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fractions and decimals

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Loren Mytko

on 18 January 2013

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Transcript of fractions and decimals

Fractions, Decimals, and Percent
Staring Mr.Shinkaruk 3.1
Fractions To Decimals Mr. Shinkaruk was invited to go golfing with his buddies. They arrived at the golf course and started playing. Mr. Shinkaruk noticed golf was math and since he hit two out of the four balls, in math it would be 2/4. Then he wanted to change 2/4 into a decimal. He remembered that you need to divide the numerator by the denominator. so two divided by four equals 0.5. 3.2
Comparing And Ordering Fractions and Decimals Mr. Shinkaruk and his friends wanted to have a competition. They decided that they would see how many holes in one they could get.
His friend, Mr. Motut went first and got 3/5 holes in one. Mr. Shinkaruks other friend, Mr. Christianson went second and got 4/10 holes in one. Finally it was Mr. Shinkaruks turn. He got 9/10.
After they got these results, they wanted to know who won. Mr. Motut preferred to shange the fractions to decimals to find the answer but Mr. Shinkaruk liked to find the common denominator. Mr. Motut started to change the fractions to decimals by dividing the numerator by the denominator. These were Mr.Motut's results:
3/5 = 0.6 4/10 = 0.4 9/10 = 0.9

To get Mr. Shinkaruk's answer, you need to find the common denominator. The common denominator is 10. since 5 goes into 10 2 times, you multiply 3 by 2. so it becomes 6/10. For 9/10 and 4/10 already has a denominator of 10 so you don't change anything. Results: 6/10, 4/10, and 9/10.
To find out who won, you look at whoever has the highest number. if you change the fractions to decimals, you look at who has the highest number in the tenths place.

Greatest to least:
Mr. Shinkaruk with 9/10 then Mr. Motut with 3/5 then Mr. Christianson with 4/10 Example 1 Here are some more results. Help Mr. Shinkaruk by changing the fractions to decimals.
a) 9/16 b) 5/16 c) 2/4

Answers:
a) 0.5625 b) 0.3125 c) 0.5 Example 2 Order each set of numbers from least to greatest.
a) 7/2, 13/4, 25/8 b) 7/5, 4/7, 3/2
Answers:
a) 25/8, 13/4, 7/2 b)4/7, 7/5, 3/2 Example 3 In this set of numbers,identify what number is not placed correctly.
29/5, 62/10, 6.25, 122/20
Answer:
122/20 is not placed correctly. It should be the second number in the set. Example 2 Write each fraction as a decimal.
a)12/6 b) 2/10 c) 8/20 d) 7/20
Answers:
a) 2 b) 0.2 c) 0.4 d) 0.35 Example 3 Write 1/5 as a decimal. Use this decimal to write the fractions below as a decimal.
a) 4/5 b) 7/5 c) 9/5 d) 11/5
Answers:
a) 0.8 b) 1.4 c) 1.8 d) 2.2 3.3
Adding And Subtracting Decimals You add and subtract decimals. To subtract decimals, you subtract the same way when you subtract whole numbers except you would line up the decimals with each other and put the decimal Where it lines up in the answer.
For example
3.6 - 2.1

first you would subtract one from six which equals five.


Then you would subtract two from three.




All you do to know where to put the decimal, you just line up the decimal.



the answer is 1.5 3.6
-2.1
5 3.6
-2.1
1 5 3.6
-2.1
1.5 When you add, you do the same thing but you add the numbers instead of subtract. you would Add six and one firs which equals seven.


Then you would add two and three together which equals five.

Now you would just line the decimals up.


The answer is 5.7 3.6
+2.1
7 3.6
+2.1
5 7 3.6
+2.1
5.7 Example 1 you can use front end estimation to estimate the answer.
Example: 3.6-2.1
3.6 would become 4 because 6 is closer to ten which would be a whole number. If the 6 was a 4 or under, the number would just stay as 3.
You would round 2.1 to 2 because 1 is closer to 0 than to 10.
So the whole equation would be 4-2. Your estimate of the answer of 3.6-2.1 would be 2. When you add
you would do the same thing except add instead of subtract. Mr. Shinkaruk wanted to find the difference between the decimals shown below. Help Mr. Shinkaruk subtract the decimals.
a) 4.5-1.4 b) 7.9 - 3.2
Answers:
a) 3.1 b) 4.7 Example 2 After a while of playing golf, Mr. Shinkaruk was tracking the results of how many holes in one they got. Mr. Shinkaruk wanted to know about how many hole in ones they got all together. Help Mr. Shinkaruk by using front end estimation to add the following results.
a) 6.8 and 3.4 b) 4.9 and 1.3
Answers:
a) 10 b) 6 Front End Estimation Example 3 Find the pattern in Mr. Shinkaruks results and find the next three numbers of the pattern.
2.09, 2.13, 2.17, 2.21....
Answer:
The pattern is that you add 4 to the decimal place each time.
The next three numbers are 2.25, 2.29, 2.33 3.4
Multiplying decimals


Then you add 36 and 720 together.

6+0= 6
3+2= 5
Now you count the number of decimal places before the decimal which is 2 decimal places in the equation.



Since there are 2 decimal places in the equation, you move the decimal 2 places up in the answer you got when you added the two numbers. That is where the decimal goes




The decimal goes in front of the seven so the answer of 3.6 x 2.1 is 7.56 3.6
x2.1
3 6 720
+ 36
756 3.6
x2.1 7 5 6

2 1 Example 2 Multiply. Describe the pattern you see
8.36 x 10
8.36 x 100
8.36 x 1000
8.36 x 10 000

Answers =
8.36 x 10= 83.6
8.36 x 100= 836
8.36 x 1000= 8360
8.36 x 10 000=83600
The digits in the product move one place to the left each time. Example 1 Multiply these golfing results.
a) 4.2 x 3.7 b) 8.9 x 0.3
c) 0.6 x 0.9 d) 5.6 x 2.1
Answers:
a) 15.54 b) 2.67
c) 0.54 d) 11.76 Example 3 The fuel consumption estimates of Mr. Shinkaruk's car are:
City: 21.2 km/L Highway:23.3 km/L
The car's gas tank holds 40.2 L of fuel

a) how far can Mr. Shinkaruk drive on a full tank of gas on a highway before he runs out of fuel?
b) How far can Mr.Shinkaruk drive on a full tank of gas in the city?

