FractionsPercentsCircle graphs

Unit 5

•Add fractions with like denominators•Order and compare fractions•Convert between fractions and percents•Draw a circle graph for a set of data•Measure pieces of a circle graph•Interpret a circle graph•Convert between fractions and mixed numbers

•Find equivalent fractions

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Key Goals

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tutorial on fractions!

• A fraction has two parts: the numerator and the denominator

• The numerator is the number on top, the denominator is the one that’s DOWN on the bottom.

• The numerator is the NUMBER of pieces you have

• The denominator is the size of the pieces

Add fractions with like denominators

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worksheet!

Try It Out

1/6 of the sections on the 1st ball are red.3/6 of the sections on the second ball are

red. What is the fraction of red sections?

1/6 + 3/6 =

4/12 7/94/6 2/12

The answer is 4/6 because the size of the pieces are sixths. When you add 1/6 to 3/6 you add the numerators (1 +3) and keep the denominator the same (6).

4/9 + 3/9 = Try It Out

7/18

1/9

7/9

1/18

The answer is 7/9 because the size of the pieces are ninths. When you add 4/9 to 3/9 you add the numerators (4 +3) and keep the denominator the same (9).

6/8 + 7/8 = Try It Out

13/16

1/8

8/13

13/8

The answer is 13/8 because the size of the pieces are eighths. When you add 6/8 to 7/8 you add the numerators (6 +7) and keep the denominator the same (8).

• The numerator is the NUMBER of pieces you have

• The denominator is the size of the pieces

• If something is cut into more pieces those pieces are going to be smaller.

Play a game

Order and compare fractions

• One strategy for comparing fractions is to think about their relationship to one and zero. For example, 5/6 is almost all of the pieces, so it would be close to 1; 1/6 is close to none of the pieces, so it would be closer to zero.

• Another strategy is to convert the fractions to a decimal and then compare the decimals. (numerator divided by denominator = decimal)

• A third strategy is to find a common denominator among your fractions and compare the numerators.

It helps to simplify the fractions!

If you need a set of fraction bars, click here

Strategies for comparing and ordering fractions…

Try It Out….

4/9 _____ 6/9

< > =

The correct answer is 4/9 < 6/9 because in these two fractions, the denominators are the same.Therefore, the pieces are the same size.Four of these pieces are less than six.

1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9

1/9 1/9 1/9 1/9 1/9 1/9 1/91/9 1/9

Try It Out….

8/9 _____ 7/8

< > =

8/9 is > 7/8

In each of these two fractions, there is all but one piece. However, because 9ths are smaller than 8ths, the remaining 1/9 is smaller than the remaining 1/8.

Try It Out….

1/3 _____ 5/12

< > =

1/3 is < 5/12

If you change 1/3 into an equivalent fraction, it would be equal to 4/12. 4 out of 12 is less than 5 out of 12.

Convert between fractions and percents

•Fractions and percents are both ways of representing a part out of a whole.

•An equivalent percent for a decimal or a fraction can be found by finding an equivalent fraction out of 100 since “percent” means “per 100”. In this case, the numerator would be the percent.

•A fraction or decimal can be formed from a percent by creating a fraction where the numerator is the percentage and the denominator is 100, or by dividing the percent by 100.

Here are some examples….

34% = 34/100 = 17/50

125% = 125/100 = 1 ¼

.5% = .5 /100 = 1/200

¾ = 75/100 = 75%2/5 = 40 / 100 = 40%14/50 = 28/100 = 28%

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practice games!

Click on the characters to play fraction and percent games and activities!

Draw a circle graph for a set of data.

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circle graph.

How to Make a Pie ChartPie charts are an easy way to visualize percentages. They are useful for analyzing polls, statistics, and managing time or money.

Steps1.Organize your data. First gather your data. 2.Add it all together. Add all of the numbers to get a denominator. 3.Get the numerator. Get the numerators by taking each part of the data. 4.Convert your fractions to a decimal. By taking the numerator divided by the denominator. 5.Convert the decimal to a percent. Move the decimal two places to the right. 6.Get the angle. Multiply the percent by 360 to get an angle. 7.Use a compass to draw a circle. If you don't have a compass, try tracing something round such as a lid. 8.Draw the radius. Start in the exact center of the circle and draw a radius to the outside of it. ( Hint: Use the dot made by the compass to find the center. 9.Place your protractor. Place your protractor on the circle so that the 90 degrees are directly above the center of the circle. 10.Draw each section. Draw the sections by using the angles you got in step six. Each time you add a section the radius changes to the line you just drew.

Tips• Remember that all good graphs have a title and labels. • Add the name of the sections and the percent they represent to the chart. • Color each section of the pie chart a different color to easily visualize the results. • If you do not have a very good compass, it is easier to draw the circle by holding the compass still and turning the paper.

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Measure Pieces of a Circle GraphClick the links next to each step for more information.

Steps

1. Measure the angle of the sector you are trying to measure using a protractor.

2. Turn that measurement into a fraction out of 360°

3. Change that fraction into a decimal by dividing the measurement by 360°

4. Then multiply the decimal by 100 to change it into a percent.

A full circle will consist of 360 degrees. Therefore 1% on a pie chart will be represented by 3.6 degrees.

Just multiply the angle measure by 3.6.

Interpret a circle graphClick me to test

your skills!

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(Answer Key included)

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When you interpret a circle graph, there are some key things to remember:

-Look carefully at the title and key so that you can tell

what data is being represented.

-Remember that each section represents a part out of the whole.

- The larger the section, the greater the percentage.

Convert between fractions and mixed numbers.

• A FRACTION is a part out of a whole. The numerator tells the number of parts you have, the denominator tells how many parts it takes to make one whole.

• A fraction that has more parts than it takes to make one whole is called an improper or top-heavy fraction. In these fractions, the numerator is greater than the denominator.

• A MIXED NUMBER is a whole number with a fraction.

This drawing represents the fraction 5/4 and the mixed number 1 ¼.

It’s good to understand both forms of this quantity because at times it is easier to work with mixed numbers (adding and subtracting so that you don’t have to simplify as much), and at others it’s easier to work with improper fractions (multiplying and dividing so that you don’t forget to multiply all of the numbers together.)

Learn about and practice converting improper fractions and mixed

numbers by clicking the objects on this slide.

Finding Equivalent Fractions

For example

3/6 is equivalent to 10/20 because the relationship between the numerator and the denominator is the same in each case: 3 is ½ of 6, and 10 is ½ of 20.

Two fractions are EQUIVALENT if they are equal.This means that the relationship between the numerator and the denominator of one fraction is the same as the relationship between the numerator and denominator of the other fraction.

Another way you can look at it is if two fractions are equivalent, they will have a scale factor between them. The SCALE FACTOR is the number that you multiply or divide the numerator and denominator in one fraction by to get the numerator and denominator of the second fraction.

3 9

5 15=

x3

x3

By multiplying 3/5 by 3/3 (remember, that is the same as multiplying by 1 whole), I will arrive at the answer 9/15.

Remember that when you are doing this you must BE FAIR and perform the same operation to both the numerator and the denominator.

Don’t forget that when you multiply fractions, you multiply the numerators together and you multiply the denominators together.

A third way to determine if two fractions are equivalent is to CROSS MULTIPLY.

4 2

6 3=

=

x

=12

x

=

12

Multiply the numerator of one fraction by the denominator of the other.

Repeat this with the other numerator and denominator.

If the products are equal, then the fractions are equivalent.

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Find equivalent fractions

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