# Fractions (Easy)

This 11-plus Maths quiz introduces the ideas of an 'improper fraction' and a 'mixed fraction'. In this quiz we are going to do a few simple calculations with fractions. An improper fraction is a fraction in which the numerator is greater than or equal to the denominator, e.g. 53 and 99. A mixed fraction (also called a mixed number) is a number that has a whole number part and a fractional part, which is not written as a decimal, written as a single unit, e.g. 235. Here are a couple of tips.

TIP 1: Don't forget: the numerator is the number at the top and the denominator is the number at the bottom of a fraction.

TIP 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.
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1. What is 12 of 14?
12 × 14 = 18. You multiply the numbers in the denominator together, and you multiply the numbers in the numerator together to form a single fraction
2. If you are asked to find 18 of something, what is the best method of doing it?
The word 'of' means multiply; therefore, one-eighth OF something means multiply by 18 BUT multiplying by an eighth is the same as dividing by eight because 18 × 32 = 328. The same applies in similar situations
3. First, Anne had 416 of the cake. Then, James had 916 and finally, Henry had 616 of the cake. Is there anything wrong here?
416 + 916+ 616 = 1916 which is more than 1 cake! In fact, Henry only got 316 of the cake, which was less than Anne got
4. Harry lost three-quarters of half the money his aunt had given him. If half of the money was £64, how much did Harry lose?
34 × £64 = (3 × £64) ÷ 4 = 192 ÷ 4 = £48
5. What is 335 as an improper fraction?
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: 3 × 5 = 15. STEP 2: 15 + 3 = 18. STEP 3: 185
6. What is 5418 as a mixed fraction?
5418 = 3: REDUCE the fraction to its simplest form: divide the numerator and the denominator by 18. Be on the LOOKOUT for this sort of thing. Note: we could have written 311 but this is pointless
7. Mary says that you can have one fifth of her sweets. If she has 125 sweets, how many sweets will you get?
The word 'of' means multiply; therefore one-fifth OF something means multiply by 15 BUT multiplying by a fifth is the same as dividing by five (see question 3): 125 ÷ 5 = 25
8. What is the improper fraction 165 as a mixed fraction?
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: 16 ÷ 5 = 3. STEP 2: Remainder 1. STEP 3: 315
9. What is one seventh of 49?
17 × 49 = 49 ÷ 7 = 7
10. What is 639 as an improper fraction?
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: 6 × 9 = 54. STEP 2: 54 + 3 = 57. STEP 3: 579 BUT you must now REDUCE the fraction to its simplest form: divide the numerator and the denominator by 3 to get 193

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