REVIEW: 4.1 • Simplify each fraction using your preferred method. 3 4 4 2 50 55 − 36 6 54 4 − 306 234
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REVIEW: 4.1
• Simplify each fraction using your preferred method.
3𝑎𝑥4
4 𝑎2𝑥5055
−36𝑐 𝑑6
54𝑐 𝑑4−306234
4.2- MULTIPLYING FRACTIONSMultiply the fractions and then simplify the result.
58𝑜𝑓45
×
×
product
product
¿2040
simplify
÷
÷
22
quotient
quotient
12
1125𝑜𝑓1011
product
product
¿ ❑❑
simplify
÷
÷
❑❑
quotient
quotient
❑❑
4.2- MULTIPLYING FRACTIONSTo multiply two fractions, multiply the numerators and multiply the denominators. Simplify the result, if possible.
12∙35
¿310
×
×
product
product
78∙35
¿2140
×
×
product
product
4.2- MULTIPLYING FRACTIONS
−34 ( 75 )=¿−
2120
(− 56 )(− 13 )=¿518
Apply the rules for multiplying integers when multiplying fractions.
4.2- MULTIPLYING FRACTIONS
34
(−3 )=¿ −94
(− 14 ) (−9 )=¿
When multiplying by a whole number or integer, make the whole number or integer into an equivalent fraction.
34 (− 31 )=¿
product
product
−14 (−❑
❑ )=¿94
4.2- MULTIPLYING FRACTIONS
23 (− 914 )(− 710 )=¿
Multiply and simplify (cross-cancel).
3
1
1
2
1
5
1∙3 ∙11∙2 ∙5
¿310
4.2- MULTIPLYING FRACTIONSThe same rules apply when multiplying algebraic fractions.
−𝑡 2
21𝑟∙14 𝑟𝑡4
=¿−𝑡 ∙𝑡 ∙2 ∙7 ∙𝑟
3 ∙7 ∙𝑟 ∙ 𝑡 ∙𝑡 ∙ 𝑡 ∙ 𝑡
¿−2
3 𝑡 2
5𝑏2∙47𝑏
−2𝑎3
15𝑏∙35𝑎𝑏8 𝑎5
4.2- MULTIPLYING ALGEBRAIC FRACTIONS
4.2- MULTIPLYING ALGEBRAIC FRACTIONS
14
(4 𝑦 ) ¿ 14∙( 4 𝑦1 )
¿1∙ 4 ∙ 𝑦4 ∙1
¿ 𝑦
9𝑎 ∙13𝑎
12𝑚 ( 16𝑚 )
4.2- MULTIPLYING ALGEBRAIC FRACTIONS
4.2- EXPONENTIAL EXPRESSIONS WITH FRACTIONAL BASES
The exponent applies to both the numerator and denominator.
( 25 )3
¿ ( 2 ∙2 ∙25∙5 ∙5 )❑
¿8125
4.2- EXPONENTIAL EXPRESSIONS WITH FRACTIONAL BASES
The exponent applies to both the numerator and denominator.
(− 34 )2
¿ (−3 ∙−3−4 ∙−4 )❑
¿916
4.2- EXPONENTIAL EXPRESSIONS WITH ALGEBRAIC FRACTIONAL BASES
(− 3 𝑡4 )2
¿−(−3 ∙−3 ∙−𝑡 ∙−𝑡−4 ∙−4 )❑
¿ 9 𝑡2
16
(− 4 𝑥5 )3
−( 2𝑥3 )2
4.2- SOLVE APPLICATION PROBLEMS BY MULTIPLYING FRACTIONS
If the President vetoes a bill, it takes of those voting in the House of Representatives and the Senate to override the veto for it to become law. If all 435 members of the house cast a vote, how many of their votes does it take to override a presidential veto?
What is of 435?
What is of 435?
23𝑜𝑓4351
×
׿8703
¿290
290 votes would be needed to override a presidential veto if all members of the House were present.
If only 96 Senators are present and cast a vote, how many of their votes does it take to override a presidential veto?
base
height height
base
height
base
𝐴=12(𝑏𝑎𝑠𝑒)(h h𝑒𝑖𝑔 𝑡 )𝐴=
12∙𝑏 ∙ h 𝐴=
h𝑏2
27 in.16 in.
h = 6 feeth = 200 miles
b = 11 feetb = 405 miles
Answers must be in square units!
HW PROBLEMS FOR 4.2
Page 327- #1, 2, 3, 4, 5, 6, 123, 124, 125, 126Page 421- #21-38 (all)