# 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 3Text 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.

(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:

- 49 + 125 + 75
- 347 + 63 + 37
- 88 + 72 + 12
- ¼ + 1 ¾ + 2
- 15.5 + 0.25 + 0.75
- 8.2 + 3.6 + 6.4

ANSWERS:

Here we can apply (x + y) + z = x + (y + z) - 49 + 125 + 75 = 49 + (125 + 75) = 49 + 200 = 249
- 347 + 63 + 37 = 347 + (63 + 37) = 347 + 100 = 447
- 88 + 72 + 12 = (88 + 12) + 72 = 100 + 72 = 172
- ¼ + 1 ¾ + 2 = (¼ + 1 ¾) + 2 = 2 + 2 = 4
- 15.5 + 0.25 + 0.75 = 15.5 + (0.25 + 0.75) = 15.5 + 1 = 16.5
- 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: - (135 – 73) – 27
- (37 – 1 ½) – ½
- (298 – 4.5) – 3.5
- (128 + 79) – 29
- (298 + 4.5) – 3.5
- (149 + 3 ½) – 2 ½

ANSWERS: - (135 – 73) – 27 = 135 – (73 + 27) = 135 – 100 = 35
- (37 – 1 ½) – ½ = 37 – (1 ½ + ½) = 37 – 2 = 35
- (298 – 4.5) – 3.5 = 298 – (4.5 + 3.5) = 298 – 8 = 290
- (128 + 79) – 29 = 128 + (79 – 29) = 128 + 50 = 178
- (298 + 4.5) – 3.5 = 298 + (4.5 – 3.5) = 298 + 1 = 299
- (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: - (135 – 73) + 23
- (38 – 8 ½) + ½
- (19 – 6.5) + 5.5
- 135 – (35 – 18)
- 4.2 – (3.2 – 2.3)

ANSWERS: - (135 – 73) + 23 = 135 – (73 – 23) = 135 – 50 = 85
- (38 – 8 ½) + ½ = 38 – (8 ½ – ½) = 38 – 8 = 30
- (19 – 6.5) + 5.5 = 19 – (6.5 – 5.5) = 19 – 1 = 18
- 135 – (35 – 18) = (135 – 35) + 18 = 100 + 18 = 118
- 4.2 – (3.2 – 2.3) = (4.2 – 3.2) + 2.3 = 1 + 2.3 = 3.3

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