NCERT6 CLASS 6 MATHS 2025 CHAPTER 10E THE SIDE OF ZERO PAGES 251, 252, 253, 254 скачать в хорошем качестве

NCERT6 CLASS 6 MATHS 2025 CHAPTER 10E THE SIDE OF ZERO PAGES 251, 252, 253, 254

NCERT6 CLASS 6 MATHS 2025 CHAPTER 10E THE SIDE OF ZERO PAGES 251, 252, 253, 254 ADDING, SUBTRACTING AND COMPARING ANY NUMBERS To add and subtract even larger integers, we can imagine even larger lifts! In fact, we can imagine a lift that can extend forever upwards and forever downwards, starting from Level 0. There does not even have to be any building or mine around — just an ‘infinite lift’! We can use this imagination to add and subtract any integers we like. For example, suppose we want to carry out the subtraction + 2000 – (– 200). We can imagine a lift with 2000 levels above the ground and 200 below the ground. Recall that, Target Level – Starting Level = Movement needed To go from the Starting Floor – 200 to the Target Floor + 2000, we must press + 2200 (+ 200 to get to zero, and then + 2000 more after that to get to + 2200). Therefore, (+ 2000) – (– 200) = + 2200. Notice that (+ 2000) + (+ 200) is also + 2200. Try evaluating the following expressions by similarly drawing or imagining a suitable lift: a. – 125 + (– 30) b. + 105 – (– 55) c. + 105 + (+ 55) e. + 80 + (+ 150) g. – 99 + (+ 200) d. + 80 – (– 150) f. – 99 – (– 200) h. + 1500 – (– 1500) In the other exercises that you did above, did you notice that subtracting a negative number was the same as adding the corresponding positive number? Take a look at the ‘infinite lift’ above. Does it remind you of a number line? In what ways? BACK TO NUMBER LINE The ‘infinite lift’ we saw above looked very much like a number line, didn’t it? In fact, if we rotate it by 90°, it basically becomes a number line. It also tells us how to complete the number ray to a number line, answering the question that we had asked at the beginning of the chapter. To the left of 0 are the negative numbers – 1, – 2, – 3, … Usually we drop the ‘+’ sign on positive numbers and simply write them as 1, 2, 3, … Instead of traveling along the number line using a lift, we can simply imagine walking on it. To the right is the positive (forward) direction, and to the left is the negative (backward) direction. Smaller numbers are now to the left of bigger numbers and bigger numbers are to the right of smaller numbers. If, from 5 you wish to go over to 9, how far must you travel along the number line? You must travel 4 steps. That is why 5 + 4 = 9. (Remember: Starting number + Movement = Target number) The corresponding subtraction statement is 9 – 5 = 4. (Remember: Target number – Starting number = Movement needed) Now, from 9, if you wish to go to 3, how much must you travel along the number line? You must move 6 steps backward, i.e., you must move –6. Hence, we write 9 + (–6) = 3. (Remember again : Starting number + Movement = Target number) The corresponding subtraction statement is 3 – 9 = – 6. (Remember again: Target number – Starting number = Movement needed) Now, from 3, if you wish to go to – 2, how far must you travel? You must travel – 5 steps, i.e., 5 steps backward. Thus, 3 + (– 5) = – 2. The corresponding subtraction statement is: – 2 – 3 = – 5. FIGURE IT OUT 1. Mark 3 positive numbers and 3 negative numbers on the number line above. 2. Write down the above 3 marked negative numbers in the following boxes: 3. Is 2 greater than – 3? Why? Is – 2 less than 3? Why? 4. What are a. – 5 + 0 b. 7 + (– 7) c. – 10 + 20 d. 10 – 20 e. 7 – (– 7) f. – 8 – (– 10)?