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2.3 and 2.4
Multiplying and Dividing Fractions
• dimensional analysis
• Multiply positive and negative fractions.
Multiplying Fractions
When multiplying two fractions, you multiply the numerator of one fraction by the numerator of the other fraction, then
multiply the denominator of one fraction by the denominator of the other fraction. Then reduce your answer. Final answer
is circled in purple.
25 ·
12
=2
10
210
reduces to15
Multiply Positive Fractions
Answer:
Simplify.
Multiply the numerators.Multiply the denominators.
Divide 3 and 9 by their GCF, 3.3
1
Multiply Negative Fractions
Divide –3 and 12 by their GCF, 3.
The numerator and denominator have different signs, so the product is negative.
Multiply the numerators.Multiply the denominators.
Answer:
Multiplying Mixed Numbers
Change mixed numbers into improper fractions
Multiply numerator
Multiply denominator
Reduce
Multiply Mixed Numbers
Divide 16 and 4 by their GCF, 4.
Multiply the numerators.Multiply the denominators.
Estimate 3 × 2 = 6.
Multiply Mixed Numbers
Answer:
Simplify. Compare to the estimate.
VOLUNTEER WORK Last summer, the 7th graders
performed a total of 250 hours of community service.
If the 8th graders spent this much time
volunteering, how many hours of community service
did the 8th graders perform?
The 8th graders spent the amount of time as the
7th graders on community service.
Answer: The 8th graders did 300 hours of community service last summer.
1. A
2. B
3. C
4. D0% 0%0%0%
A. 175 hours B. 190 hours
C. 200 hours D. 225 hours
VOLUNTEER WORK Last summer, the 5th graders
performed a total of 150 hours of community service.
If the 6th graders spent this much time
volunteering, how many hours of community service
did the 6th graders perform?
Use Dimensional Analysis
WATER USE Low–flow showerheads use gallons
of water per minute. If family members shower a total
of hours per week, how much water does the
family use for showers each week?
Words Water used equals the time multiplied by the water flow rate.
Variable Let w represent the gallons of water used.
Equation
Divide by common factors and units.
Use Dimensional Analysis
Use Dimensional Analysis
Answer: If the family showers hours per week at a
rate of gallons per minute, they will use
350 gallons of water.
1. A
2. B
3. C
4. D
A. 15 gallons B. 38 gallons
C. 775 gallons D. 897 gallons 0% 0%0%0%
• multiplicative inverses
• reciprocals
• Divide positive and negative fractions.
Dividing Fractions
When dividing fractions one must multiply the first fraction by the reciprocal of the second fraction. Then reduce the final answer.
12 / 1
4= ?
1
4reciprocal =
41
12
●41
=42
42
= 2
Change division to multiplication with a twist
Divide Fractions and Mixed Numbers
The fractions have different signs, so the quotient is negative.
Answer:
Multiply by the multiplicative
Dividing Mixed Number
1. Change Mixed numbers into improper fractions
2. Change division to multiplication with a twist
3. Multiply the numerators; multiply the denominators
4. Reduce
Divide Fractions and Mixed Numbers
The multiplicative
inverse of
Divide 4 and 8 by their GCF, 4.
Estimate 3 ÷ (–2) = –1.5
Simplify.
Divide Fractions and Mixed Numbers
Check for Reasonableness
Compare to the estimate. The answer seems reasonable
because –1.5 is close to
Answer:
Divide by common factors.
= 5 Simplify.
Answer: The cinema shows the movie 5 times that day.
1. A
2. B
3. C
4. D
0% 0%0%0%
A. 4 times
B. 5 times
C. 6 times
D. 7 times
PAINTING It took the five members of the Johnson
family 10 days to paint the seven rooms of their
house. At this rate, how long will it take the four
members of the Reyes family to complete a similar
task in their house?
If 5 persons each worked days, the project required
person-days of work. Divide this number by
4 persons to find the number of days it will take the Reyes
family to complete their painting.
Multiply by the multiplicative inverse of 4,
which is .
Simplify.
Answer:
