# 11-Plus Maths Quiz - Fractions 3 (Difficult) (Questions)

Welcome to the third quiz in our Difficult section of Eleven Plus maths on fractions. In it you will be tested on your ability to perform multiplication and division with fractions, and more besides!

As in previous quizzes, you will need to know the difference between a numerator and denominator, or between a mixed and an improper fraction. If you have played the previous quizzes then of course you will know. If not, don’t worry – everything is explained in the helpful comments after each question.

Make sure you read each question carefully before you choose your answer. Let’s see if you can get all ten questions right first time. Good luck!

1. What is 24 + 32 + 46 expressed as a mixed fraction?
 [ ] 22⁄3 [ ] 24⁄6 [ ] 12⁄3 [ ] 15⁄6
2. What is 399 as a mixed fraction in its simplest form?
 [ ] 43⁄9 [ ] 41⁄3 [ ] 41⁄4 [ ] 42⁄3
3. What is 266 as a mixed fraction in its simplest form?
 [ ] 42⁄6 [ ] 41⁄6 [ ] 41⁄3 [ ] 42⁄3
4. If 2528 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 2315 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 15 are there in 610?
 [ ] 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 78 of them. How many letters has Peter still to deliver?
 [ ] 490 [ ] 70 [ ] 120 [ ] 60
10. What is 469 as an improper fraction in its simplest form?
 [ ] 11⁄3 [ ] 42⁄9 [ ] 14⁄3 [ ] 33⁄9
11-Plus Maths Quiz - Fractions 3 (Difficult) (Answers)
1. What is 24 + 32 + 46 expressed as a mixed fraction?
 [x] 22⁄3 [ ] 24⁄6 [ ] 12⁄3 [ ] 15⁄6
24 + 32 + 46 = 612 + 1812 + 812 = 812 = 3212 = 2 812 = 223
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 399 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: 439. Step 4: 413
3. What is 266 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: 426. Divide the numerator and denominator by 2 to reduce the fraction to its simplest form: 413
4. If 2528 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
2528 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 2315 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: 3315. Divide the numerator and denominator by 3 to reduce the fraction to its simplest form: 115
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: 78 × 812 = 5696 = 712. 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 15 are there in 610?
 [ ] 12 [ ] 8 [x] 3 [ ] 6
610 can be reduced to 35 (divide the numerator and the denominator by 2). Now you can see that 35 is thrice as much as 15.
8. A fifth of a fifth is the same as how many hundredths?
 [ ] 20 [ ] 10 [ ] 5 [x] 4
The word OF means multiply: 15 × 15 = 125. You now have to divide 100 by 25 to find how many hundredths equal 125. 100 ÷ 25 = 4
9. Peter the Postman had 560 letters to deliver. So far he has delivered 78 of them. How many letters has Peter still to deliver?
 [ ] 490 [x] 70 [ ] 120 [ ] 60
If Peter has delivered 78 of the letters, all you have to do is find 18 of 560: 18 x 560 = 560 ÷ 8 = 70
10. What is 469 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: 429. Divide the numerator and denominator by 3 to reduce the fraction to its simplest form: 143