UNIT 3
THE PRESENT PERFECT
PRESENTATION
1. Read the text about “Fractions”.
FRACTIONS
Every fraction has a numerator and denominator. The denominator tells you the
number of parts of equal size into which some quantity is divided. The numerator tells
you how many of these parts are to be taken.
2
Fractions representing values less than 1, like for example, are called proper
3
2 3
fractions. Fractions which name a number equal to or greater than 1, like or , are
2 2
1
called improper fractions. There are numerals like 1 , which name a whole number
2
and a fractional number. Such numerals are called mixed fractions. Fractions which
1 2 3 4
represent the same fractional number like , , , and so on, are called equivalent
2 4 6 8
fractions.
We have already seen that if we multiply a whole number by 1 we leave the number
unchanged. The same is true of fractions when we multiply both integers in a fraction
1 1
by the same number. For example, 1× = . We can also use the idea that 1 can be
2 2
2 3 4
expressed as a fraction in various ways , , and so on.
2 3 4
1 2
Now see what happens when you multiply by . You will have
2 2
1 1 2 1 2 ×1 2
= 1× = × = = .
2 2 2 2 2× 2 4
As a matter of fact in the above operation you have changed the fraction to its higher
terms.
6 6 2 6: 2 3
Now look at this: :1 = : = = . In both of the above operations the number
8 8 2 8: 2 4
2
you have chosen for 1 is .
2
6
In the second example you have used division to change to lower terms, that is to
8
3
. The numerator and denominator in this fraction are prime and accordingly we call
4
such a fraction the simplest fraction for the given rational number.
20
, 2. Grammar questions
2.1 Why is the Present Perfect tense used in the text?
2.2 Complete the rule:
The Present Perfect is formed with the auxiliary verb………+ the…………..
• Speaking
Work in pairs
Answer the questions below.
a. What have you seen if you multiply a whole number by 1?
1 2
b. Have you changed the fraction when you multiply by ?
2 2
6
c. What division have you used to change to lower terms?
8
PRACTICE
1. Grammar
1.1 Read the following newspaper extracts and say when these actions took place.
If you do not have information, write “don’t know”.
1. has extended don’t know 6. plummeted ..........................
2. announced at the weekend 7. seemed ..........................
3. came ……………… 8. built ..........................
4. warned ……………… 9. has survived ..........................
5. hit ……………… 10. has paid off ..........................
1.2 Underline the correct tense.
21
THE PRESENT PERFECT
PRESENTATION
1. Read the text about “Fractions”.
FRACTIONS
Every fraction has a numerator and denominator. The denominator tells you the
number of parts of equal size into which some quantity is divided. The numerator tells
you how many of these parts are to be taken.
2
Fractions representing values less than 1, like for example, are called proper
3
2 3
fractions. Fractions which name a number equal to or greater than 1, like or , are
2 2
1
called improper fractions. There are numerals like 1 , which name a whole number
2
and a fractional number. Such numerals are called mixed fractions. Fractions which
1 2 3 4
represent the same fractional number like , , , and so on, are called equivalent
2 4 6 8
fractions.
We have already seen that if we multiply a whole number by 1 we leave the number
unchanged. The same is true of fractions when we multiply both integers in a fraction
1 1
by the same number. For example, 1× = . We can also use the idea that 1 can be
2 2
2 3 4
expressed as a fraction in various ways , , and so on.
2 3 4
1 2
Now see what happens when you multiply by . You will have
2 2
1 1 2 1 2 ×1 2
= 1× = × = = .
2 2 2 2 2× 2 4
As a matter of fact in the above operation you have changed the fraction to its higher
terms.
6 6 2 6: 2 3
Now look at this: :1 = : = = . In both of the above operations the number
8 8 2 8: 2 4
2
you have chosen for 1 is .
2
6
In the second example you have used division to change to lower terms, that is to
8
3
. The numerator and denominator in this fraction are prime and accordingly we call
4
such a fraction the simplest fraction for the given rational number.
20
, 2. Grammar questions
2.1 Why is the Present Perfect tense used in the text?
2.2 Complete the rule:
The Present Perfect is formed with the auxiliary verb………+ the…………..
• Speaking
Work in pairs
Answer the questions below.
a. What have you seen if you multiply a whole number by 1?
1 2
b. Have you changed the fraction when you multiply by ?
2 2
6
c. What division have you used to change to lower terms?
8
PRACTICE
1. Grammar
1.1 Read the following newspaper extracts and say when these actions took place.
If you do not have information, write “don’t know”.
1. has extended don’t know 6. plummeted ..........................
2. announced at the weekend 7. seemed ..........................
3. came ……………… 8. built ..........................
4. warned ……………… 9. has survived ..........................
5. hit ……………… 10. has paid off ..........................
1.2 Underline the correct tense.
21
