chapter 3 (7) fractions, decimals, percent 2016
TRANSCRIPT
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Chapter 3 Fractions, Decimals, and
Percent
3.1 Fractions to Decimals
How can we write a whole number as a decimal or fraction?
Example 1.
4
As a Decimal?
As a Fraction?
***This is always the case for out whole numbers, we just don’t always write it!...It’s assumed.
1 is 0.10 in decimal form10
You can figure this out, just by doing the operation in your calculator.
INVESTIGATE…looking for patternsTypes of Decimals
Terminating:Example:
Repeating:Example:
Each decimal has a definite number of decimal places (ends)0.1, 0.25
Some digits repeat forever (as far as you can see). We draw a bar over those that repeat.0.1212121212…we write this as 0.12
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Example 1. Example 2.Write each decimal as a fraction in simplest form.a) 0.02
b) 0.625
How many decimal places there are determines our denominator (a power of 10)
Example 3. For each fraction, write an equivalent fraction with denominator 10, 100, or 1000. Then, write the fraction as a decimal.a) 45
b) 350
c) 720
Practice
Pages 89 – 90
1i*ii*iv* 3i*ii* 4a*c*e* 7 9ai, aii 12
3.2 Comparing and Ordering Fractions and Decimals
ReviewWrite each decimal as a fraction in simplest form.a) 0.03 b) 0.27 c) 0.333333…
Write each fraction as a decimal.
a b) 1 c)
Improper Fractions to Mixed Numbers
How do I change into a mixed number?
What about back to a mixed number?
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Investigate Example 1Order the following numbers from least to greatest using: ‐ Benchmarks
‐ Decimals
Example 2Order the following numbers from least to greatest using: ‐ Equivalent fractions
‐ Decimals‐ Benchmarks
Example 3Order the following numbers from least to greatest using 1 of the following:
‐ Benchmarks‐ Equivalent Fractions‐ Decimals
Example 4Write a fraction between:
a
b
Example 5Write a number between:a 0.6 0.7
b 1.3 1.4
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Practice
Page 94‐95
1* 2* 4a* 6a* 8ac 11ab
Which method is best?‐ Benchmarks?‐ Equivalent Fractions?‐ Decimals?
3.3 Adding and Subtracting Decimals
INVESTIGATE
When we add or subtract decimals, we estimate if we do not need to find an exact answer.**Then we must check to see if the answer makes sense
Example 1.
5.763 + 3.94
1) First, use Front‐End Estimation to estimate an answer.‐ This means that we add the whole number part of each decimal.
2) Second, Add vertically by lining up the decimals; use 0 place holders so that each number has the same number of digits after the decimal.
5.763+ 3.940
Example 2.
Subtract 7. 456 ‐ 3. 74
a) Front‐ end estimation
b) Line up vertically
7. 456 ‐ 3. 740
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Example 3.Find two numbers with a sum of 254.791. + Example 4.
Example 5.Althea bought 3.6 kg of beef, 1.7 kg of cheese, 3 kg of fish and 2.28 kg of rice. What was the total mass she had to carry?Estimate to check your answer is reasonable.
Practice
Pages 98 – 99
1a* 2* 4 7 9* 11a
3.4Multiplying Decimals
Review
20x 16
Remind me how to do this!
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Example 1 – Method 1
Example 1 – Method 2
**Use the same method as multiplying two whole numbers
To Multiply Decimals
1. Multiply as if there was no decimal
2. Once you have an answer go back to the question and count the number of places that are to the right of the decimal.
3. Put the same amount of digits to the right of the decimal in your answer
Example 22.65
X 1.40
Since there are 3 digits to the right of the decimal in in question, there must be the sameamount in the answer 3.710
Example 3.
Multiply using blocks4.5 x 2.3
Example 4.Multiply using BOTH methods!
