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
54 ÷ 6 = 9
x4 = x, x, x, x
x2 = x, x
54x4 ÷ 6x2 = 9x2
Solution: 9x2
Answer (a) is the correct solution
27 ÷ 9 = 3
x3 = x, x, x
x4 = x, x, x, x
27x3 ÷ 9x4 = 3x
Solution: 3x
Answer (a) is the correct solution
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
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
9 ÷ 3 = 3
x3 = x, x, x
x2 = x, x
9x3 ÷ 3x2 = 3x
Solution: 3x
Answer (d) is the correct solution
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
16 ÷ 4 = 4
x4 = x, x, x, x
x = x
16x4 ÷ 4 = 4x3
Solution: 4x3
Answer (c) is the correct solution
6 ÷ 3 = 2
x = x
x = x
6x ÷ 3x = 2 (the “x” is cancelled out)
Solution: 2
Answer (b) is the correct solution
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
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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