Unit 3.7 Relating Fractions Decimals and Percents Handout - Mr. Gillam

[Pages:8]Mathematics Grade 7

File Name: Unit 3.7 Lesson

Unit 3.7: Fractions, Decimals and Percent Lesson: Relating Fractions Decimals and Percents

Objectives: Students will review where they have seen percents and to discuss where and how

they are applied in society. Students will review how fractions, decimals and percents are related and convert between the three.

Procedure:

So far we have discussed fractions and decimals and how to convert between each of them. Now it is time to introduce the third, percents.

When we first introduced the concepts of decimals, fractions and percents we found that they were the same thing written in different ways.

Review: For example:

In the table above there are 3 out of 6 boxes shaded, so as a fraction this is 3 , this can be 6

simplified by reducing to 1 . As a decimal, there are 0.5 of the boxes shaded. (1 divided by 2

2). As a percent this can be expressed, as 50% of the boxes are shaded.

As you can see, fractions, decimals and percents are all different ways of expressing the same number.

So what is a percent?

A percent is a comparison to the number 100. We usually say that it is a number out of 100. We use percents to compare numbers in the same way so that understanding is easier.

For example:

It is easier to think of 30% off rather than 3/10 `s off. It is easier to think of a test mark of 64% rather than 16/25. It is easier to think of 12% improvement, rather than 0.12:1 improvement.

Unit 3.7 Relating Fractions Decimals and Percents Handout.doc

1

Mathematics Grade 7

File Name: Unit 3.7 Lesson

Where have you seen percents in your life? Some examples are; shopping, weight gain and loss; business profits; etc. Percents Percent is a number that is out of 100, so if we think of it as a box with 100 cells, we can create fractions out of 100. The following box has 100 squares.

What fraction is shaded? 50 100

What is this as a decimal? 50 ?100 = 0.5 Since percent is out of 100, that means that this must have 50% shaded.

So ____, _______ and _______ must all be the same.

Lets break this down into smaller parts:

Fraction to Percent:

To convert a fraction to a percent there are two methods, which can be used. Since percent is out of 100, you can convert the fraction to an equivalent fraction with a denominator of 100. (Percent is out of 100).

Example:

3 is what percent? Convert this fraction to an equivalent fraction that has a denominator 4 of 100.

3= 4 100 4 100, multiply by 20. So multiply 3 by 20 to get an equivalent fraction

3 = 75 (3? 20) 4 100 (4? 20)

Unit 3.7 Relating Fractions Decimals and Percents Handout.doc

2

Mathematics Grade 7

File Name: Unit 3.7 Lesson

Since percent is always out of 100, 3 is 75%. 4

There is another way that some people find easier, we can convert 3 into a decimal and 4

then multiply by 100. 3 = 3 ? 4 = 0.75?100 = 75% 4

convert multiply

to

by

decimal 100

Why do we multiply by 100, well it is simple really. All numbers have a denominator of 1, so when you divide the fraction out, you get 0.75 . Now convert that into an equivalent

1 fraction with a denominator of 100.

0.75 = 75 (0.75?100) 1 100 (1?100)

Since all decimals can be treated as if they have a denominator of 1, we can simply multiply by 100 each time.

Lets try another example;

7 is what percent? 8

Convert to a decimal: ___________________

Multiply by 100: ___________________

Unit 3.7 Relating Fractions Decimals and Percents Handout.doc

3

Mathematics Grade 7 Example: 13 is what percent? 20

Convert to a decimal: ___________________ Multiply by 100: ___________________

File Name: Unit 3.7 Lesson

Example: Bob received a mark of 7 out of 35 on his math test. What percent is this? Solution:

Write as a fraction first gives us ___. Now convert this to decimal: ___________________

Finally convert the decimal to percent by multiplying by 100. ___________________ Bob received a mark of ______ on his math test.

Example:

It is 217 km from Sedgewick to Bobs Farm near Edmonton. If Bob has driven 144 km on the way to his farm, what percent of the distance has he traveled so far? Round your answer to the nearest percent.

Write as a fraction:

____.

Convert to a decimal: ___________________

Convert to a percent: ___________________

Round to nearest percent

___________________

Bob has driven _______ of the way to his farm.

Unit 3.7 Relating Fractions Decimals and Percents Handout.doc

4

Mathematics Grade 7

File Name: Unit 3.7 Lesson

Example:

Bob wants to grow to be 2 metres tall. He is 1.45 metres now, what percent of the way is he so far? Round your answer to the nearest tenth.

Create a fraction:

_____

Create a decimal:

___________________

Convert to a percent: ___________________

Bob is _______ of the way to his goal of 2 metres tall.

Converting Percent to decimals and fractions: Since a percent is always out of a 100, creating a fraction is simply a matter of writing the percent over 100 to create a fraction and then reducing the fraction. What is 20 percent as a fraction? Written as a fraction: 20

100 Now reduce by dividing the top and bottom by the same number until reduced to simplest form. 20 ?20 = 1 100 ?20 5 Example: Bob received a mark of 40 percent on his math test. What fraction of the questions did he get correct?

Write as a fraction out of 100: _____

Now reduce to lowest form: ___________________

Bob got ___of the questions correct.

Unit 3.7 Relating Fractions Decimals and Percents Handout.doc

5

Mathematics Grade 7

File Name: Unit 3.7 Lesson

Example: Write the following percents as a fraction with a denominator of 100.

a) 24%

b) 16%

c) 76%

Converting Percents to Decimals

To convert a percent to a decimal, we need to think of what a percent is. It is a number out of 100, so we need to divide by 100.

Example:

75% is what number as a decimal?

Since 75% is out of 100, you can think of it as 75 . This can be converted to a decimal by 100

dividing. 75 ?100 = 0.75

You can do this without writing the fraction down, if you can remember that a percent is always out of 100.

Example:

What is 60% as a decimal?

Example:

Write the following percents as a decimal.

a) 24%

b) 16%

c) 76%

Unit 3.7 Relating Fractions Decimals and Percents Handout.doc

6

Mathematics Grade 7

File Name: Unit 3.7 Lesson

Converting Decimals to Percents

To get a percent from a decimal, all we have to do is reverse what we just did. To go from a percent to a decimal, we divided by 100. So to go from a decimal to a percent, reverse this and multiply by 100.

What is 0.75 as a percent? (multiply by 100)

What is 0.657 as a percent?

Example:

Write the following decimals as percents.

a) 0.54

b) 0.346

c) 0.7765

Example:

Josh got 47 out of 59 on his test. Marcie stated that she received 80% on her test. Who received the higher mark and by how many percent?

Josh's percent:

Since Marcie got 80%, she received the higher mark. How much higher was her mark?

Her mark was ________ higher than Josh's. Complete Page 112#1,2,3,4

Unit 3.7 Relating Fractions Decimals and Percents Handout.doc

7

Mathematics Grade 7

File Name: Unit 3.7 Lesson

Homework Book Pages 66#1,2,3,4,5,6 first table only, 7,8,9,

Unit 3.7 Relating Fractions Decimals and Percents Handout.doc

8

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download