Practice
Page 102 – 103
1a* 2b* 5* 7 8b* 9
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3.5Dividing Decimals
Review from yesterday…
How is division related to multiplication? INVESTIGATEHow can you solve this problem with your partner?
First, what is our division statement?...Then solve
Example 1.Example 2.
Divide as you would whole numbers.
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Example 3.92.34 ÷ 0.6
Example 4.Cameron has a board 3.8 m long. He wants to make shelves for his room.Each shelf is to be 0.6 m long.
How many shelves will Cameron get from this board?
Practice
Page 106 – 107
4* 5a*b* 6c* 9 12
3.6Order of Operations with Decimals
What is the answer to the following question?
6 x 15.9 + 36.4 ÷ 4
How many different answers can you get?How do we know which answer is correct?
INVESTIGATE
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Memorize this!!!!
Example 1.57.2 + 28.1 4
Example 2.72.9 ÷ 0.3 x 3
Example 3.
3.26 + (4.85 0.05) – 3.75 4.2
Example 4.
Practice
Pages 109 – 110
1b* 2* 3* 4a*b* 6
3.7 Relating Fractions, Decimals, and
Percent
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INVESTIGATE
We can use number lines as one way to relate fractions, decimals, and percent Fraction to Percent
To change a fraction to percent: change the fraction to a denominator of 100
3 754 100
X 25
X 25
**Remember – Whatever we do to the bottom we must do to the top to make equivalent fractions
Example 1.Change to a percent
7 20
Because percent is always out of 100, this fraction is 75%
Percent to FractionTo change a percent to a fraction: put the percent over 100 then reduce to lowest terms.
35% = 35 = 7 100 20
Example 2.Change to a fraction
78%
Decimal to Percent
To change a decimal to a percent : move the decimal 2 spaces to the right (round if necessary)
0.35 = 35%1.56 = 156%
This is the same thing as multiplying by 100
Example 3.Change these decimals to percent.
2.34
.005
.6
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Percent to Decimal
To change a percent to a decimal: move the decimal two places to the left (remember that if you don't see the decimal it is at the end of the number)
26% = 0.26 This is the same thing as dividing by 100
Example 4.Change the following percent to decimals.
45%102%.7%3.2%
Example 5.
Example 6.In 5 min, Benjamin completed 27 of 30 multiple‐choice questions. Madison completed 83% of the questions. Who completed more questions? How do you know? Practice
Page 112 – 113
1* 2a*d* 3b*d* 4 6a
3.8 Solving Percent Problems
Review from yesterday…
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INVESTIGATE Discounts and Tax
Discount means to subtract a percent from the original amount.
Ask yourself 'what is the percent of the original number? (20% of $240.00)
1) Change % to a decimal (move decimal 2 places to the left) 2) Multiply (remember of means multiply)
(0.2 X $240.00)= 48.00 (this is your discount)3) *Subtract that number from your original cost
240.00 ‐ 48.00 =$192.00This is your new cost.
Tax is a percent that you add on to the original amount.
To find the tax: ( GST ‐ 5%)1) Change % to a decimal (move decimal 2 places to the left) 2) Find 5% of your new amount ($192.00)2) Multiply 0.05 x 192.003) $9.60 ‐ this is the amount of tax you need to add to your price.
So 192.00 + 9.60 = $201.60
Example 1.
A snow board regularly sells for $399.95. On Saturday, the snow board will be on sale for 30% off
1) How much money will you save if you buy the board on sale?
2) What is the total cost of the board, on sale, if you add in the G.S.T. ? (5%)
Example 2.Sandi works at Fancies Flowers on Saturdays. The owner pays Sandi 3% of all money she takes in on a day.Last Saturday, Sandi took in $1200.00.
How much money did Sandi earn last Saturday?
Example 3.A paper back novel originally costs $7.99. It is on sale for 15% off.How much will you save?
What will be the price of the paper back when it ison sale?
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Practice
Page 115 – 116
1b*d* 2a*c* 3* 5b*c 6 8b