This document provides instruction on dividing monomials and polynomials by monomials. It explains that when dividing monomials, the exponent of the base in the quotient is found by subtracting the exponent of the denominator from the exponent of the numerator. Several examples are worked through step-by-step to demonstrate this process. The document then directs students to practice problems on external websites to assess their understanding of dividing polynomials by monomials.

1. Dividing polynomials
by a monomial
Module 10 - Topic 4

2. Dividing a Monomial by a Monomial

3. Dividing a Monomial by a Monomial
Apply the rules for dividing
exponents:

4. Dividing a Monomial by a Monomial
Apply the rules for dividing
exponents:
Like bases, subtract smaller from
the larger exponent to get the
new exponent and keep the same
base.

5. Dividing a Monomial by a Monomial
Apply the rules for dividing
exponents:
Like bases, subtract smaller from
the larger exponent to get the
new exponent and keep the same
base.
If the larger exponent is in the
numerator, the result goes in the
numerator.

6. Dividing a Monomial by a Monomial
Apply the rules for dividing
exponents: x5
Like bases, subtract smaller from 3
the larger exponent to get the
x
new exponent and keep the same
base.
If the larger exponent is in the
numerator, the result goes in the
numerator.

7. Dividing a Monomial by a Monomial
Apply the rules for dividing
exponents: x 5
Like bases, subtract smaller from 3
the larger exponent to get the
x
new exponent and keep the same
5− 3
base. =x
If the larger exponent is in the
numerator, the result goes in the
numerator.

8. Dividing a Monomial by a Monomial
Apply the rules for dividing
exponents: x 5
Like bases, subtract smaller from 3
the larger exponent to get the
x
new exponent and keep the same
5− 3
base. =x
If the larger exponent is in the
numerator, the result goes in the
numerator. =x 2

9. Dividing a Monomial by a Monomial
Apply the rules for dividing
exponents: x 5
Like bases, subtract smaller from 3
the larger exponent to get the
x
new exponent and keep the same
5− 3
base. =x
If the larger exponent is in the
numerator, the result goes in the
numerator. =x 2
If the larger exponent is in the
denominator, the result goes in
the denominator.

10. Dividing a Monomial by a Monomial
Apply the rules for dividing
exponents: x 5
a4
Like bases, subtract smaller from 3 9
the larger exponent to get the
x a
new exponent and keep the same
5− 3
base. =x
If the larger exponent is in the
numerator, the result goes in the
numerator. =x 2
If the larger exponent is in the
denominator, the result goes in
the denominator.

11. Dividing a Monomial by a Monomial
Apply the rules for dividing
exponents: x 5
a 4
Like bases, subtract smaller from 3 9
the larger exponent to get the
x a
new exponent and keep the same
base. =x 5− 3 1
= 9− 4
If the larger exponent is in the a
numerator, the result goes in the
numerator. =x 2
If the larger exponent is in the
denominator, the result goes in
the denominator.

12. Dividing a Monomial by a Monomial
Apply the rules for dividing
exponents: x 5
a 4
Like bases, subtract smaller from 3 9
the larger exponent to get the
x a
new exponent and keep the same
base. =x 5− 3 1
= 9− 4
If the larger exponent is in the a
numerator, the result goes in the
numerator. =x 2
1
If the larger exponent is in the = 5
denominator, the result goes in a
the denominator.

13. Simplify.
5 3
8a b
2 7
6a b

14. Simplify.
5
8a b 3
Reduce the
2 7 numerical part by
6a b
dividing the 8 and
6 by 2.

15. Simplify.
5
8a b 3
Reduce the
2 7 numerical part by
6a b
dividing the 8 and
4
8a b 5 3
6 by 2.
2 7
3 6a b

16. Simplify.
5
8a b 3
Reduce the
2 7 numerical part by
6a b
dividing the 8 and
4
8a b 5 3
6 by 2.
2 7
3 6a b
Apply the rules for
dividing powers
with like bases.

