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Maths Quiz - Fractions 3 (Difficult) (Questions)

Fractions help us understand how parts make a whole. In 11 Plus Maths, they test your logic, accuracy and skill with numbers in exciting ways.

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Fascinating Fact:

Two thirds of the human body is water, so if you weigh 60 kilograms, around 40 kilograms of you is H2O.

In 11 Plus Maths, pupils use fractions to explore real-life proportions, conversions and number relationships. Understanding fractions builds the foundation for advanced maths topics such as algebra and ratio.

Key Terms

  • Proportion: A way of showing how quantities relate to each other in size or amount.
  • Numerator: The top number in a fraction that shows how many parts are being counted.
  • Denominator: The bottom number in a fraction that shows how many equal parts make the whole.

Parents can learn more about 11 Plus learning resources in our guide to 11 Plus courses and materials.

Frequently Asked Questions (Click to see answers)

How are fractions used in real life?

Fractions are used when measuring ingredients, dividing money, calculating discounts and comparing amounts. They are a key part of everyday maths.

How do you turn a fraction into a percentage?

To change a fraction into a percentage, divide the numerator by the denominator, then multiply the result by 100.

What is the difference between a fraction and a ratio?

A fraction shows part of a whole, while a ratio compares one quantity to another. For example, 1/2 is a fraction, but 1:2 is a ratio.

