simplifying if terms have the same letters they are called like terms. if they have different...
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ALGEBRA REMINDER 1
Simplifying
If terms have the same letters they are called LIKE terms. If they have different letters they are called UNLIKE terms. Order of letters does not matter
LIKE terms can be added or subtracted. 3a + 5a = 8a 7bc – 4bc + 2bc = 5bc 3ab + 7ba = 10ab
UNLIKE terms ______ be added or subtracted. 3a + 5b = 3a + 5b
If there are both LIKE and UNLIKE terms just add or subtract the like ones.
3y + 5z + 11y = 3y + 11y + 5z = 14y +5z
REMEMBER: The sign in front of each number belongs to that number (no sign means +).
10e + 5a – 5e - 20a + 2e = 10e – 5e + 2e + 5a - 20a = 7e - 15a
Questions
1. 3a + 7a =
2. 13b – 5b =
3. 5c - 2c + 10c =
4. 5d + d + 6d =
5. 9e – 4e + e =
6. 12f + 5g =
7. 19h - 3h + 7i =
8. 12j + 3k – k =
9. 100L – 17M + 3M =
10. 7xz – 6yx + 3zx – 19yz + 12xy – zy =
Questions
1. 3a + 7a =
2. 13b – 5b =
3. 5c - 2c + 10c =
4. 5d + d + 6d =
5. 9e – 4e + e =
6. 12f + 5g =
7. 19h - 3h + 7i =
8. 12j + 3k – k =
9. 100L – 17M + 3M =
10. 7xz – 6yx + 3zx – 19yz + 12xy – zy =
10a8b
13c
12d
6e
12f + 5g 16h +
7i12j + 2k 100L -14M
10xz + 6xy – 20z
Questions
1. 5a + 13a =
2. 23b – 11b =
3. 4c - 2c + 200c =
4. 13d + 5d – d =
5. 3e – 10e + e =
6. 17.35F – 0.055G =
7. 12h – 3i + 7h =
8. 100j + 30k – 7k =
9. 5L – 17M – 30L=
10. 7Y – 5Z + 30Y – 11ZY + 12Z – Y + YZ =
18a12b
202c17d6e
17.35F – 0.055G19h – 3i
100j + 23k– 25L – 17M 36Y + 7Z –
10YZ
Algebra Multiplying
There are three steps to multiply things in algebra.
Signs Numbers Letters
Step 1
Decide if your answer is positive or negative.
+ times + Answer is _________. – times – Answer is _________. – times + Answer is _________. + times – Answer is _________.
e.g. -3a x 5b answer is _________.
positive
positivenegative
negative
negative
Step 2
Multiply the numbers.
Just multiply the numbers, ignore signs and letters.
e.g. -3a x 5b number is _________.
8C x 10g number is _________.
15
80
Step 3
Write all of the letters in the question next to the sign and number.
REMEMBER: Powers are where there are lots of the same type of letter. t3 is ttt.
e.g. -3a x 5b letters are _________. 8C x 10g letters are _________. 0.5f x 20t3 letters are _________.
abCgft3
Then you put it all together
e.g. 5p x -3ysign = negativenumber = 15letters = pyAnswer = -15py
1. 9c x 3b2. 12a x -3e3. 7c x 6c4. -5d x - 2y5. 5e x 20eb6. -2y x -7y2
7. -8tu x -4rt3
8. 4d x -12d2r
9. 19a x -2by2
10.-4de x -9ek
11.5 x 7u12.-8 x -7y2
13.12e2y x -414.y x 12e15.8d x d16.-100G x G2
17.0.4r x -10br18.0.1G2 x 52GT19.2d x 15r x -2t20.4y x -0.1y2 x
= 27cb= -36ae=
42c2= 10dy= 100e2b= 14y3= 32rt4u
= -48rd3= -38aby2= 36de2k
= 35u
= 56y= -48e2y
= 12ey= 8d2
= -100G3= -4br2= 5.2G3T= -60drt= -0.8y3x2
Algebra Dividing
There are three steps to divide things in algebra.
Signs Numbers Letters
Step 1
Decide if your answer is positive or negative.
+ divided by + Answer is _________. – divided by – Answer is _________. – divided by + Answer is _________. + divided by – Answer is _________.
e.g. -3a ÷ -5b answer is _________.
positive
positivenegative
negative
positive
Step 2
Simplify the numbers.
Make the numbers into a fraction.Simplify the fraction if you can.
e.g. 3a ÷ 5b fraction is ___.
9C ÷ 21g number is ___ = ___.
35
921
37
Step 3
Write all of the letters. REMEMBER: Powers are where there are lots of the same type of letter. t3 is ttt.
Cross out any letters that are on both the top and the bottom.
e.g. -3ac x 5bc top letters are _________.
bottom letters are _________.
acbc
ab
Put your answer together as a fraction.
If one of the numbers is a 1. You don’t have to write it unless it is the only thing on top of the fraction.
