Egypt Primary 6 Mathematics, Week 22: Finding the part, the whole or the percent

Percent: part, whole and percent

Week 22 · Percent, fractions and decimals; the part, the whole and the percent · 3 lessons

Finding the part, the whole or the percent

Discover Mathematics P6: Term 2, Unit 10, Lessons 7–9

GoalRecognise the three kinds of percent problem and solve each with a tape diagram.

New words

part · the amount that is taken from the wholewhole · the full amount, which is 100%tape diagram · a drawing of a bar split into equal parts to show the numbers

Explanation

Every percent problem has three numbers: the PART, the WHOLE and the PERCENT. “25% of 80 is 20” has whole 80, percent 25 and part 20. One of the three is missing in each problem. To find the part, change the percent into a fraction and take it of the whole: 25% of 80 = 1/4 of 80 = 20. To find the percent, write part/whole as a fraction and make the denominator 100: 18 out of 60 is 18/60 = 3/10 = 30%. To find the whole, use the tape: the whole is 100%, so find 1% or 10% first. Draw a tape for the whole and mark the part on it.

★Remember

Part = percent of the whole. The whole is 100%. Ask first: which of the three is missing?

Worked examples

Find the part. A school trip has 80 pupils and 25% of them are girls. Part = 25% of 80 = 80 ÷ 4 = 20 girls.

Find the percent. 18 of the 60 books on a shelf are stories. Percent = 18/60 = 3/10 = 30/100 = 30%.

Find the whole. 15 is 30% of a number. 30% is three tenths, so 10% is 15 ÷ 3 = 5. The whole is 100%, which is 10 × 5 = 50. Check: 30% of 50 = 15.

Class activity

Three kinds. Make your own three problems about your class: one that asks for the part, one for the percent and one for the whole. Give them to a friend to solve.

Practice

What is 50% of 64?

20 of 50 pupils wear glasses. What percent is that?

9 is 10% of a number. What is the number?

Find 75% of 200.

In which of these is the whole 60: “30% of 60 is 18” or “18% of 30 is 60”? Which statement is true?