Chapter 7 · Practice set 1Textbook pages 119, 126–127

Practice Set 1 – Animated Solutions ചിന്തിക്കാം

First the six warm-up sums from page 119, done with the three Class 8 rules. Then the three questions of pages 126–127, which use the new meaning of adding a negative number: x + (−y) = x − y. Try each one in your notebook before you press Next ▶.

📖 Tools you will use

For positive x, y: x < y ⇒ x − y = −(y − x); −x + y = y − x; −x − y = −(x + y) (page 119).
Adding a negative number is subtracting: x + (−y) = x − y (page 125).
On the number line a positive change moves right, a negative change moves left (page 5 of this guide).

1. Warm-up: six sums (page 119)

Compute: (i) 6 − 8 (ii) −6 + 8 (iii) −6 − 8 (iv) 2½ − 3½ (v) −2½ + 3½ (vi) −2½ − 3½

ഇവ ഉപയോഗിച്ച്, ചുവടെ പറഞ്ഞിരിക്കുന്ന കണക്കുകൾ ചെയ്യാമല്ലോ?

Decide which rule fits: a smaller number minus a bigger one, a negative plus a positive, or a negative minus a positive.

🎬 Solution animation

Answer: (i) 6 − 8 = −(8 − 6) = −2 (ii) −6 + 8 = 8 − 6 = 2 (iii) −6 − 8 = −(6 + 8) = −14 (iv) 2½ − 3½ = −(3½ − 2½) = −1 (v) −2½ + 3½ = 3½ − 2½ = 1 (vi) −2½ − 3½ = −(2½ + 3½) = −6

2. Question 1 · Complete the table

Q1. Complete the table of x, y and x + y.

ചുവടെക്കൊടുത്തിരിക്കുന്ന പട്ടിക പൂർത്തിയാക്കുക.

x	y	x + y
6	−10	?
−6	10	?
−6	−10	?
−6	6	?
6	−6	?

Think of x as a starting position and y as a move: positive y moves right, negative y moves left.

🎬 Solution animation – one row at a time

Answer: 6 + (−10) = 6 − 10 = −4; −6 + 10 = 4; (−6) + (−10) = −(6 + 10) = −16; −6 + 6 = 0; 6 + (−6) = 0.

💡 Note

The last two rows show that a number and its negative always add to 0: going 6 one way and 6 back brings you home to O.

3. Question 2 · Find the pairs

Q2. In each case find two pairs x, y of the kind described.

(i) x positive, y negative, x + y = 1 (ii) x negative, y positive, x + y = 1 (iii) x positive, y negative, x + y = −1 (iv) x negative, y positive, x + y = −1

Start at x and make a move y that ends at 1 (or −1). For x + y = 1 with y negative, x must be 1 more than the size of y.

🎬 Solution animation

Answer (many are possible): (i) 3, −2 and 10, −9 (ii) −2, 3 and −9, 10 (iii) 2, −3 and 4, −5 (iv) −3, 2 and −5, 4.

🎚️ Find your own pair

x y

4. Question 3 · Grouping does not matter

Q3. Complete the table with (x + y) + z and x + (y + z).

x	y	z	(x + y) + z	x + (y + z)
2	4	−5	?	?
2	−4	5	?	?
−2	4	−5	?	?
2	−4	−5	?	?
−2	4	5	?	?
−2	−4	5	?	?
−2	−4	−5	?	?

Work out the bracket first, then add the remaining number. Do it both ways.

🎬 Solution animation – both groupings

Answer: rows give 1, 1 · 3, 3 · −3, −3 · −7, −7 · 7, 7 · −1, −1 · −11, −11. In every row (x + y) + z = x + (y + z): grouping does not matter, with negative numbers too.

5. Side box: a different subtraction വ്യത്യസ്ത വ്യത്യാസം (page 127)

🎬 17 − 9 and 57 − 29 the new way

🌍 Why this matters

Mental arithmetic gets easier: 57 − 29 = (50 − 20) + (7 − 9) = 30 + (−2) = 28. Subtract the tens, subtract the units even when the result is negative, then add.

6. Check yourself

🧭 Summary

6 − 8 = −2, −6 + 8 = 2, −6 − 8 = −14: the Class 8 rules.
x + (−y) = x − y: 6 + (−10) = −4, (−6) + (−10) = −16, and a number plus its negative is 0.
Grouping does not matter: (x + y) + z = x + (y + z) for any numbers.

Next: Change of position – subtracting negative numbers ▶