The document discusses the rules for dividing monomials by monomials:
- Like bases are kept the same, and the exponent of the resulting monomial is found by subtracting the smaller exponent from the larger exponent.
- If the larger exponent is in the numerator, the result goes in the numerator. If the larger exponent is in the denominator, the result goes in the denominator.
- Examples are provided to demonstrate applying these rules to simplify expressions involving dividing monomials.
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The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
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Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
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Model Attribute Check Company Auto PropertyCeline George
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2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
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
base. =x 5− 3
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
base. =x 5− 3
If the larger exponent is in the
numerator, the result goes in the 2
numerator. =x
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
base. =x 5− 3
If the larger exponent is in the
numerator, the result goes in the 2
numerator. =x
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
base. =x 5− 3
If the larger exponent is in the
numerator, the result goes in the 2
numerator. =x
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 2
numerator. =x
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 2
numerator. =x
1
If the larger exponent is in the = 5
denominator, the result goes in a
the denominator.
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
4a 5−2
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
12 f 2 −1
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
12 f 2 −1
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.
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
Homework Assignment.
Good luck!