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? 1 is 0.10 in decimal form 10 As a Fraction? You can figure this out, just by doing the operation in your calculator. ***This is always the case for out whole numbers, we just don t always write it!...it s assumed. INVESTIGATE looking for patterns Types of Decimals Terminating: Example: Each decimal has a definite number of decimal places (ends) 0.1, 0.25 Repeating: Example: 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 1
Example 1. Example 2. Write each decimal as a fraction in simplest form. a) 0.02 How many decimal places there are determines our denominator (a power of 10) b) 0.625 For each fraction, write an equivalent fraction with denominator 10, 100, or 1000. Then, write the fraction as a decimal. a) 45 Pages 89 90 b) 350 1i*ii*iv* 3i*ii* 4a*c*e* 7 9ai, aii 12 c) 720 3.2 Comparing and Ordering Fractions and Decimals Review Write each decimal as a fraction in simplest form. a) 0.03 b) 0.27 c) 0.333333 Improper Fractions to Mixed Numbers How do I change into a mixed number? What about back to a mixed number? Write each fraction as a decimal. a b) 1 c) 2
Investigate Example 1 Order the following numbers from least to greatest using: Benchmarks Decimals Example 2 Order the following numbers from least to greatest using: Equivalent fractions Decimals Benchmarks Example 3 Order the following numbers from least to greatest using 1 of the following: Benchmarks Equivalent Fractions Decimals Example 4 Write a fraction between: a b Example 5 Write a number between: a 0.6 0.7 b 1.3 1.4 3
Page 94 95 1* 2* 4a* 6a* 8ac 11ab Which method is best? Benchmarks? Equivalent Fractions? Decimals? INVESTIGATE 3.3 Adding and Subtracting Decimals 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. Example 2. Subtract 7. 456 3. 74 a) Front end estimation 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 b) Line up vertically 7. 456 3. 740 4
+ 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. Pages 98 99 1a* 2* 4 7 9* 11a Review 3.4 Multiplying Decimals 20 x 16 Remind me how to do this! 5
Example 1 Method 2 **Use the same method as multiplying two whole numbers To Multiply Decimals 1. Multiply as if there was no decimal Example 1 Method 1 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 2 2.65 X 1.40 Multiply using blocks 4.5 x 2.3 Since there are 3 digits to the right of the decimal in in question, there must be the same amount in the answer 3.710 Example 4. Multiply using BOTH methods! Page 102 103 1a* 2b* 5* 7 8b* 9 6
Review from yesterday 3.5 Dividing Decimals How is division related to multiplication? INVESTIGATE How can you solve this problem with your partner? Example 1. Example 2. Divide as you would whole numbers. First, what is our division statement?...then solve 7
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? Page 106 107 4* 5a*b* 6c* 9 12 3.6 Order of Operations with Decimals INVESTIGATE 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? 8
Example 1. 57.2 + 28.1 4 Memorize this!!!! Example 2. 72.9 0.3 x 3 3.26 + (4.85 0.05) 3.75 4.2 Example 4. Pages 109 110 3.7 Relating Fractions, Decimals, and Percent 1b* 2* 3* 4a*b* 6 9
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 X 25 3 75 4 100 X 25 **Remember Whatever we do to the bottom we must do to the top to make equivalent fractions Because percent is always out of 100, this fraction is 75% Example 1. Change to a percent 7 20 Percent to Fraction To change a percent to a fraction: put the percent over 100 then reduce to lowest terms. Decimal to Percent To change a decimal to a percent : move the decimal 2 spaces to the right (round if necessary) 35% = 35 = 7 100 20 0.35 = 35% 1.56 = 156% This is the same thing as multiplying by 100 Example 2. Change to a fraction 78% Change these decimals to percent. 2.34.005.6 10
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 5. Example 4. Change the following percent to decimals. 45% 102%.7% 3.2% 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? Page 112 113 1* 2a*d* 3b*d* 4 6a Review from yesterday 3.8 Solving Percent Problems 11
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 =$192.00 This 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 192.00 3) $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? 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 is on sale? 12
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