Expressing one quantity as a percentage of another is in the Primary 5 Percentage chapter. The lesson film below teaches it with its own questions, and the practice set is written for Primary 5.
Lesson video, with the working
Name the whole first
4 min 14 s
The film teaches 2 questions in turn. Each question shows first; its working is written as the film explains it.
There are 75 books on a shelf. Fifteen of them are comic books. Express the number of comic books as a percentage of the number of books on the shelf.
Comic books are 20% of the shelf
Ans: 20%
Example 1
A lesson lasted 45 minutes. Eighteen minutes of the lesson were spent on practice. Express the time spent on practice as a percentage of the length of the whole lesson.
40% of the whole lesson was practice
Ans: 40%
How to solve it
Name the whole first: the amount the question puts after the words percentage of. Here it is all 75 books, which is 100 percent.
Write the part over the whole: 15 comic books over 75 books.
Simplify the fraction: 15 and 75 both divide by 15, which leaves 1 over 5, or one fifth.
Times it by 100 percent: one fifth of 100 is 20, so the comic books are 20 percent.
Use the same method for a new whole: 18 minutes out of 45 is 18 over 45, which is two fifths, or 40 percent.
A part turns into a percentage as the part over the whole, times one hundred percent. So name the whole first: whatever amount the question puts after the words percentage of, and here that is all 45 minutes of the lesson.
Practice questions with worked solutions
Question 1 is free to try. The other 9 open in the free trial, each with its full working.
Question 1 of 10 · Basic · free to tryBala answered 17 of the 20 questions in a quiz correctly. Express the number…Bala answered 17 of the 20…
Bala answered 17 of the 20 questions in a quiz correctly. Express the number of questions he answered correctly as a percentage of the total number of questions.
How do you work out P5 part of a whole as a percentage questions?
When the whole is not 100, your child needs a method to express a part of it as a percentage.
What your child learns here
When the whole is not 100, your child needs a method to express a part of it as a percentage. This page teaches part over whole times 100%, simplifying the fraction first so that the multiplication is easy, as with 15 comic books out of 75 books.
Write the part over the whole: 15 comic books out of 75 books is 15/75.
Simplify before multiplying: 15/75 = 1/5, and 1/5 × 100% = 20%.
The whole is the quantity named after the words 'as a percentage of'.
When the question asks about the rest, find that part first: 50 m of wall with 15 m painted leaves 35 m unpainted.
The answer carries the % sign, and it can include a half, such as 37.5%.
Does the answer make sense?
Multiply back. 85% of 20 questions is 20 ÷ 100 × 85 = 17, the number Bala answered correctly, so 85% is right. A size check agrees: 17 out of 20 is close to full marks, so the percentage should be close to 100%.
How to practise these questions
Free Question 1 gives Bala's quiz score of 17 out of 20 and asks for it as a percentage of all the questions. Basic questions train part over whole times 100% with shaded parts of a rectangle, books on a shelf, minutes of a lesson and sheets used from a packet. Intermediate questions find the part that is left first, such as the wall still unpainted or the pastries that were tarts. Challenge questions build the part or the whole from several amounts, use water from a tank on two days, or take their numbers from a bar graph or a pie chart. If the part and the whole get swapped, open its worked solution and try the question again later from Revision.
Questions parents ask
What does 'express as a percentage' mean? It means writing one quantity as a number out of 100 of another. The working is part over whole, times 100%, and the answer ends with the % sign.
How does my child know which number is the whole? The whole is the quantity named after 'as a percentage of', such as the number of books on the shelf or the length of the whole lesson.
Is expressing a part as a percentage in the P5 syllabus? Yes. Expressing a part of a whole as a percentage is the first Primary 5 percentage outcome, and every later percentage question leans on it.
