Understanding Percentages
Year 5 · Maths · Free — no account needed
Understanding Percentages
What does "percent" mean?
The word "percent" means "out of 100". The symbol % is a quick way to write "per hundred". So 25% means 25 out of 100 equal parts of something.
100% is the whole
When something is 100%, that means all of it — the complete whole, with nothing left over. If a bucket is 100% full, there is no room left. If 100% of a class attended an excursion, every single student went.
Familiar percentages and their partners
Some percentages are so common that it helps to know their fraction and decimal partners by heart:
- 100% = 1 whole = 1.0
- 50% = 1/2 = 0.5
- 25% = 1/4 = 0.25
- 75% = 3/4 = 0.75
- 10% = 1/10 = 0.1
- 20% = 1/5 = 0.2
To turn a percentage into a decimal, divide by 100 (move the decimal point two places left). For example, 40% = 40 ÷ 100 = 0.4.
Using percentages to compare
Percentages let us compare amounts fairly, even when they come from different situations. Because every percentage is "out of 100", 60% is always bigger than 40%, no matter what it is a percentage of.
Worked Example
Two shops have sales on the same day. Shop A takes 30% off. Shop B takes 1/4 off. Which shop offers the bigger discount? Step 1: Change 1/4 into a percentage so both discounts are in the same form. 1/4 = 25/100 = 25%. Step 2: Compare the two percentages: 30% and 25%. Step 3: 30 is greater than 25, so 30% is bigger than 25%. Shop A offers the bigger discount.
Practice
What does 100% represent?
Flashcards
What does the word "percent" mean?
"Out of 100" — the % symbol is a short way of writing per hundred.
What does 100% represent?
The complete whole — all of something, with nothing left out.
What is 50% as a fraction and a decimal?
1/2 and 0.5
What is 25% as a fraction and a decimal?
1/4 and 0.25
How do you change a percentage into a decimal?
Divide by 100 (move the decimal point two places left).
How do you compare two percentages?
Compare the numbers directly — since both are out of 100, the bigger number is the bigger percentage.
All 15 practice questions
What does 100% represent?
- A tiny fraction
- Half of the whole
- None of the whole
- The complete whole
Show the answer to question 1
Answer: The complete whole
100% means 100 out of 100 parts, so it represents the complete whole.
What is 50% written as a fraction?
- 1/2
- 1/4
- 1/10
- 1/5
Show the answer to question 2
Answer: 1/2
50% = 50/100, which simplifies to 1/2.
What is 25% written as a decimal?
- 0.025
- 0.25
- 2.5
- 25.0
Show the answer to question 3
Answer: 0.25
25% = 25 ÷ 100 = 0.25.
What is 75% written as a fraction?
- 3/4
- 1/4
- 7/5
- 3/5
Show the answer to question 4
Answer: 3/4
75% = 75/100, which simplifies to 3/4.
Which is bigger, 60% or 45%?
- 45%
- 60%
- Cannot tell
- They are equal
Show the answer to question 5
Answer: 60%
Both are out of 100, and 60 is more than 45, so 60% is bigger.
Which is bigger, 1/2 or 30%?
- They are equal
- Cannot tell
- 1/2
- 30%
Show the answer to question 6
Answer: 1/2
1/2 = 50%, and 50% is bigger than 30%, so 1/2 is bigger.
What is 0.1 written as a percentage?
- 0.1%
- 1%
- 10%
- 100%
Show the answer to question 7
Answer: 10%
0.1 × 100 = 10, so 0.1 as a percentage is 10%.
What is 1/5 written as a percentage?
- 5%
- 50%
- 20%
- 15%
Show the answer to question 8
Answer: 20%
1/5 = 20/100, so 1/5 as a percentage is 20%.
A jug is 100% full. How much water is missing?
- A quarter missing
- Half missing
- None missing
- All missing
Show the answer to question 9
Answer: None missing
100% represents the complete whole, so nothing is left over — None missing is correct.
Which decimal equals 20%?
- 0.2
- 0.02
- 2.0
- 0.5
Show the answer to question 10
Answer: 0.2
20% = 20 ÷ 100 = 0.2.
A garden bed is 10% weeds. What fraction of the garden bed is weeds?
- 1/4
- 1/10
- 1/5
- 1/2
Show the answer to question 11
Answer: 1/10
10% = 10/100, which simplifies to 1/10 of the garden bed.
What is 90% written as a decimal?
- 9.0
- 0.09
- 0.19
- 0.9
Show the answer to question 12
Answer: 0.9
90% = 90 ÷ 100 = 0.9.
Which is smaller, 10% or 1/4?
- 1/4
- 10%
- Cannot tell
- They are equal
Show the answer to question 13
Answer: 10%
1/4 = 25%, and 10% is less than 25%, so 10% is smaller.
In a class, 100% of students attended the excursion. How many students did NOT attend?
- Half the class
- A few students
- Most of the class
- None - every student attended
Show the answer to question 14
Answer: None - every student attended
100% represents the complete whole, so every student attended and None - every student attended is correct.
Which percentage is equivalent to 0.75?
- 0.75%
- 7.5%
- 75%
- 750%
Show the answer to question 15
Answer: 75%
0.75 × 100 = 75, so 0.75 as a percentage is 75%.
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