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Fractions (Difficult)
Before you do this quiz, do all the other 11-plus Maths quizzes on fractions – that way, this quiz won't seem so difficult!
By now you should have a good grasp of fractions. Remember the best way to learn any new subject is to keep practising every day until you are confident you know what you are doing.
Remember that all fractions have a numerator and a denominator.
As always, take your time when practicing. Read the questions carefully - even read them aloud to help - and look at all four answers before choosing. If you get it wrong (or even if you get it right), make sure you read the comment that pops up after the question has been answered. These comments will help you understand how the calculation is worked out.
Good luck!
1 .
What is 54⁄8 as an improper fraction in its simplest form?
44⁄8
11⁄2
22⁄4
5⁄2
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: 5 × 8 = 40. STEP 2: 40 + 4 = 44. STEP 3: 44/8. Divide the numerator and denominator by 4 to reduce the fraction to its simplest form: 11/2
2 .
What is 18⁄4 as a mixed fraction in its simplest form?
41⁄2
32⁄6
41⁄3
42⁄4
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: 18 ÷ 4 = 4. STEP 2: Remainder 2. STEP 3: 42/4. Divide the numerator and denominator by 2 to reduce the fraction to its simplest form: 41/2
3 .
What is 4⁄6 + 8⁄3 + 5⁄15 expressed as a mixed fraction?
33⁄2
22⁄3
34⁄6
32⁄3
4/6 + 8/3 + 5/15 = 2/3 + 8/3 + 1/3 = 11/3 = 32/3. Reduce the fractions to their simplest forms, 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
4 .
What is 96⁄8 as an improper fraction in its simplest form?
72⁄8
27⁄4
39⁄2
39⁄4
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: 9 × 8 = 72. STEP 2: 72 + 6 = 78. STEP 3: 78/8. Divide the numerator and denominator by 2 to reduce the fraction to its simplest form: 39/4
5 .
What is 24⁄7 as a mixed fraction in its simplest form?
210⁄7
37⁄24
33⁄7
73⁄7
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: 24 ÷ 7 = 3. STEP 2: Remainder 3. STEP 3: 33/7
6 .
What is four-fifths of five-sixteenths in its simplest form?
5⁄4
20⁄80
4⁄5
1⁄4
The word OF means multiply: 4/5 × 5/16 = 1/4. 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 6⁄15 are there in 4⁄5?
4
24
2
3
6/15 can be reduced to 2/5 (divide the numerator and the denominator by 3). Now you can see that 4/5 is twice as much as 2/5
8 .
If 17⁄30 of the class voted against extra homework, how many pupils in the class voted in favour of extra homework?
17 pupils
13 pupils
13⁄30 of the class
23⁄5
13/30 of the class voted in favour of extra homework BUT fractions alone DO NOT tell you the actual number of people or things involved. If you had been told that there were 30 pupils in the class, then choice 2 would have been the best answer. Always be on the lookout for the BEST answer
9 .
An eighth of an eighth is the same as what fraction of a fourth?
1⁄2
1⁄16
1⁄8
3⁄4
The word OF means multiply: 1/8 × 1/8 = 1/64. You now have to find a fraction which multiplied with 1/4 gives 1/64. Well, 4 × 16 = 64, so the fraction (in its simplest form) must be 1/16
10 .
There are 360° in a circle. If you walk round 5⁄8 of the circumference of a circle, how many degrees will you have walked around?
225°
576°
125°
252°
All you have to do is find 5/8 of 360°: 5/8 × 360° = (5 × 360°) ÷ 8 = 1,800° ÷ 8 = 225°. Do the brackets first
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