −6, −5, −4, −3, −2, −1. Work backward and forward.
27, 19, 12, 6, 1, −3, −6, −8, −9, −9.
Question 7
Choose cards −2, −9, +18 and +1.
Compute (−2)+(−9)−(+18)−(+1).
−30.
Question 8
Think of subtraction as adding the opposite.
Compare the sizes when the signs differ.
Positive−negative: positive. Positive+negative: either. Negative+negative: negative. Negative−negative: either. Negative−positive: negative. Negative+positive: either.
Question 9
Group the repeating pattern into equal blocks.
Cancel positive-negative pairs; count the unpaired tokens.
20.
Question 10
Rewrite subtraction as adding the opposite.
For opposite signs, compare magnitudes.
Positive−negative: positive; positive+negative: depends on magnitudes; negative+negative: negative; negative−negative: depends on magnitudes; negative−positive: negative; negative+positive: depends on magnitudes.
Question 11
Add all eight boundary entries; do not include the centre.
−10+10+4+5+9−10+5−5=8.
Border sum = 8.
Question 12
Add the eight boundary cells only.
Choose seven boundary numbers, then set the eighth to target minus their sum.
For example, seven zeros and a final +4 give +4; seven zeros and a final −2 give −2.
One valid pair: use boundary values 0,0,0,0,0,0,0,+4 for the first grid and 0,0,0,0,0,0,0,−2 for the second; the centre may be any integer.
Question 13
The printed grid shows the border total as −3.
Repeat that total for each copy in the sequence.
−3, −3, −3, −3.
Question 14
Find the constant or alternating change in each list.
For the third sequence, differences decrease by 1 each time.
First: −16, −10, −4. Second: −1, 8, −2. Third: 27, 19, 12, 6, 1, −3, −6, −8, −9, −9.
Textbook pages 263–265
Question 1
Add the eight outer entries once each.
−10+10+4+5+9−10+5−5=8.
The border sum is 8. The centre cell is not included.
Question 2
Choose any seven border values.
Subtract their total from the required sum to get the eighth border value.
For target +4, seven zeros and one +4 work; for target −2, seven zeros and one −2 work.