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6⁄5 is an improper fraction, equal to the mixed fraction 1 1⁄5.
Fractions 2 (Difficult)
If you’ve been playing all our Eleven Plus maths quizzes in order, you’ll know by now that fractions are very important. But you will also be very confident when dealing with them, won’t you?
You should, by now, know the difference between a numerator and a denominator and be familiar with improper and mixed fractions. You should also be able to add and subtract fractions, and use them to work out proportions as fractions.
With all that experience under your belt, even though it’s difficult, this quiz should pose you no problems. Just make sure you read the questions carefully and consider them a while before you choose your answers. You might also like to read the helpful comments after each question – they clarify each point, making sure you understand.
And now, if you are ready, it’s time to begin. Good luck!
1 .
What is 26⁄6 as a mixed fraction in its simplest form?
4 1⁄2
4 1⁄3
4 1⁄4
4 1⁄6
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: 4 2?6. Divide the numerator and denominator by 2 to reduce the fraction to its simplest form: 4 1?3
2 .
What is 5⁄6 + 2⁄3 + 6⁄18 expressed as a mixed fraction?
1 1⁄3
1 2⁄3
1 5⁄6
1 17⁄18
First, make all the fractions have the same denominator: 5?6 + 2?3 + 6?18 = 5?6 + 4?6 + 2?6. Here we see a shortcut: 4?6 + 2?6 = 1, so the answer is 1 5?6
3 .
If 51⁄100 of the electorate voted for the government, how many people voted against the government?
24 people
49 people
24⁄50 of the electorate
49⁄100 of the electorate
51?100 of the electorate voted for the government BUT fractions alone DO NOT tell you the actual number of people involved. If you had been told that there were 100 voters, then choice 2 would have been the best answer. Always be on the lookout for the BEST answer
4 .
What is 42⁄8 as a mixed fraction in its simplest form?
5 2⁄4
5 1⁄2
5 1⁄4
5 1⁄8
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: 42 ÷ 8 = 5. STEP 2: Remainder 2. STEP 3: 5 2?8. Simplify the fraction by dividing the numerator and denominator by the same number, in this case 2, to get your final answer, 5 1?4.
5 .
There are 28 pupils in a class. If 4⁄7 of them are girls, how many boys are in the class?
8
12
16
14
All you have to do is find 4?7 of 28 and subtract it from 28: 4?7 × 28 = (4 × 28) ÷ 7 = 112 ÷ 7 = 16. That's the number of girls. To find the number of boys, just subtract 16 from 28: 28 - 16 = 12
6 .
What is 3⁄4 of 4⁄15 in its simplest form?
1⁄5
1⁄4
1⁄3
1⁄6
The word OF means multiply: 3?4 x 4?15 = 12?60. 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 .
What is 14 8⁄10 as an improper fraction in its simplest form?
74⁄5
148⁄10
120⁄8
31⁄2
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: 14 × 10 = 140. STEP 2: 140 + 8 = 148. STEP 3: 148?10. Divide the numerator and denominator by 2 to reduce the fraction to its simplest form: 74?5
8 .
What is 5 4⁄16 as an improper fraction in its simplest form?
11⁄2
21⁄4
41⁄8
84⁄16
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: 5 × 16 = 80. STEP 2: 80 + 4 = 84. STEP 3: 84?16. Divide the numerator and denominator by the same number, in this case 4, to reduce the fraction to its simplest form: 21?4
9 .
A 1⁄12 x 1⁄12 is the same as what fraction of a sixth?
1⁄12
1⁄36
1⁄24
1⁄48
1?12 x 1?12 = 1?144. You now have to find a fraction which multiplied with 1?6 gives 1?144. Well, 144 ÷ 6 = 24, so the fraction (in its simplest form) must be 1?24
10 .
How many 4⁄18 are there in 2⁄3?
6
4
2
3
4?18 can be reduced to 2?9 (divide the numerator and the denominator by 2) and 2?3 can be turned into 6?9 (multiply the numerator and the denominator by 3) . Now you can see that 6?9 is thrice as much as 2?9
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