Try These Related Quizzes

1. What is 2⁄4 + 3⁄2 + 4⁄6 expressed as a mixed fraction?
[ ] 22⁄3
[ ] 24⁄6
[ ] 12⁄3
[ ] 15⁄6
2. What is 39⁄9 as a mixed fraction in its simplest form?
[ ] 43⁄9
[ ] 41⁄3
[ ] 41⁄4
[ ] 42⁄3
3. What is 26⁄6 as a mixed fraction in its simplest form?
[ ] 42⁄6
[ ] 41⁄6
[ ] 41⁄3
[ ] 42⁄3
4. If 25⁄28 of students passed their maths test, how many students failed their maths test?
[ ] 3 students
[ ] 5 students
[ ] 1⁄9 of students
[ ] 3⁄28 of students
5. What is 23⁄15 as an improper fraction in its simplest form?
[ ] 11⁄5
[ ] 33⁄15
[ ] 7⁄3
[ ] 12⁄5
6. What is seven-eighths of eight-twelfths in its simplest form?
[ ] 3⁄4
[ ] 7⁄12
[ ] 2⁄3
[ ] 5⁄6
7. How many 1⁄5 are there in 6⁄10?
[ ] 12
[ ] 8
[ ] 3
[ ] 6
8. A fifth of a fifth is the same as how many hundredths?
[ ] 20
[ ] 10
[ ] 5
[ ] 4
9. Peter the Postman had 560 letters to deliver. So far he has delivered 7⁄8 of them. How many letters has Peter still to deliver?
[ ] 490
[ ] 70
[ ] 120
[ ] 60
10. What is 46⁄9 as an improper fraction in its simplest form?
[ ] 11⁄3
[ ] 42⁄9
[ ] 14⁄3
[ ] 33⁄9
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Maths Quiz - Fractions 3 (Difficult) (Answers)
1. What is 2⁄4 + 3⁄2 + 4⁄6 expressed as a mixed fraction?
[x] 22⁄3
[ ] 24⁄6
[ ] 12⁄3
[ ] 15⁄6
2/4 + 3/2 + 4/6 = 6/12 + 18/12 + 8/12 = 8/12 = 32/12 = 2 8/12 = 22/3
First convert all the fraction to the same denominator (in this case twelfths), then add them. If the denominators are the same, you can add/subtract the fractions by simply adding/subtracting their numerators - it really is as easy as that! Finally, write the improper fraction as a mixed fraction
2. What is 39⁄9 as a mixed fraction in its simplest form?
[ ] 43⁄9
[x] 41⁄3
[ ] 41⁄4
[ ] 42⁄3
To convert an improper fraction to a mixed fraction, follow these steps:
1. Divide the numerator by the denominator.
2. Note the whole number remainder.
3. Write the number from step 1 as the whole number in front of the fractional part AND write the fractional part with the remainder in the numerator and keep the original denominator.
4. Simplify if possible STEP 1: 39 ÷ 9 = 4. STEP 2: Remainder 3. STEP 3: 43/9. Step 4: 41/3
3. What is 26⁄6 as a mixed fraction in its simplest form?
[ ] 42⁄6
[ ] 41⁄6
[x] 41⁄3
[ ] 42⁄3
To convert an improper fraction to a mixed fraction, follow these steps:
1. Divide the numerator by the denominator.
2. Note the whole number remainder.
3. Write the number from step 1 as the whole number in front of the fractional part AND write the fractional part with the remainder in the numerator and keep the original denominator.
STEP 1: 26 ÷ 6 = 4. STEP 2: Remainder 2. STEP 3: 42/6. Divide the numerator and denominator by 2 to reduce the fraction to its simplest form: 41/3
4. If 25⁄28 of students passed their maths test, how many students failed their maths test?
[ ] 3 students
[ ] 5 students
[ ] 1⁄9 of students
[x] 3⁄28 of students
25/28 of students passed their maths test BUT fractions alone DO NOT tell you the actual number of people or things involved. If you had been told that 28 took the test, then the answer would have been 3 students. Always be on the lookout for the BEST answer
5. What is 23⁄15 as an improper fraction in its simplest form?
[x] 11⁄5
[ ] 33⁄15
[ ] 7⁄3
[ ] 12⁄5
To convert a mixed fraction to an improper fraction, follow these steps:
1. Multiply the whole number part by the denominator.
2. Add this result to the numerator.
3. Write the fraction with step 2 in the numerator and keep the original denominator.
STEP 1: 2 × 15 = 30. STEP 2: 30 + 3 = 33. STEP 3: 33/15. Divide the numerator and denominator by 3 to reduce the fraction to its simplest form: 11/5
6. What is seven-eighths of eight-twelfths in its simplest form?
[ ] 3⁄4
[x] 7⁄12
[ ] 2⁄3
[ ] 5⁄6
The word OF means multiply: 7/8 × 8/12 = 56/96 = 7/12. You multiply the numbers in the denominator together, and you multiply the numbers in the numerator together to form a single fraction. This fraction can then be reduced to its simplest form: sometimes you can reduce the fractions before you multiply them together
7. How many 1⁄5 are there in 6⁄10?
[ ] 12
[ ] 8
[x] 3
[ ] 6
6/10 can be reduced to 3/5 (divide the numerator and the denominator by 2). Now you can see that 3/5 is thrice as much as 1/5.
8. A fifth of a fifth is the same as how many hundredths?
[ ] 20
[ ] 10
[ ] 5
[x] 4
The word OF means multiply: 1/5 × 1/5 = 1/25. You now have to divide 100 by 25 to find how many hundredths equal 1/25. 100 ÷ 25 = 4
9. Peter the Postman had 560 letters to deliver. So far he has delivered 7⁄8 of them. How many letters has Peter still to deliver?
[ ] 490
[x] 70
[ ] 120
[ ] 60
If Peter has delivered 7/8 of the letters, all you have to do is find 1/8 of 560: 1/8 x 560 = 560 ÷ 8 = 70
10. What is 46⁄9 as an improper fraction in its simplest form?
[ ] 11⁄3
[ ] 42⁄9
[x] 14⁄3
[ ] 33⁄9
To convert a mixed fraction to an improper fraction, follow these steps:
1. Multiply the whole number part by the denominator.
2. Add this result to the numerator.
3. Write the fraction with step 2 in the numerator and keep the original denominator.
STEP 1: 4 × 9 = 36. STEP 2: 36 + 6 = 42. STEP 3: 42/9. Divide the numerator and denominator by 3 to reduce the fraction to its simplest form: 14/3
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