SCERT Kerala Class 7 Mathematics/ Unchanging Relations – Chapter 3

SCERT Kerala Class 7 Mathematics/ Unchanging Relations – Chapter 3 is designed for SCERT Class 7 Mathematics students. Here you can find out textbook solutions and notes of Chapter 3 – Unchanging Relations.

SCERT Kerala Class 7 Mathematics/ Unchanging Relations – Chapter 3
Text book solutions and Notes/ Model Questions
If we add to any number, one more than itself or if we double the number and add one to it, we get the same number as the result.
x + (x + 1) = 2x + 1, for every number x.
(x + y) – y = x, for all numbers x, y.
2x + 2y = 2(x + y), for all numbers x, y.
x + x = 2x, for all numbers x.
(x + y) + z = x + (y + z), for all numbers x, y, z.
Using the above rules, find:

1. 49 + 125 + 75
2. 347 + 63 + 37
3. 88 + 72 + 12
4. ¼ + 1 ¾ + 2
5. 15.5 + 0.25 + 0.75
6. 8.2 + 3.6 + 6.4
   ANSWERS:
   Here we can apply (x + y) + z = x + (y + z)
7. 49 + 125 + 75 = 49 + (125 + 75) = 49 + 200 = 249
8. 347 + 63 + 37 = 347 + (63 + 37) = 347 + 100 = 447
9. 88 + 72 + 12 = (88 + 12) + 72 = 100 + 72 = 172
10. ¼ + 1 ¾ + 2 = (¼ + 1 ¾) + 2 = 2 + 2 = 4
11. 15.5 + 0.25 + 0.75 = 15.5 + (0.25 + 0.75) = 15.5 + 1 = 16.5
12. 8.2 + 3.6 + 6.4 = 8.2 + (3.6 + 6.4) = 8.2 + 10 = 18.2
    (x – y) – z = x – (y + z), for all numbers x, y, z.
    (x + y) – z = x + (y – z), for all numbers x, y, z with y>z
    Using the above rules, find:
13. (135 – 73) – 27
14. (37 – 1 ½) – ½
15. (298 – 4.5) – 3.5
16. (128 + 79) – 29
17. (298 + 4.5) – 3.5
18. (149 + 3 ½) – 2 ½
    ANSWERS:
19. (135 – 73) – 27 = 135 – (73 + 27) = 135 – 100 = 35
20. (37 – 1 ½) – ½ = 37 – (1 ½ + ½) = 37 – 2 = 35
21. (298 – 4.5) – 3.5 = 298 – (4.5 + 3.5) = 298 – 8 = 290
22. (128 + 79) – 29 = 128 + (79 – 29) = 128 + 50 = 178
23. (298 + 4.5) – 3.5 = 298 + (4.5 – 3.5) = 298 + 1 = 299
24. (149 + 3 ½) – 2 ½ = 149 + (3 ½ – 2 ½) = 149 + 1 = 150
    (x – y) + z = x – (y – z) for all numbers x, y, z with y>z
    Using the above rules, find:
25. (135 – 73) + 23
26. (38 – 8 ½) + ½
27. (19 – 6.5) + 5.5
28. 135 – (35 – 18)
29. 4.2 – (3.2 – 2.3)
    ANSWERS:
30. (135 – 73) + 23 = 135 – (73 – 23) = 135 – 50 = 85
31. (38 – 8 ½) + ½ = 38 – (8 ½ – ½) = 38 – 8 = 30
32. (19 – 6.5) + 5.5 = 19 – (6.5 – 5.5) = 19 – 1 = 18
33. 135 – (35 – 18) = (135 – 35) + 18 = 100 + 18 = 118
34. 4.2 – (3.2 – 2.3) = (4.2 – 3.2) + 2.3 = 1 + 2.3 = 3.3