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Percent of a quantity, discounts and budgets

الأسبوع 23 · النسبة المئوية من كمية والخصومات ومسائل النسبة · 3 دروس
1

Finding a percent of a quantity with models

Discover Mathematics P6: Term 2, Unit 10, Lessons 10–11
GoalFind a percent of a quantity using 10% steps, fractions and grid or tape models.
New words
percent of a quantity · the part of the amount that the percent describes10% step · find 10% by dividing by 10, then build other percents from itcompare · to decide which amount is greater
Explanation

To find a percent of a quantity, pick the easiest road. Road 1: use 10%. Divide the quantity by 10 to get 10%, then build the percent: 30% is 3 tens, 5% is half of 10%. Road 2: use a fraction: 25% is 1/4, 50% is 1/2, 20% is 1/5. Road 3: use 1%. Divide by 100 and multiply: 12% of 50 is 0.5 × 12 = 6. A grid or a tape shows the same thing: each small square is 1% of the whole. Be careful when you compare. A bigger percent of a smaller whole can be a smaller amount than a smaller percent of a bigger whole.

★Remember
10% = quantity ÷ 10. 1% = quantity ÷ 100. Build any percent from 10%, 5% or 1%.
Worked examples
Percent10%30%5%35%
Amount of 20020601070
Find 35% of 200. 10% is 20, so 30% is 60. 5% is half of 20, which is 10. Then 35% = 60 + 10 = 70.
Find 12% of 50. 10% of 50 is 5 and 1% is 0.5, so 2% is 1. Then 12% = 5 + 1 = 6. Check with 1%: 0.5 × 12 = 6.
Compare 20% of 150 with 30% of 90. 20% of 150 = 30. 30% of 90 = 27. The bigger percent (30%) of the smaller whole gives the smaller amount.
Class activity

Percent hunt. Choose a number between 100 and 500 that ends in 0. Find 10%, 20%, 25%, 50% and 5% of it. Which one is easiest to find, and why?

Practice
1
Find 10% of 340.
2
Find 25% of 120.
3
Find 60% of 45.
4
Find 15% of 80.
5
Salma says: “25% of 40 is 25.” What is wrong? What is the right answer?