All About Fractions

Kelsey CharnawskasEDU 290 – Technology in

Education3-1-11

Fractions “describe a part of a whole after

the whole is cut into equal parts.”¹

Fractions can tell, in a group of various

objects, how many objects are the same

thing.

Ex: You have 4 blue marbles and 5 green

marbles. of the marbles are blue.

What Are Fractions?

Fractions are composed of two numbers, one

of top of the other, separated by a horizontal

line.

The top number is called the numerator.

This tells “how many parts are showing.”¹

Parts of a Fraction

The bottom number is called the

denominator.

It tells the “number of parts in the whole.”¹

Parts of a Fraction

denominator

numerator

Fractions can be added together but they

must have the same denominator.

If the denominators are the same, then the

numerators can be added together.

The denominator will remain the same.

Adding Fractions

68+18=78

Example

In order for fractions with different

denominators to be added together, the least

common denominator needs to be found.

The least common denominator is the smallest

multiple that both numbers have in common.²

Whatever you multiply the bottom number by

to get the least common denominator, you

have to multiply the numerator by.

Adding Fractions with Different Denominators

The lowest common denominator is 15.

The first fraction must be multiplied by giving

The second fraction must be multiplied by

giving .

The equation becomes:

Example

Just like with addition, when subtracting, the

denominators have to be the same.

If the denominators are the same, then the

numerators can be subtracted from one

another.

The denominator will remain the same.

Subtracting Fractions

68−18=58

Example

The least common denominator has to be found.

Once the least common denominator is found,

you figure out what the denominator had to be

multiplied by to get that common number.

Whatever the bottom number is multiplied by,

the numerator also has to be multiplied by.

Subtract

Subtracting Fractions with Different Denominators

The least common denominator is 15.

The first fraction must be multiplied by , giving

.

The second fraction must be multiplied by

giving .

Example

There are two ways that fractions can be multiplied.

1. They can be turned into decimals and multiplied.

Example:

Multiplying Fractions

2. The fractions can be left as fractions and

multiplied together.

First, the fractions have to be set up so the

numerators and denominators align with each other.

Next, see if the numbers diagonal from each other

have a greatest common factor (GCF). Reduce

these numbers using the GCF to the smallest they

can be.

Then, multiply straight across.

Multiplying Fractions

Looking diagonally:

Between the 9 and 18, the greatest common factor

is 9. Therefore, the 9 and 18 are both divided by 9.

Between the 8 and 24, the greatest common factor

is 8. Therefore, the 8 and 24 are both divided by 8.

Example

Reducing fractions, or simplifying, is when a

fraction is in its lowest terms.

This means that “there is no number, except 1,

that can be divided evenly into both the

numerator and denominator” (www.math.com).

Divide both the numerator and denominator by

their greatest common factor and it will be in

simplest/reduced form.

Reducing Fractions

reduced to ?

The greatest common factor is 20. Therefore,

the top and bottom numbers get divided by 20.

After they are both divided, the fraction is

reduced to .

reduced to

Reducing Fractions Example

Improper fractions are fractions where the numerator is larger than the denominator. (

A mixed number is composed of a whole number and a fraction. (1

To change: divide the top number by the bottom to get the whole number.

The remainder from that division becomes the new numerator of the fraction.

Converting from Improper Fractions to Mixed Numbers

as a mixed number is ?

8 goes into 9 one time.

The whole number is 1.

There is a remainder of 1 from the division. The denominator stays the same and the remainder becomes the new numerator.

Therefore, the fraction is .

as a mixed number is

Example

The denominator gets multiplied by the

whole number.

The numerator is then added to that new

number.

The denominator remains the same.

Converting Mixed Numbers to Improper Fractions

as an improper fraction is ?

The denominator gets multiplied by the whole

number.

9 x 1 = 9

The numerator is added: 9 + 2 = 11.

This new number is put over the same denominator.

as an improper fraction is

Example

7. 8.

Add

Subtract

Convert to Improper Fraction or Mixed Number

Practice Problems

Reduce9. 10. 11.

Multiply12. 13. 14.

Answers to Practice Problems

8. 9.

10.3

11.

12.

13.

1. Information and direct quotes on slides 2-4 from “Understanding Fractions” http://library.thinkquest.org/J002328F/understanding%20fractions.htm

Information on slides 5 and 7 from “Understanding Fractions: Adding Fractions” http://library.thinkquest.org/J002328F/understanding%20fractions.htm

Information on slides 9 and 11 from “Understanding Fractions: Subtracting Fractions” http://library.thinkquest.org/J002328F/understanding%20fractions.htm

Information on slides 13 and 14 from “Understanding Fractions: Multiplying Fractions” http://library.thinkquest.org/J002328F/understanding%20fractions.htm

Works Cited

Information on slide 16 from “Reducing Fractions” http://www.math.com/school/subject1/lessons/S1U4L2GL.html

Information on slides 18 and 20 from “Understanding Fractions: Other Fractions” http://library.thinkquest.org/J002328F/understanding%20fractions.htm

2. Definition of “Least Common Denominator” on slide 7 from http://www.google.com/search?hl=en&rlz=1T4TSNA_enUS386US388&defl=en&q=define:Least+Common+Denominator&sa=X&ei=BkppTeqNDJPQgAeV5t3LCg&ved=0CBQQkAE

Image on slide 3 from http://spfractions.wikispaces.com/file/view/proper+fraction.bmp

All of the examples are my own including slide 22 with the various practice problems.

Works Cited Continued