UNIT 1 Fractions and Decimals. Activities 2 (3º ESO)

8/3/2019 UNIT 1 Fractions and Decimals. Activities 2 (3 ESO)

1/4

Unit 1: Fractions and Decimals. ACTIVITIES 2 Mathematics - 3 ESO

IES Albayzn (Granada) Pgina 1

UNIT 1: Fractions and Decimals

Rational NumbersRational NumbersRational NumbersRational Numbers

The numbers that fall between the integers on the number line are either

rational or irrational. In this section, we discuss the rational numbers.

Rational numbers are used to express a part of a whole, a part of a quantity.

(Five eighths)

The number below the fraction line is called denominator, and expresses the

number of parts into which the whole is divided. The number above the fraction

line is called the numerator, and expresses the number of parts taken.

A more formal definition of rational numbers could be:

So any number that can be expressed as a quotient of two integers

(denominator not zero) is a rational number:

56 = 0.833. ..

105 = 2

254 = 6.25

37 = 0.42857142

When the numerator and denominator have a common divisor, we can reduce

the fraction to its lowest terms (or simplest form):

618 =

39 =

= 0.3333

A fraction is said to be in its lowest terms (or reduced, or simplified) when the

numerator and the denominator are relatively prime.

The set of rational numbers, denoted by , is the set of all numbersof the form

, where pand qare integers, and 0.


2/4



Now we can introduce the definition of equivalent fractions:

Proper and Improper Fractions. Mixed Numbers.

Rational numbers less than 1 or greater than -1 are represented by proper

fractions. A proper fraction is a fraction whose numerator is less than its

denominator:

47 511

Consider the number 2 . It is an example of a mixed number. It is called amixed number because it consists of an integer, 2, and a fraction

, and it is

equal to 2 + . The mixed number 4means 4 +

.

Rational numbers greater than 1 or less than -1 that are not integers may berepresented as mixed numbers, or as improper fractions. An improper fraction

is a fraction whose numerator is greater than its denominator.

= 2 +

34

Two fractions are said to be equivalent when simplifying both of

them produces the same fraction, which cannot be further

reduced.

Equivalent fractions look different but represent the same portion

of the whole.

Equivalent fractions have the same numerical value. They are

represented by the same rational number.

Equivalent fractions are represented by the same point on the

number line.

We can test if two fractions are equivalent by cross-multiplying(or cross-product) their numerators and denominators.


3/4



Exercises

1) How do you read fractions? Complete the following table using the

rules to read and write fractions.

Fraction Write down how the fraction is read

12

32

53

34

25

1859

2) Simplify or cancel each of these fractions down to their simplest form.

a)

= b)

= c)

= d)

=

3) Fill in the required number:

a) = b)

= c) =

d)

=


4/4



Finding Fractions of quantities: Problems Involving

Fractions

1) Calculate in your head and then answer:

a) How many minutes are there in 1/5 of an hour

b) How many minutes are there in 5/6 of an hour

c) What fraction of an hour is 20 minutes?

d) What fraction of an hour is 40 minutes?

2) A shelf in a supermarket holds 80 one-quarter litre bottles and 44 one

and a half litre bottles. How many litres of water are there on the self?

3) When David Conway finished his first year of high school, his height was69 inches. When he returned to school after the summer, Davids heightwas 71 inches. How much did Davids height increase over thesummer? (1 inch = 2.54 cm)

4) A lorrys tank contains 225 litres of diesel, and the gauge says the tank is

full. How many litres can the tank hold?

5) In a bicycle race, cyclist A has covered 4/5 of the total route and has 21

km left before the finish line. How many kilometres are left before cyclist

B reaches the finish line, if he has covered 6/7 of the route?

6) A bag contains twenty beads numbered from 1 to 20.

a) Which of the bead numbers are multiples of 5?

b) Express as a fraction the probability of obtaining a multiple of 5 by

drawing one bead at random from the bag

Dont Forget

=

7) A vineyard sells two-fifths of its harvest to a wholesaler, and one-third of

the rest to a supermarket. If the vineyard still has 40 hectolitres left, how

much did it produce?

Documents

UNIT 1 Fractions and Decimals. Activities 2 (3º ESO)