10 Arithmetic: Fractions

Transcription

1 MEP Y Practice Book A 0 Arithmetic: Fractions 0. Fractions This unit deals with the important topic of fractions. These are numbers of the form a b when a and b are whole numbers and b 0. We first see what is meant by a fraction when related to geometrical shapes. Example What fraction of each shape is shaded? Solution 0, but this is the same as 0 (as there are shaded triangles and in total) or.

2 MEP Y Practice Book A Exercises. What fraction of each of the following shapes is shaded? (f) (h) (i). Copy each of these shapes and shade the fraction stated. (f) 0

3 0. MEP Y Practice Book A (h) (i). On a copy of this rectangle, draw lines to divide it into equal parts. Shade of the rectangle. What fraction has not been shaded?. Copy each shape and shade the fraction stated. (f) (h) 0 0. On separate diagrams, shade the stated fraction of this shape.

4 MEP Y Practice Book A. Copy this shape. Shade of the shape. Shade another of the shape. What is the total fraction now shaded? How much is left unshaded?. Sarah shades of a shape. What fraction of the shape is left unshaded?. A cake is divided into equal parts. John eats eats another. What fraction of the cake is left? of the cake and Kate. A car park contains 0 spaces. There are cars parked in the car park. What fraction of the car park is full? What fraction of the car park is empty? 0. Ali eats 0 of the sweets in a packet. Tariq eats another of the sweets. 0 What fraction of the sweets has been eaten? What fraction of the sweets is left?. Draw as many ways as you can of shading of a shape. Be as imaginative as you can. Here is an idea to get you thinking.

5 MEP Y Practice Book A 0. Equivalent Fractions It is easy to see from the diagram opposite that and are equivalent fractions, i.e. they both have the same value. Another way of looking at this is to note that the fractions are at the same place on a number line. 0 0 ( = ) Example Use the diagram below to shade of the rectangle in different ways. Solution Here are two possible answers. In fact, shading any 0 of the small triangles (out of ) gives the fraction (which is equivalent to 0 or 0, etc.)

6 MEP Y Practice Book A Exercises. The diagrams show that is equivalent to 0. Draw a diagram to show that is also equivalent to 0.. Use the diagrams below to show that = =.. Write down the equivalent fractions shown by these diagrams.. Use the diagram on the next page to fill in the missing numbers.??????? = = = = = = = 0???? = = = =??? = = =?? = = 0 =?

7 0. MEP Y Practice Book A (f) =? =? ONE WHOLE 0. Write down the missing numbers.??? = = = 0??? = = (f) =??? = (h) = (i) =

8 MEP Y Practice Book A??? (j) = (k) = (l) = 0 0. Write out each of these pairs of fractions, inserting either a < or a > into each one to make it correct. 0 (f) (h) 0 (i) (j) (k) (l). Write down the missing numbers. =? 0 =? =? =? =? (f) =? 0 0 =? (h) 0 =? (i) =? (j) =? (k) =? (l) 00 =?. Write each set of fractions in increasing order.,,,, 0,,,,,,,,,,,,,,

9 0. MEP Y Practice Book A. Write each fraction in its simplest form. 0 (f) 0 (h) 00 (i) State whether each of the following is true or false. If false, explain why. > = = > > (f) < 0 > (h) < (i) = 0 0. Fractions of Quantities Now we start to use fractions in a practical way. Example Find of 0. Find of 0 Solution You can, of course, do this practically, but it is much easier to work out 0 = 0 = 0 0 = 0 = = = 0

10 MEP Y Practice Book A Exercises. Find: of of of of of 0 (f) of 0 of (h) of (i) of 0 (j) of (k) of (l) of. Find: of of 0 of of of 0 (f) of of (h) of (i) of (j) of (k) of (l) of. In a test there are 0 marks. Nasir gets of the marks. How many marks does he get?. In a school of the pupils are girls. There are pupils in the school. How many girls are there in the school?. In a class there are pupils. Of these, many pupils come to school by bus? come to school by bus. How. In a school, of the pupils have pets. There are 0 pupils in the school. 0 How many of them have pets? How many of them do not have pets?

11 0. MEP Y Practice Book A. There are 0 houses in a street and of them have satellite TV. How many of these houses do not have satellite TV?. Rachel has 0 stamps in her stamp collection. of these stamps are foreign. How many foreign stamps has she got?. Ben and Chris sell their old toys at a car boot sale. They get. They agree that Ben will have of the money and Chris the rest. How much do they each get? 0. In a school there are 0 pupils. If of the pupils are left-handed, how 0 many left-handed pupils are there in the school? 0. Mixed Numbers and Vulgar (Improper) Fractions So far we have worked with fractions of the form a b where a < b, e.g.,,,... We also need to work with what are sometimes called vulgar or improper fractions, e.g.,, which are of the form a when a and b are whole b numbers and a > b. Example Show that the numbers and are equivalent. Solution You can illustrate as opposite.

12 MEP Y Practice Book A If you count the quarters, you can see that there are =, i.e. the number is. (You can see that = ( ) + =.) Note that is called a mixed number. Exercises. Write each of the numbers represented by these diagrams, in two different ways. (f). Draw diagrams for these mixed numbers. Write each number as an improper fraction.

13 0. MEP Y Practice Book A. Draw diagrams to show these improper fractions. Write each improper fraction as a mixed number.. Convert these improper fractions to mixed numbers. (f) (h) (i) (j) (k) (l) (m) (n) (o) 0. Convert these mixed numbers to improper fractions. (f) (h) (i) (j) (k) (l) (m) (n) (o). Write these fractions in order of increasing size.,,,,

14 MEP Y Practice Book A. Write out each of these pairs of fractions, inserting either <, > or = into each one to make it correct. (f) (h) (i) 0 (j) (k) (l). Explain why =.. In an office there are packets of paper. There are 00 sheets of paper in each full packet. How many sheets of paper are there in the office? 0. A young child is months old. Find the age of the baby in years as a mixed number in the simplest form.