The document provides step-by-step instructions for algebraic terms and operations involving variables and constants. It covers topics such as combining like and unlike terms, distributing operations, and solving simple equations. Examples are provided for each concept to illustrate the different possibilities and corrections are given for examples containing mistakes. The goal is to teach the fundamentals of algebraic expressions and equations.

1. Step by Step Approach
Manik
Algebraic Terms

2. Terms (made
from × or ÷)
All Possibilities Examples
Variable alone 𝑦𝑦
Constant alone 2
Variable × Constant 𝑦𝑦 × 2 (or 2𝑦𝑦)
Variable ÷ Constant
𝑦𝑦
2
Constant × Variable 2 × 𝑦𝑦 (or 2𝑦𝑦)
Constant ÷ Variable
2
𝑦𝑦

3. D.I.Y.
(Do it
yourself)
All Possibilities Examples
Variable alone
Constant alone
Variable × Constant
Variable ÷ Constant
Constant × Variable
Constant ÷ Variable

4. Types of
Term
Like Unlike
𝑚𝑚, 2𝑚𝑚 𝑚𝑚, 2𝑛𝑛
3𝑛𝑛, 5𝑛𝑛 3𝑥𝑥, 5
−2𝑦𝑦, 2𝑦𝑦 −2, 2𝑦𝑦
−𝑥𝑥, −7𝑥𝑥 −𝑥𝑥, −7
𝑡𝑡
2
, 𝑡𝑡
𝑡𝑡
2
, 4
4𝑏𝑏
3
, − 3𝑏𝑏
4
3
, − 3𝑏𝑏

5. D.I.Y.
(Do it
yourself)
Like Unlike

6. Like Terms can
be added or
subtracted.
All Possibilities Examples
Term + Term
2𝑦𝑦 + 𝑦𝑦
2𝑦𝑦 + 3𝑦𝑦
𝑦𝑦
2
+ 2𝑦𝑦
𝑦𝑦
2
+
2𝑦𝑦
5
Term − Term
2𝑦𝑦 − 𝑦𝑦
2𝑦𝑦 − 3𝑦𝑦
𝑦𝑦
2
− 2𝑦𝑦
𝑦𝑦
2
−
2𝑦𝑦
5

7. D.I.Y.
(Do it
yourself)
All Possibilities Examples
Term + Term
Term − Term

8. Unlike Terms
are kept
separated
with + or −
All Possibilities Examples
Term + Term
𝑦𝑦 + 2
2𝑦𝑦 + 2
𝑦𝑦
2
+ 2
Term − Term
𝑦𝑦 − 2
2𝑦𝑦 − 2
𝑦𝑦
2
− 2

9. D.I.Y.
(Do it
yourself)
All Possibilities Examples
Term + Term
Term − Term

10. Finding
number of
Terms - I
Examples Count
2𝑦𝑦 1
𝑦𝑦
2
1
𝑦𝑦 + 2 2
𝑦𝑦 − 2 2
𝑦𝑦 1
2 1

11. Finding
number of
Terms - II
Examples Count
2𝑦𝑦 + 4𝑦𝑦 1
5𝑎𝑎 − 𝑎𝑎 1
𝑚𝑚
2
+ 𝑚𝑚 1
5𝑓𝑓 ÷ 2 1
3𝑦𝑦 × 5 1
15
4
× 8𝑤𝑤 1

12. D.I.Y.
(Do it
yourself)
Examples Count
2𝑦𝑦 + 4
7𝑎𝑎 ÷ 8
𝑚𝑚
2
× 16
5𝑦𝑦 − 2𝑦𝑦
3𝑦𝑦 × 5 + 2𝑦𝑦
5𝑤𝑤
4
+ 3𝑤𝑤

13. Find the
mistakes
(If it's there)
Question Answer
12𝑦𝑦 − 4 8𝑦𝑦
8
3
+ 𝑎𝑎
8
3
𝑎𝑎
5𝑚𝑚
4
− 2
3𝑚𝑚
4
5𝑦𝑦 − 𝑦𝑦 4𝑦𝑦
3𝑦𝑦 × 5 + 2 3𝑦𝑦 × 7
𝑤𝑤
2
+
𝑤𝑤
3
𝑤𝑤
5

