1.4 Compound Proportions and Rates of Work

• Proportional parts
• Ratios
• Rates of work

• divide quantities into proportional parts in real-life situations
• relate different proportional parts in real-life situations
• work out compound proportions using the ratio method in different situations
• calculate rates of work in real-life situations
• appreciate the use of compound proportions and rates of work in real-life situations

“What are proportions?”

“Why do we work fast?”

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1. What a proportion is
   40 min · 1 practice tasks · quiz
   A proportion is two equal ratios. Scale a mix or a share by multiplying every part by the same number.
2. Divide a quantity in the ratio 2:3
   40 min · 1 practice tasks · quiz
   Split KSh 5000 into five equal parts. Ama takes two parts, Bora takes three.
3. Three-part ratio 2:3:5
   40 min · 1 practice tasks · quiz
   Share KSh 10000 among three people in 2:3:5 using ten equal parts of 1000.
4. A share as a fraction of the whole
   40 min · 1 practice tasks · quiz
   In 2:3, Ama is 2/5 of the money and Bora is 3/5. Multiply the fraction by the total.
5. Relating different proportional parts
   40 min · 1 practice tasks · quiz
   Compare 2:3 and 3:5 by writing each first share as a fraction of the same whole.
6. Compound proportion when B already matches
   40 min · 1 practice tasks · quiz
   If A:B = 2:3 and B:C = 3:5, then A:B:C = 2:3:5 because B is already the same 3.
7. Compound proportion when B must be scaled
   40 min · 1 practice tasks · quiz
   If A:B = 2:3 and B:C = 4:5, scale to 8:12 and 12:15 so B matches, then join 8:12:15.
8. Rate of work: job per hour
   40 min · 1 practice tasks · quiz
   Wanjiku paints one classroom in 6 hours, so her rate is 1/6 of the classroom each hour.
9. More workers, less time
   40 min · 1 practice tasks · quiz
   4 workers take 6 days, so the job is 24 worker-days. 8 workers take 3 days. Double workers, half the time.
10. A and B working together
    40 min · 1 practice tasks · quiz
    Add rates. A at 1/6 per hour and B at 1/3 per hour paint 1/2 classroom per hour, so they finish in 2 hours.
11. Kenya word problems: share, mix, paint
    40 min · 1 practice tasks · quiz
    Four local stories: a matatu fare 1:2, ugali 2:3, concrete 1:2:4, and 60 worker-days on a classroom.
12. Review: parts, compound, rates
    40 min · 1 practice tasks · quiz
    Four tools on one page: add parts, write fractions, match B, then work over time. Check every answer against the whole job or the whole money.