Algebra Rules - Addition and Subtraction - Corollary

Oct 29, 20146 likes2,197 views

This document provides examples and rules for addition, subtraction, and combining decimals, fractions, and algebraic expressions in algebra. It explains that for like terms: add or subtract the coefficients and keep the variable; for fractions: find the least common multiple; and for mixed decimals and fractions, convert one to the other form before combining. It also notes that for unlike terms or expressions with different variables, the terms should be kept separate.

Algebra – Class 3a
Basic Rules of
Algebra – Corollary
1
Edishta Resource Centre www.edishta.com

$2 Algebra - Rules You know about decimals and fractions, aren’t you? Just have a quick glance at them and try recalling them… 4.5 + 3.3 = 7.8 1.25 + 2.98 = 4.23 3.4 – 1.7 = 1.7 23.45 - 12.58 = 10.87 Edishta Resource Centre www.edishta.com$

$3 Algebra - Rules You know about decimals and fractions, aren’t you? Just have a quick glance at them and try recalling them… 4.5 + 3.3 = 7.8 1.25 + 2.98 = 4.23 3.4 – 1.7 = 1.7 23.45 - 12.58 = 10.87 15)19( 1 15 04 Edishta Resource Centre www.edishta.com$

$4 Algebra - Rules You know about decimals and fractions, aren’t you? Just have a quick glance at them and try recalling them… 4.5 + 3.3 = 7.8 1.25 + 2.98 = 4.23 3.4 – 1.7 = 1.7 23.45 - 12.58 = 10.87 LCM of 9,12 is 36 Edishta Resource Centre www.edishta.com$

$5 Algebra - Rules You know about decimals and fractions, aren’t you? Just have a quick glance at them and try recalling them… 4.5 + 3.3 = 7.8 1.25 + 2.98 = 4.23 3.4 – 1.7 = 1.7 23.45 - 12.58 = 10.87 4 X 3 = 12 12 + 2 = 14 Edishta Resource Centre www.edishta.com$

$6 Algebra - Rules You know about decimals and fractions, aren’t you? Just have a quick glance at them and try recalling them… 4.5 + 3.3 = 7.8 1.25 + 2.98 = 4.23 3.4 – 1.7 = 1.7 23.45 - 12.58 = 10.87 Same thing continues here also. Edishta Resource Centre www.edishta.com$

$Algebra - Rules What is the rules of addition and subtraction? It is adding or subtracting the numbers then joining coefficient with the total No other rules for decimals and fractions… Edishta Resource Centre www.edishta.com$

8
Algebra – Addition and Subtraction (Decimals)
Shall we move ahead to see some examples?...
Addition
1.2x + 4.6x = 5.8x 2.3y + 5.8y = 8.1y 6.8a + a = 7.8a
8.45m + 4.835m = 13.285m 53.2qp + 32pq = 85.2pq 19.302abc + 0.8abc = 20.102abc
Edishta Resource Centre www.edishta.com

9
Algebra – Addition and Subtraction (Decimals)
(a= 1a)
Shall we move ahead to see some examples?...
Addition
1.2x + 4.6x = 5.8x 2.3y + 5.8y = 8.1y 6.8a + a = 7.8a
8.45m + 4.835m = 13.285m 53.2qp + 32pq = 85.2pq 19.302abc + 0.8abc = 20.102abc
1.2
4.6
5.8
Coeff. is x so
Ans. is 5.8x
2.3
5.8
8.1
Coeff. is y so
Ans. is 8.1y
Edishta Resource Centre www.edishta.com

10
Algebra – Addition and Subtraction (Decimals)
Shall we move ahead to see some examples?...
Addition
1.2x + 4.6x = 5.8x 2.3y + 5.8y = 8.1y 6.8a + a = 7.8a
8.45m + 4.835m = 13.285m 53.2qp + 32pq = 85.2pq 19.302abc + 0.8abc = 20.102abc
8.45
+ 4.835
13.285
and m so 13.285m
19.302
+ 0.8 `
20.102
So 20.102abc
Edishta Resource Centre www.edishta.com

11
Algebra – Addition and Subtraction (Decimals)
Shall we move ahead to see some examples?...
Addition
1.2x + 4.6x = 5.8x 2.3y + 5.8y = 8.1y 6.8a + a = 7.8a
8.45m + 4.835m = 13.285m 53.2qp + 32pq = 85.2pq 19.302abc + 0.8abc = 20.102abc
Subtraction
3.8x – 2.2x = 1.6x 19.3c - 8.8c = 10.5c 2.41def –def = 1.41def
7.51k - 6.894k = 0.616k 21.325uv - 1.325uv = 20uv 53xyz – 24.21yxz = 28.79xyz
Edishta Resource Centre www.edishta.com

12
Algebra – Addition and Subtraction (Decimals)
Shall we move ahead to see some examples?...
Addition
1.2x + 4.6x = 5.8x 2.3y + 5.8y = 8.1y 6.8a + a = 7.8a
3.8
-2.2
1.6
19.3
- 8.8
10.5
8.45m + 4.835m = 13.285m 53.2qp + 32pq = 85.2pq 19.302abc + 0.8abc = 20.102abc
Coeff. is x so
Ans. is 1.6x
Coeff. is c so
Ans. is 10.5c
Subtraction (def= 1def)
3.8x – 2.2x = 1.6x 19.3c - 8.8c = 10.5c 2.41def –def = 1.41def
7.51k - 6.894k = 0.616k 21.325uv - 1.325uv = 20uv 53xyz – 24.21yxz = 28.79xyz
Edishta Resource Centre www.edishta.com

13
Algebra – Addition and Subtraction (Decimals)
Shall we move ahead to see some examples?...
Addition
1.2x + 4.6x = 5.8x 2.3y + 5.8y = 8.1y 6.8a + a = 7.8a
7.51
8.45m + 4.835m = 13.285m 53.2qp + 32pq = 85.2pq 19.302abc + 0.8abc = 20.102abc
Subtraction
- 6.894
0.616
and k so
Ans. is 0.616k
3.8x – 2.2x = 1.6x 19.3c - 8.8c = 10.5c 2.41def –def = 1.41def
7.51k - 6.894k = 0.616k 21.325uv - 1.325uv = 20uv 53xyz – 24.21yxz = 28.79xyz
xyz= yxz
Edishta Resource Centre www.edishta.com

14
Algebra – Addition and Subtraction (Decimals)
Shall we move ahead to see some examples?...
Addition
1.2x + 4.6x = 5.8x 2.3y + 5.8y = 8.1y 6.8a + a = 7.8a
8.45m + 4.835m = 13.285m 53.2qp + 32pq = 85.2pq 19.302abc + 0.8abc = 20.102abc
Subtraction
3.8x – 2.2x = 1.6x 19.3c - 8.8c = 10.5c 2.41def –def = 1.41def
7.51k - 6.894k = 0.616k 21.325uv - 1.325uv = 20uv 53xyz – 24.21yxz = 28.79xyz
Edishta Resource Centre www.edishta.com

15
Algebra – Addition and Subtraction (Fractions)
Shall we move ahead to see some examples?...
Addition
Edishta Resource Centre www.edishta.com

16
Algebra – Addition and Subtraction (Fractions)
Shall we move ahead to see some examples?...
Addition
LCM is 12
and x so
Edishta Resource Centre www.edishta.com

17
Algebra – Addition and Subtraction (Fractions)
Shall we move ahead to see some examples?...
Addition
LCM is 42 2n =
Edishta Resource Centre www.edishta.com

18
Algebra – Addition and Subtraction (Fractions)
Shall we move ahead to see some examples?...
Addition
Coeff. is x so
Ans. is LCM is 9
Subtraction lkm= 1klm
Edishta Resource Centre www.edishta.com

19
Algebra – Addition and Subtraction (Fractions)
Shall we move ahead to see some examples?...
Addition
Subtraction
LCM is 24
Edishta Resource Centre www.edishta.com

20
Algebra – Addition and Subtraction (Fractions)
Shall we move ahead to see some examples?...
Addition
Subtraction
Edishta Resource Centre www.edishta.com

$Algebra – Mixed Types What if we have fractions and decimals both? Convert either fraction to decimals or vice versa depending on easiness. Edishta Resource Centre www.edishta.com$

$Algebra – Mixed Types What if we have fractions and decimals both? Convert either fraction to decimals or vice versa depending on easiness. Fraction to decimal 3/5 = 0.6 Edishta Resource Centre www.edishta.com$

$Algebra – Mixed Types What if we have fractions and decimals both? Convert either fraction to decimals or vice versa depending on easiness. Fraction to decimal 3/4 = 0.75 + 2 = 2.75 Edishta Resource Centre www.edishta.com$

$Algebra – Mixed Types What if we have fractions and decimals both? Convert either fraction to decimals or vice versa depending on easiness. Decimal to fraction 0.3 = 3/10 (Multiply and divide by powers of 10 to remove decimal) Edishta Resource Centre www.edishta.com$

$Algebra – Mixed Types What if we have fractions and decimals both? Convert either fraction to decimals or vice versa depending on easiness. Fraction to decimal 5/16 = 0.3125 Edishta Resource Centre www.edishta.com$

$Algebra – Mixed Types What if we have fractions and decimals both? Convert either fraction to decimals or vice versa depending on easiness. Decimal to fraction 2.25 = 225/100 (Multiply and divide by powers of 10) 225/100 = 9/4 (Simplifying) Edishta Resource Centre www.edishta.com$

$Algebra – Mixed Types What if we have fractions and decimals both? Convert either fraction to decimals or vice versa depending on easiness. Edishta Resource Centre www.edishta.com$

Algebra – Mixed Types
What if we have
–ve number
greater among
two?
Basic rules says to
apply the sign of
greater number
Edishta Resource Centre www.edishta.com

Algebra – Mixed Types
What if we have
–ve number
greater among
two?
Basic rules says to
apply the sign of
greater number
3.2xy - 4.6yx = -1.2xy 3.13y - 10.9y = -7.77y -6.8a + 0.801a = -6.001a
Edishta Resource Centre www.edishta.com

Algebra – Mixed Types
What if we have
–ve number
greater among
two?
Basic rules says to
apply the sign of
greater number
When you have two
different signs +
3.2xy - 4.6yx = -1.2xy 3.13y - 10.9y = -7.77y -6.8a + 0.801a = -6.001a
and – then do
subtraction from
bigger with smaller
and assign sign of
bigger number.
Edishta Resource Centre www.edishta.com

Algebra – Unlike Terms
If there are
unlike
terms
Don’t do
anything
Just keep
the same
thing
Edishta Resource Centre www.edishta.com

Algebra – Unlike Terms
If there are
unlike
terms
Don’t do
anything
Just keep
the same
thing
5.2x + 2.548xy = 5.2x + 2.548xy 8.75t + 4.37y = 8.75t + 4.37y
Edishta Resource Centre www.edishta.com

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Algebra Rules - Addition and Subtraction - Corollary

1. Algebra – Class 3a Basic Rules of Algebra – Corollary 1 Edishta Resource Centre www.edishta.com

2. 2 Algebra - Rules You know about decimals and fractions, aren’t you? Just have a quick glance at them and try recalling them… 4.5 + 3.3 = 7.8 1.25 + 2.98 = 4.23 3.4 – 1.7 = 1.7 23.45 - 12.58 = 10.87 Edishta Resource Centre www.edishta.com

3. 3 Algebra - Rules You know about decimals and fractions, aren’t you? Just have a quick glance at them and try recalling them… 4.5 + 3.3 = 7.8 1.25 + 2.98 = 4.23 3.4 – 1.7 = 1.7 23.45 - 12.58 = 10.87 15)19( 1 15 04 Edishta Resource Centre www.edishta.com

4. 4 Algebra - Rules You know about decimals and fractions, aren’t you? Just have a quick glance at them and try recalling them… 4.5 + 3.3 = 7.8 1.25 + 2.98 = 4.23 3.4 – 1.7 = 1.7 23.45 - 12.58 = 10.87 LCM of 9,12 is 36 Edishta Resource Centre www.edishta.com

5. 5 Algebra - Rules You know about decimals and fractions, aren’t you? Just have a quick glance at them and try recalling them… 4.5 + 3.3 = 7.8 1.25 + 2.98 = 4.23 3.4 – 1.7 = 1.7 23.45 - 12.58 = 10.87 4 X 3 = 12 12 + 2 = 14 Edishta Resource Centre www.edishta.com

6. 6 Algebra - Rules You know about decimals and fractions, aren’t you? Just have a quick glance at them and try recalling them… 4.5 + 3.3 = 7.8 1.25 + 2.98 = 4.23 3.4 – 1.7 = 1.7 23.45 - 12.58 = 10.87 Same thing continues here also. Edishta Resource Centre www.edishta.com

7. Algebra - Rules What is the rules of addition and subtraction? It is adding or subtracting the numbers then joining coefficient with the total No other rules for decimals and fractions… Edishta Resource Centre www.edishta.com

8. 8 Algebra – Addition and Subtraction (Decimals) Shall we move ahead to see some examples?... Addition 1.2x + 4.6x = 5.8x 2.3y + 5.8y = 8.1y 6.8a + a = 7.8a 8.45m + 4.835m = 13.285m 53.2qp + 32pq = 85.2pq 19.302abc + 0.8abc = 20.102abc Edishta Resource Centre www.edishta.com

9. 9 Algebra – Addition and Subtraction (Decimals) (a= 1a) Shall we move ahead to see some examples?... Addition 1.2x + 4.6x = 5.8x 2.3y + 5.8y = 8.1y 6.8a + a = 7.8a 8.45m + 4.835m = 13.285m 53.2qp + 32pq = 85.2pq 19.302abc + 0.8abc = 20.102abc 1.2 4.6 5.8 Coeff. is x so Ans. is 5.8x 2.3 5.8 8.1 Coeff. is y so Ans. is 8.1y Edishta Resource Centre www.edishta.com

10. 10 Algebra – Addition and Subtraction (Decimals) Shall we move ahead to see some examples?... Addition 1.2x + 4.6x = 5.8x 2.3y + 5.8y = 8.1y 6.8a + a = 7.8a 8.45m + 4.835m = 13.285m 53.2qp + 32pq = 85.2pq 19.302abc + 0.8abc = 20.102abc 8.45 + 4.835 13.285 and m so 13.285m 19.302 + 0.8 ` 20.102 So 20.102abc Edishta Resource Centre www.edishta.com

11. 11 Algebra – Addition and Subtraction (Decimals) Shall we move ahead to see some examples?... Addition 1.2x + 4.6x = 5.8x 2.3y + 5.8y = 8.1y 6.8a + a = 7.8a 8.45m + 4.835m = 13.285m 53.2qp + 32pq = 85.2pq 19.302abc + 0.8abc = 20.102abc Subtraction 3.8x – 2.2x = 1.6x 19.3c - 8.8c = 10.5c 2.41def –def = 1.41def 7.51k - 6.894k = 0.616k 21.325uv - 1.325uv = 20uv 53xyz – 24.21yxz = 28.79xyz Edishta Resource Centre www.edishta.com

12. 12 Algebra – Addition and Subtraction (Decimals) Shall we move ahead to see some examples?... Addition 1.2x + 4.6x = 5.8x 2.3y + 5.8y = 8.1y 6.8a + a = 7.8a 3.8 -2.2 1.6 19.3 - 8.8 10.5 8.45m + 4.835m = 13.285m 53.2qp + 32pq = 85.2pq 19.302abc + 0.8abc = 20.102abc Coeff. is x so Ans. is 1.6x Coeff. is c so Ans. is 10.5c Subtraction (def= 1def) 3.8x – 2.2x = 1.6x 19.3c - 8.8c = 10.5c 2.41def –def = 1.41def 7.51k - 6.894k = 0.616k 21.325uv - 1.325uv = 20uv 53xyz – 24.21yxz = 28.79xyz Edishta Resource Centre www.edishta.com

13. 13 Algebra – Addition and Subtraction (Decimals) Shall we move ahead to see some examples?... Addition 1.2x + 4.6x = 5.8x 2.3y + 5.8y = 8.1y 6.8a + a = 7.8a 7.51 8.45m + 4.835m = 13.285m 53.2qp + 32pq = 85.2pq 19.302abc + 0.8abc = 20.102abc Subtraction - 6.894 0.616 and k so Ans. is 0.616k 3.8x – 2.2x = 1.6x 19.3c - 8.8c = 10.5c 2.41def –def = 1.41def 7.51k - 6.894k = 0.616k 21.325uv - 1.325uv = 20uv 53xyz – 24.21yxz = 28.79xyz xyz= yxz Edishta Resource Centre www.edishta.com