14. Find the
mistakes
(If it's there)
Question Answer Correction
12𝑦𝑦 − 4 8𝑦𝑦 ✘ 12𝑦𝑦 − 4
8
3
+ 𝑎𝑎
8
3
𝑎𝑎 ✘
8
3
+ 𝑎𝑎
5𝑚𝑚
4
− 2
3𝑚𝑚
4
✘
5𝑚𝑚
4
− 2
5𝑦𝑦 − 𝑦𝑦 4𝑦𝑦 ✔ 4𝑦𝑦
3𝑦𝑦 × 5 + 2 3𝑦𝑦 × 7 ✘ (3𝑦𝑦 × 5) + 2
𝑤𝑤
2
+
𝑤𝑤
3
𝑤𝑤
5
✘
3𝑤𝑤 + 2𝑤𝑤
6

15. Find the
mistakes
(If it's there)
Question Answer
2(3𝑦𝑦 − 4) 6𝑦𝑦 − 4
4 − (5𝑎𝑎 + 6) 4 − 5𝑎𝑎 + 6
−6(7𝑏𝑏 − 3) −42𝑏𝑏 − 18
5
𝑦𝑦
2
− 4
5𝑦𝑦
10
− 20
3(5𝑥𝑥 + 2) 3 + (5𝑥𝑥 + 2)
14𝑤𝑤
28
2𝑤𝑤

16. Find the
mistakes
(If it's there)
Question Answer Correction
2(3𝑦𝑦 − 4) 6𝑦𝑦 − 4 6𝑦𝑦 − 8
4 − (5𝑎𝑎 + 6) 4 − 5𝑎𝑎 + 6 4 − 5𝑎𝑎 − 6
−6(7𝑏𝑏 − 3) −42𝑏𝑏 − 18 −42𝑏𝑏 + 18
5
𝑦𝑦
2
− 4
5𝑦𝑦
10
− 20
5𝑦𝑦
2
− 20
3(5𝑥𝑥 + 2) 3 + (5𝑥𝑥 + 2) 3 × (5𝑥𝑥 + 2)
14𝑤𝑤
28
2𝑤𝑤
𝑤𝑤
2

17. Find the
mistakes
(If it's there)
Question Answer
4 − 𝑦𝑦 = 5 𝑦𝑦 = 5 − 4
8
3
+ 𝑎𝑎 = 4 8 + 𝑎𝑎 = 4 × 3
5 = 4
𝑥𝑥
2
− 9 5 = 2 4
𝑥𝑥
2
− 9
13 = 3(6𝑦𝑦 + 8) 13 − 3 = (6𝑦𝑦 + 8)
5 = 4
𝑥𝑥
2
− 9 5 × 2 = 4 𝑥𝑥 − 9
3𝑤𝑤
2
−
𝑤𝑤 + 2
2
= 6
3𝑤𝑤 − 𝑤𝑤 + 2
2
= 6

18. Question Answer Correction
4 − 𝑦𝑦 = 5 𝑦𝑦 = 5 − 4 −𝑦𝑦 = 5 − 4
8
3
+ 𝑎𝑎 = 4 8 + 𝑎𝑎 = 4 × 3 𝑎𝑎 = 4 −
8
3
5 = 4
𝑥𝑥
2
− 9 5 = 2
4
𝑥𝑥
2
− 9 5 = 2
4
𝑥𝑥 − 18
2
13 = 3(6𝑦𝑦 + 8) 13 − 3 = (6𝑦𝑦 + 8)
13
3
= (6𝑦𝑦 + 8)
5 = 4
𝑥𝑥
2
− 9 5 × 2 = 4 𝑥𝑥 − 9 5 = 2 4
𝑥𝑥 − 18
2
3𝑤𝑤
2
−
𝑤𝑤 + 2
2
= 6
3𝑤𝑤 − 𝑤𝑤 + 2
2
= 6
3𝑤𝑤 − (𝑤𝑤 + 2)
2
= 6

19. D.I.Y.
(Do it
yourself)
Solve the Equations: 𝑥𝑥 = ?
5𝑥𝑥 − 3 2𝑥𝑥 + 1 = 6 − 21 + 𝑥𝑥
𝑥𝑥
2
+
𝑥𝑥
3
+
𝑥𝑥
4
= 13
5𝑥𝑥 + 8 2𝑥𝑥 − 9 = 54
3𝑥𝑥 − 2
4
−
2𝑥𝑥 + 3
3
=
2
3
− 𝑥𝑥
16 − 3 𝑥𝑥 ÷ 7 = −14
5𝑥𝑥
3
+
2
5
= 4 + 𝑥𝑥