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Have you heard of 'improper fractions' and 'mixed fractions'? An improper fraction is a fraction in which the numerator is greater than or equal to the denominator, e.g. ^{5}⁄_{3} and ^{9}⁄_{9}. 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. 2^{3}⁄_{5}. 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:

- Multiply the whole number part by the denominator.
- Add this result to the numerator.
- Write the fraction with step 2 in the numerator and keep the original denominator.

1.

What is ^{54}⁄_{18} as a mixed fraction?

3^{3}⁄_{18}

3^{1}⁄_{18}

1^{1}⁄_{3}

3

2.

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?

£96

£32

£24

£48

3.

What is one seventh of 49?

42

56

7

343

4.

What is 6^{3}⁄_{9} 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: ^{57}⁄_{9} BUT you must now REDUCE the fraction to its simplest form: divide the numerator and the denominator by 3 to get ^{19}⁄_{3}

5.

What is ^{1}⁄_{2} of ^{1}⁄_{4}?

6.

If you are asked to find ^{1}⁄_{8} of something, what is the best method of doing it?

Subtract 8

Add 8

Multiply by 8

Divide by 8

The word 'of' means multiply; therefore, one-eighth OF something means multiply by ^{1}⁄_{8} BUT multiplying by an eighth is the same as dividing by eight because ^{1}⁄_{8} × 32 = ^{32}⁄_{8}. The same applies in similar situations

7.

What is the improper fraction ^{16}⁄_{5} as a mixed fraction?

3^{16}⁄_{5}

3^{1}⁄_{5}

16^{1}⁄_{5}

10^{6}⁄_{5}

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: 3^{1}⁄_{5}

8.

Mary says that you can have one fifth of her candies. If she has 125 candies, how many candies will you get?

75

25

45

65

The word 'of' means multiply; therefore one-fifth OF something means multiply by ^{1}⁄_{5} BUT multiplying by a fifth is the same as dividing by five (see question 3): 125 ÷ 5 = 25

9.

First, Anne had ^{4}⁄_{16} of the cake. Then, James had ^{9}⁄_{16} and finally, Henry had ^{6}⁄_{16} of the cake. Is there anything wrong here?

Anne should have been given more cake because she is a girl

No. Bon appétit!

Yes. Henry didn't get the stated amount of cake

Yes. there won't be any cake left for Henry

10.

What is 3^{3}⁄_{5} 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: ^{18}⁄_{5}

^{54}⁄_{18}= 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 3^{1}⁄_{1}but this is pointless