14. 14 Algebra – Addition and Subtraction (Decimals) Shall we move ahead to see some examples?... Addition 1.2x + 4.6x = 5.8x 2.3y + 5.8y = 8.1y 6.8a + a = 7.8a 8.45m + 4.835m = 13.285m 53.2qp + 32pq = 85.2pq 19.302abc + 0.8abc = 20.102abc Subtraction 3.8x – 2.2x = 1.6x 19.3c - 8.8c = 10.5c 2.41def –def = 1.41def 7.51k - 6.894k = 0.616k 21.325uv - 1.325uv = 20uv 53xyz – 24.21yxz = 28.79xyz Edishta Resource Centre www.edishta.com

15. 15 Algebra – Addition and Subtraction (Fractions) Shall we move ahead to see some examples?... Addition Edishta Resource Centre www.edishta.com

16. 16 Algebra – Addition and Subtraction (Fractions) Shall we move ahead to see some examples?... Addition LCM is 12 and x so Edishta Resource Centre www.edishta.com

17. 17 Algebra – Addition and Subtraction (Fractions) Shall we move ahead to see some examples?... Addition LCM is 42 2n = Edishta Resource Centre www.edishta.com

18. 18 Algebra – Addition and Subtraction (Fractions) Shall we move ahead to see some examples?... Addition Coeff. is x so Ans. is LCM is 9 Subtraction lkm= 1klm Edishta Resource Centre www.edishta.com

19. 19 Algebra – Addition and Subtraction (Fractions) Shall we move ahead to see some examples?... Addition Subtraction LCM is 24 Edishta Resource Centre www.edishta.com

20. 20 Algebra – Addition and Subtraction (Fractions) Shall we move ahead to see some examples?... Addition Subtraction Edishta Resource Centre www.edishta.com

21. Algebra – Mixed Types What if we have fractions and decimals both? Convert either fraction to decimals or vice versa depending on easiness. Edishta Resource Centre www.edishta.com

22. Algebra – Mixed Types What if we have fractions and decimals both? Convert either fraction to decimals or vice versa depending on easiness. Fraction to decimal 3/5 = 0.6 Edishta Resource Centre www.edishta.com

23. Algebra – Mixed Types What if we have fractions and decimals both? Convert either fraction to decimals or vice versa depending on easiness. Fraction to decimal 3/4 = 0.75 + 2 = 2.75 Edishta Resource Centre www.edishta.com

24. Algebra – Mixed Types What if we have fractions and decimals both? Convert either fraction to decimals or vice versa depending on easiness. Decimal to fraction 0.3 = 3/10 (Multiply and divide by powers of 10 to remove decimal) Edishta Resource Centre www.edishta.com

25. Algebra – Mixed Types What if we have fractions and decimals both? Convert either fraction to decimals or vice versa depending on easiness. Fraction to decimal 5/16 = 0.3125 Edishta Resource Centre www.edishta.com

26. Algebra – Mixed Types What if we have fractions and decimals both? Convert either fraction to decimals or vice versa depending on easiness. Decimal to fraction 2.25 = 225/100 (Multiply and divide by powers of 10) 225/100 = 9/4 (Simplifying) Edishta Resource Centre www.edishta.com

27. Algebra – Mixed Types What if we have fractions and decimals both? Convert either fraction to decimals or vice versa depending on easiness. Edishta Resource Centre www.edishta.com

28. Algebra – Mixed Types What if we have –ve number greater among two? Basic rules says to apply the sign of greater number Edishta Resource Centre www.edishta.com

29. Algebra – Mixed Types What if we have –ve number greater among two? Basic rules says to apply the sign of greater number 3.2xy - 4.6yx = -1.2xy 3.13y - 10.9y = -7.77y -6.8a + 0.801a = -6.001a Edishta Resource Centre www.edishta.com

30. Algebra – Mixed Types What if we have –ve number greater among two? Basic rules says to apply the sign of greater number When you have two different signs + 3.2xy - 4.6yx = -1.2xy 3.13y - 10.9y = -7.77y -6.8a + 0.801a = -6.001a and – then do subtraction from bigger with smaller and assign sign of bigger number. Edishta Resource Centre www.edishta.com

31. Algebra – Unlike Terms If there are unlike terms Don’t do anything Just keep the same thing Edishta Resource Centre www.edishta.com

32. Algebra – Unlike Terms If there are unlike terms Don’t do anything Just keep the same thing 5.2x + 2.548xy = 5.2x + 2.548xy 8.75t + 4.37y = 8.75t + 4.37y Edishta Resource Centre www.edishta.com

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