2.3 and 2.4 Multiplying and Dividing Fractions

Main Idea/Vocabulary 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. 2 5 · 1 2 = reduces to 1 5

KC Animation: Multiplying Fractions

Example 1 Multiply Positive Fractions Answer: Simplify. Multiply the numerators. Multiply the denominators. Divide 3 and 9 by their GCF,

1.A 2.B 3.C 4.D Example 1 A. B. C. D.

Example 2 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:

1.A 2.B 3.C 4.D Example 2 A. B. C. D.

Multiplying Mixed Numbers Change mixed numbers into improper fractions Multiply numerator Multiply denominator Reduce

Example 3 Multiply Mixed Numbers Divide 16 and 4 by their GCF, 4. Multiply the numerators. Multiply the denominators. Estimate 3 × 2 = 6.

Example 3 Multiply Mixed Numbers Answer: Simplify. Compare to the estimate.

1.A 2.B 3.C 4.D Example 3 A. B. C. D.

Example 4 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.

Example 4 Answer: The 8th graders did 300 hours of community service last summer.

1.A 2.B 3.C 4.D Example 4 A.175 hoursB. 190 hours C.200 hoursD. 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?

Example 5 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? WordsWater used equals the time multiplied by the water flow rate. VariableLet w represent the gallons of water used. Equation

Example 5 Divide by common factors and units. Use Dimensional Analysis

Example 5 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 Example 5 A.15 gallonsB. 38 gallons C.775 gallonsD. 897 gallons

Main Idea/Vocabulary multiplicative inverses reciprocals Divide positive and negative fractions.

KC 1 BrainPop: Multiplying and Dividing Fractions

Dividing Fractions When dividing fractions one must multiply the first fraction by the reciprocal of the second fraction. Then reduce the final answer. 1 2 / 1 4 =? 1 4 reciprocal = ● 4 1 = = 2 Change division to multiplication with a twist

Example 1 Find a Multiplicative Inverse Answer:

1.A 2.B 3.C 4.D Example 1 A. B. C. D.

KC 2

Example 2 Divide Fractions and Mixed Numbers The fractions have different signs, so the quotient is negative. Answer: Multiply by the multiplicative

1.A 2.B 3.C 4.D Example 2 A. B. C. D.

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

Example 3 Divide Fractions and Mixed Numbers The multiplicative inverse of Divide 4 and 8 by their GCF, 4. Estimate 3 ÷ (–2) = –1.5

Example 3 Simplify. Divide Fractions and Mixed Numbers Check for Reasonableness Compare to the estimate. The answer seems reasonable because –1.5 is close to Answer:

1.A 2.B 3.C 4.D Example 3 A. B. C. D.

Example 4

Divide by common factors. = 5Simplify. Answer: The cinema shows the movie 5 times that day.

1.A 2.B 3.C 4.D Example 4 A.4 times B.5 times C.6 times D.7 times

Example 5 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.

Example 5 Multiply by the multiplicative inverse of 4, which is. Simplify. Answer: