Class 6 Maths, Chapter 10 (NCERT). 15 questions by concept, 10 with pictures. Open “Show answer” for the answer and why.
How to teach this chapter · Common misconceptions & worked visual for this chapter
Three cards show the numbers -7, 2, -4. Use each card exactly once in the frame ? - ? + ?. What is the least possible value?
(c) -13
The card in the middle of the frame is taken away, and the other two cards are added. So for the least value you take away the greatest card. Here that card is 2, which gives -7 - 2 + (-4) = -13.
Three integer cards are shown in a row. A question mark stands between the first two cards and between the last two cards. Each question mark is either or . Work from left to right. Which pair of signs, in that order, makes the statement true?
(a) +, -
Keep the signs printed on the cards. Test +, - from left to right. First, (+4) + (-5) = -1. Then, (-1) - (+2) = -3. This gives the target -3.
The integers are the numbers . Is one of these integers? Why?
(d) It is not an integer, because it lies between 0 and 1.
On the number line the integers are one step apart. 0.5 lies halfway between 0 and 1, so it is not an integer.
A number line shows the integers from -1 to 5. How many integers lie between -1 and 5?
(c) 5 integers
The integers between -1 and 5 do not include -1 and 5 themselves. They run from 0 up to 4, and 0 is one of them. Counting them gives 5 integers.
At 12:00 noon, the temperature of a place was -9°C. In the first hour it rose by 3°C, and in the second hour it fell by 8°C. What was the temperature at 2:00 pm?
(b) -14°C
A rise is added and a fall is subtracted. Starting from -9°C, the temperature after the first hour is -6°C, and after the fall it is -14°C.
Which pair of situations are true opposites?
(b) winning by a margin of 60 votes and losing by a margin of 60 votes
Opposite situations reverse the state or direction while keeping the same size and reference point.
On the number line, two equal signed jumps start at 0. Each jump is a movement of . What is the final point?
(b) -8
Each of the two jumps is a movement of . Combining the two movements gives . So the final point is .
What is the sum of all the integers strictly between -11 and -7?
(d) -27
The integers strictly between -11 and -7 are the integers after -11 and before -7. Their sum is -27.
Bela takes the integer . She subtracts the additive inverse of from . What number does Bela get?
(d) -12
The additive inverse of -6 is +6, because (-6) + (+6) = 0. So Bela works out (-6) - (+6). Subtracting +6 means moving 6 steps to the left from -6 on the number line. That lands on -12, so (-6) - (+6) = -12.
On an unmarked number line, you can mark 0, the starting number and the endpoint without marking every integer. A positive movement is to the right and a negative movement is to the left. Which plan correctly represents (-99) - (-80) using only the needed marks?
(c) Mark only 0, -99 and -19. Start at -99, move 80 units to the right, and end at -19.
Start at -99, the first number in the subtraction. Subtracting -80 means adding +80, so move +80 units to reach -19. Mark 0, -99 and -19 on the unmarked line. The other plans either mark every integer, start at the wrong number, or move in the wrong direction.
The number line marks Start and Target. Which direction should you move first to reach the Target?
(a) Move right
Direction depends on the target's position relative to the start. Since the target is to the right of the start, you should move right.
Which sequence lists the integers -6, 3, 0, -2, 5, -8 in ascending order?
(d) -8, -6, -2, 0, 3, 5
Ascending order means moving from left to right on the number line. The negative integers come before 0, and the most negative number is the smallest. Then 0 comes before the positive integers.
Which subtraction of two negative integers has value ?
(c) (-14)-(-17)
Subtracting a negative number is the same as adding the corresponding positive number. So is the same as . Starting at floor and moving up reaches . So has value .
In the token model, the negative tokens from the added zero pairs have already been crossed out as the tokens taken away. What integer is represented by the tokens left uncrossed?
(a) 12
The model represents +9 - (-3). All 3 negative tokens have been removed. The remaining 9 original positives and 3 added positives total 12, representing +12.
The token model shows an expression of the form +7 - (-1). The bracketed negative tokens are to be taken away. What integer remains?
(c) 8
To find +7 - (-1), add 1 zero pairs so there are 1 negative tokens available. Zero pairs do not change the starting value +7. Removing 1 negative tokens leaves 8 positive tokens, so the value is +8.
Wrong
−8 °C is warmer because 8 is bigger than 3.
Why it feels right. I compare the digits and ignore the sign.
Right
Temperature increases as you move up a thermometer scale.
Worked example
