Unit 2:Fractions

In this lesson you will learn about: Equivalent fractions Comparing and ordering fractions Operations with fractions (including

powers) Solving problems

Vocabulary you need in this lesson:You are going to work with some vocabulary related to thislesson and the problems you will work with. The same wordsappear in the crosswords, in the word scramble and in theword search.

Some theoryA rational number is a number that can be expressed as a fraction or ratio(rational). The numerator and the denominator of the fraction are both inte-gers.numerator - is the number on the top of the line. In the fraction 7/8, the nu-merator is 7.denominator - is the number on the bottom of the line. In the fraction 7/8,the denominator is 8.

Equivalent fractions: they represent the same part of the total

You can find equivalent fractions amplifying and simplifying. A fraction thatcan’t be simplified any more is called fraction in its lowest terms.

Reduce fractions to common denominator consists of finding equivalent frac-tions to the original ones but with the same denominators

You have to reduce fractions to the common denominator if you want to com-pare, order, add or subtract fractions

To work out a power of a fractions you have to raise the numerator and de-nominator to the exponent of the power

Example:n

nn

b

a

b

a

125

8

5

2

5

23

33

Properties of powers with fractions: they are the same as the properties ofpowers with integers

Roots of fractions: to calculate the root of a fraction you have to calculatethe root of the numerator and the denominator and divide the results

Example:

b

a

b

a

b

a

b

a

b

a

b

a

b

a

b

a

b

a

b

a

b

a

d

c

b

a

d

c

b

a

d

c

b

a

d

c

b

a

nmnm

nmnm

nmmn

nnn

nnn

1

0

1

:

::

b

a

b

a

8

5/

64

25

Now it´s time to practice1. Exercises

1. Who am I?

a) I am a fraction equivalent to ¾. My denominator is 12.

b) I am a fraction equivalent to 4/5 my numerator is 20.

c) I am a fraction. I reduce to 3/5 in my lowest terms. My numerator and denominator

have a total of 120.

d) I am a fraction. I am one half more than one third.

e) I am a fraction. I am one quarter less than five eights.

f) I am an odd number of fifths. When one half is subtracted from me the result is

equivalent to 0.1.

2. Work out:

3. Order the fractions from least to greatest:

a. b.

c. d.

40

30,

30

22,

20

15

14

19,

7

11,

9

12

10

7,

12

5,

8

3

70

27,

50

18,

25

9

2. Problems

1. Anthony showers 2 of every 12 days. Laura showers 4 of every 15 days. Who showers more

often?

2. Anthony eats 7 servings of corn on the cob every 22 days. Laura eats 12 every 33 days.

Who eats more corn on the cob?

3. David asks 14 questions every 5 classes. Mary Jo asks 21 questions every 6 classes. Who

asks more questions?

4. I have read 6/7 of the 252 pages of a book. Next I read 2/3 of the rest.

How many pages do I have to read now to finish the book?.5. A painter has to paint a house. He painted one half of the house this morning. In the after-

noon he painted one third of the rest , but he’ll have to paint 30 m2 tomorrow to finish thejob. How big is the house in m2?.

6. . Jeremy gave 1/2 of his candy bar to 4 friends. If his friends shared the piece equally,then what fraction of the original candy bar did each one get?

7. In basketball, John scored a point in 5 out of 7 tries, Joe scored a point in 5out of 6 tries, and Tim scored a point in 5 out of 8 tries. Order these playersfrom least to greatest.

8. At the geologists convention 1/4 of the people are students, 1/4 are professors and 1/6 areindustry representatives. The rest are employees of the convention centre. If there are 348people at the convention, how many are employees of the centre?

9. Nineteen people have signed up for the bowling tournament at Snookie's Bowling Alley andArcade. This is about 3/4 of the maximum number of people allowed in the tournament. Howmany more can still sign up?

10. Which is cheaper, the red jumper or the blue one?

11. One half of the auditorium is filled with students and the rest are teachers and parents.Of the students, 1/7 is girls. What fraction of the auditorium is filled with girl stu-dents? What fraction is filled with boy students?

12. Jane and Stephen drive from Edinburgh to London. After driving 3/8 of the journey,they have to drive 250 more miles. What is the distance between Edinburgh and Lon-don?

13. A shop received some tomatoes one day. Of them, they sold 1/5 and 1/9 were spoiled.There are still 225 tomatoes left. How many tomatoes did they receive?

14. Of the distance to grandma house, 3/7 can be covered in 15 minutes. How long will ittake to reach grandma’s house?

15. Of the auditorium, 5/9 is filled by students. If the number of others is 270, what is thetotal population in the auditorium?

16. How many half-gallon bottles are required to fill eighty-four with 2/7 gallons of water?

17. Dad and Kelly painted 7/18 of the house and mum painted 9/15. Who painted more - dadand Kelly or mum? Did they finish the work? If not, how much is left?

18. Lewis lives in Seville and decides to visit his brother who lives in Gijón. The first day hecovers 2/7 of the trip and the second day 2/5. What fraction of the trip does he haveleft to cover?

19. In a news-stand, 2/3 of a batch of magazines have been sold duringthe morning. In the evening, 2/9 of the batch have been sold. What fraction of maga-zines hasn’t been sold? If 25 magazines haven’t been sold, how manymagazines were there at the beginning of the day?

20. A farm is divided in three plots. The first one is 4/7 of the total areaof the farm and the second plot is half of the first plot. What fraction of the farm isthe second plot? And the third? If the area of the farm is 14.000 m2, what is the areaof each plot?

Some interesting web sites!

If you want to read a completed piece of information about fractions torevise your knowledge, go to:

http://www.mathsisfun.com/fractions-menu.html

To check if you have learnt about comparing fractions and decimalnumbers correctly, take the next test:http://www.glencoe.com/sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=0-07-829635-8&chapter=2&lesson=2&headerFile=4&state=na

To play a game where you have to operate with fractions to get theresult, click here:

http://www.glencoe.com/sec/math/msmath/mac04/course3/group_activities/lesson.php/na/2d

To revise very easy concepts, if you are not sure about them, goto:

http://jc-schools.net/tutorials/PPT/

In this page you will find a reviwe of many of the concepts from thisunit, many exercises and their solutions for you to practice more:http://www.csu.edu.au/division/studserv/maths/docs/nurseconversions.doc

If you want to read about the origin of fractions and how they wereused in the past, click here:http://nrich.maths.org/2515