17. Simplify.
5
8a b 3
Reduce the
2 7 numerical part by
6a b
dividing the 8 and
4
8a b 5 3
6 by 2.
2 7
3 6a b
Apply the rules for
5−2
4a dividing powers
7− 3 with like bases.
3b
3 And you are done
4a
4
dividing a monomial
3b by a monomial.

18. Simplify each of the following.
8 2 3 5
12d f 27h jk
10 9 9
30d f 9h jk

19. Simplify each of the following.
8 2 3 5
12d f 27h jk
10 9 9
30d f 9h jk
2 2 −1
12 f
= 10 − 8
5 30 d

20. Simplify each of the following.
8 2 3 5
12d f 27h jk
10 9 9
30d f 9h jk
2 2 −1
12 f
= 10 − 8
5 30 d
2f
= 2
5d

21. Simplify each of the following.
8 2 3 5
12d f 27h jk
10 9 9
30d f 9h jk
2 3
2 −1
12 f 27 j
= 10 − 8
= 9− 3 9−5
5 30 d 1 9h jk
2f
= 2
5d

22. Simplify each of the following.
8 2 3 5
12d f 27h jk
10 9 9
30d f 9h jk
2 3
2 −1
12 f 27 j
= 10 − 8
= 9− 3 9−5
5 30 d 1 9h jk
2f 3
= 2 = 6 4
5d h k

23. Algebra Cruncher Problems
Follow this link to try a couple on your own at Cool Math.
Notice when you select the “Give me a Problem” button
to try new problems, 2 rows are generated. Look
carefully between them. That red line indicates this
problem is a fraction.
Do your work in a notebook before entering your answer.
When you select “What’s the Answer?” compare your
answer with the given answer.
Keep selecting new problems until you get 3
consecutive problems correct.

24. Divide a Polynomial by a Monomial
Visit this Cool math website to learn about dividing
a Polynomial by a monomial.
Be sure to click the “next page” to review the 2
pages of notes.
Complete the “Try it” problem on page 2 in your
notebook.

25. Try It - Page 2
( 4wy − 20w + 6wy − 7 ) ÷ 4wy
2 2 2

26. Try It - Page 2
( 4wy − 20w + 6wy − 7 ) ÷ 4wy
2 2 2
2 2
4wy 20w 6wy 7
= 2
− 2
+ 2
− 2
4wy 4wy 4wy 4wy

27. Try It - Page 2
( 4wy − 20w + 6wy − 7 ) ÷ 4wy
2 2 2
2 2
4wy 20w 6wy 7
= 2
− 2
+ 2
− 2
4wy 4wy 4wy 4wy
2 5 2 −1 3
4wy 20 w 6w 7
= − 2
+ 2 −1
− 2
4wy 2
1 4y 2 4 wy 4wy

28. Try It - Page 2
( 4wy − 20w + 6wy − 7 ) ÷ 4wy
2 2 2
2 2
4wy 20w 6wy 7
= 2
− 2
+ 2
− 2
4wy 4wy 4wy 4wy
2 5 2 −1 3
4wy 20 w 6w 7
= − 2
+ 2 −1
− 2
4wy 2
1 4y 2 4 wy 4wy
5w 3 7
= 1− 2 + − 2
y 2y 4wy

29. Still a little confused?
Here’s another tiny lesson dividing a
polynomial by a monomial.
Only view the “Steps for Dividing a
Polynomial by a Monomial.”

30. It’s Practice time...
Go to the Regents Prep website to
practice dividing a polynomial by a
monomial. Only practice questions 1
through 7!
Message or Pronto me if you have
questions.

31. Shall we Play a GAME?
Check your knowledge on Dividing Polynomials by playing
Jeopardy. Ok, technically it’s called Challenge Board but
it’s the same idea! There are 4 categories: horseshoes,
handgrenades, doesn’t count, and polynomial long division.
Polynomial long division is not covered in Algebra 1 so
either stay away from this topic or challenge yourself!
You have the option to play alone or against a friend or
family member.
You could even arrange a time with a classmate to meet
on Pronto to play. Try the App Share feature to see the
same game board!

32. Congratulations!
You’ve finished the notes and practice
for Dividing a Polynomial by a Monomial.
You are now ready to proceed to the
Mastery Assignment.
Good luck!