 How good are you at monomials?

Pre-Algebra - Monomials: Division

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A monomial is one number that stands on its own such as the number 8 or 9x or 15x2. To divide two monomials is really very easy. Let’s look at the following example.

25x3 ÷ 5x2

Here we can easily divide 25 by 5 giving us the answer of 5. However, our variables x3 and x2 are different. So we need to break these out as follows:

x3 = x, x, x
x2 = x, x

Next you cross off a corresponding x from each variable. When you do this, it leaves one x left. This means the solution for our problem is: 25x3 ÷ 5x2 = 5x

1.
10x6 ÷ 5x4
50x10
2x10
50x22
2x2
10x6 ÷ 5x4
10 ÷ 5 = 2
x6 = x, x, x, x, x, x
x4 = x, x, x, x
10x6 ÷ 5x4 = 2x2
Solution: 2x2
Answer (d) is the correct solution
2.
45x5 ÷ 5x4
9x9
9x
9x20
9x5
45x5 ÷ 5x4
45 ÷ 5 = 9
x5 = x, x, x, x, x
x4 = x, x, x, x
45x5 ÷ 5x4 = 9x
Solution: 9x
Answer (b) is the correct solution
3.
16x4 ÷ 4x
4x5
4x4
4x3
4x
16x4 ÷ 4x
16 ÷ 4 = 4
x4 = x, x, x, x
x = x
16x4 ÷ 4 = 4x3
Solution: 4x3
Answer (c) is the correct solution
4.
36x7 ÷ 6x4
6x
6x21
6x3
6x11
36x7 ÷ 6x4
36 ÷ 6 = 6
x7 = x, x, x, x, x, x, x
x4 = x, x, x, x
36x7 ÷ 6x4 = 6x3
Solution: 6x3
Answer (c) is the correct solution
5.
9x3 ÷ 3x2
3x3
3x5
3x6
3x
9x3 ÷ 3x2
9 ÷ 3 = 3
x3 = x, x, x
x2 = x, x
9x3 ÷ 3x2 = 3x
Solution: 3x
Answer (d) is the correct solution
6.
42x7 ÷ 7x3
6x3
6x21
6x4
6x10
42x7 ÷ 7x3
42 ÷ 7 = 6
x7 = x, x, x, x, x, x, x
x3 = x, x, x
42x7 ÷ 7x3 = 6x4
Solution: 6x4
Answer (c) is the correct solution
7.
27x3 ÷ 9x4
3x
3x7
3x2
3x12
27x3 ÷ 9x4
27 ÷ 9 = 3
x3 = x, x, x
x4 = x, x, x, x
27x3 ÷ 9x4 = 3x
Solution: 3x
Answer (a) is the correct solution
8.
54x4 ÷ 6x2
9x2
9x4
9x6
9x8
54x4 ÷ 6x2
54 ÷ 6 = 9
x4 = x, x, x, x
x2 = x, x
54x4 ÷ 6x2 = 9x2
Solution: 9x2
Answer (a) is the correct solution
9.
6x ÷ 3x
2x
2
2x2
0
6x ÷ 3x
6 ÷ 3 = 2
x = x
x = x
6x ÷ 3x = 2 (the “x” is cancelled out)
Solution: 2
Answer (b) is the correct solution
10.
2x5 ÷ 2x4
4x9
x
4x
x9
2x5 ÷ 2x4
2 ÷ 2 = 1
x5 = x, x, x, x, x
x4 = x, x, x, x
2x5 ÷ 2x4 = x
Solution: x
Answer (b) is the correct solution
Author:  Christine G. Broome

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