Answers:
a) Mr. Shinkaruk could drive 936.66 km on the highway.
b) Mr. Shinkaruk could drive 852/24 km in the city.
3 0.6

2 2 x 3= 2x0.6=
6 1.2

0.1 3 x 0.1 =0.3 0.1x0.6
= 0.06

Then you multiply 3 by 2 and put the answer in the middle of the grid.
Now you multiply 2 by 0.6 and put the answer in the box under 0.6.
Next multiply 3 by 0.1 and put the answer in the box across from 0.1.
Now multiply 0.6 by 0.1 and put the answer in the last box remaining. 6.00
0.3
1.2
+0.06
7.56

The answer is 7.56 3.5
Dividing Decimals To divide decimals, Divide as you would a whole number.
Say you wanted to find the quotient to 2.8/1.6 First take the decimals out so now the number becomes 28/16. 16 becomes the divisor and 28 is the dividend. Now as you would with a whole number, see how many times 16 goes into 28. To multiply you can also use a grid.
First you make:






Then you put the number you multiply on the grid. to multiply decimals, first you line up the numbers and multiply the last digit of the number by the two up top.

1x6= 6
1x3= 3 3.6
x2.1
36
720

Then you move on to the first digit in the number which is 2. First you add a 0 then you multiply the 2 by the 6 then the 2 by the 3.
2x6=12
2x3=6
Add a zero


Now add 36 and 720 together.

6+0= 6
3+2= 5 The answer is one time.
1 put the one on top
16 28
Subtract 16 from 28.
1
16 28
- 16 since 16 doesn't go into 12, add a
120 zero
Since 16 goes into 120 seven times, which equals 112, subtract 112 from 120. 120- 112= 8. 16 doesn't go into 8 so add a zero. Now figure out how many times 16 goes into 80.
The answer is 5 so put the 5 beside the 7.

1 7 5
16 28
16 goes into 80 exact so you don't do anything more. Now put the decimals back in.There are 2 decimal places in the equation.
1.6 2.8
In the quotient, also known as the answer, move the decimal up two places.
The quotient is 1.75 Example 1 Last week, Mr. Shinkaruk worked 37.5 hours. He earned 346.88.
a) How much did he earn per hour?
b) why is the answer different from the calculator display?

Answers:
a) He earned $9.25
b) When dealing with money, you need to round the number to the nearest hundredth. Example 2 Divide. Describe the patterns you see over all.
a) 124.5/10 b) 124.5/100
c) 124.5/1000 d) 124.5/10 000

Answer:
a) 12.45 b)1.245 c)0.1245
d) 0.012 45
The digits in the quotient move one place to the right each time. Example 3 Ashley finds a remnant of landscaping fabric at a store. The fabric is standard width, with length 9.88m. Ashley needs fourteen 0.8m pieces for a garden patio.
a) how many 0.8m pieces can Ashley cut from his remnant? What assumptions did you make?
b) Will Ashley have the amount of fabric she needs? Why or why not?
c)If your answer in part be was no, how much more fabric does she need?

Answer:
a) About 12 pieces
b) No she needs fourteen pieces and she only has twelve.
c) If Ashley can't use 0.28m to cut more pieces, she needs 1.6m.
If Ashley can use 0.28m then she will only need 1.32 m of fabric. If dividing money like $8.24/$2.34 Then in the quotient always round up to the nearest hundredth if there is a thousandths place. You need to do this because there is no such thing as $9.345. This would become $9.35. 3.6
Order Of Operation With Decimals Whenever you see an equation like:
- (46.78-23.58) x 2.5, you need to follow order of operation to get the correct answer. The order of operation is BEDMAS which is short form for Brackets, equotients, Division, Multiplication, Addition, then subtraction. This is the order you need to do to answer the equation correctly. Say you wanted to answer (46.78-23.58) x2.5, First answer the equation inside the brackets. 46.78- 23.58 =23.2 so you put 23.2x 2.5 to keep track and to show your work. Since all you need to do now is multiply, multiply 23.2 by 2.5. 23.2x2.5= 58 so 58 is your answer to (46.78-23.58)x2.5. If you didn't use the order of operation, you wouldn't have gotten the correct answer. Example 1 Evaluate:
a) 4.6+5.1-3.2 b) 8-3.6/2
c)46.4-10.8x 3 d) 85.6/0.4x 7
Answers:
a) 6.5 b) 6.2 c) 14 d) 1498 Example 2 Evaluate. Explain why the answers are different.
a) 9.8-3.2/0.4+2.6
b) (9.8-3.2) /(0.4+2.6)
Answers:
a) 4.4 b) 2.2
The answers are different because the order of operation is different. Example 3 A radio station contest used skill testing question: 4+6 x 1.3_2.4/2. Mr. Shinkaruk said the answer was 10.6 but Mr. Motut said the answer was 5.3. Who is correct? How do you know?

Answer:
Ally is correct. When you answer the question using order of operation, the answer is 10.6 3.7
Relating Fractions, Decimals, and Percents We see uses of percents everywhere. Decimals and fractions are like percents. we can use number lines to show how percents are related to decimals and fractions. Mr.Shinkaruk teaches us that decimals can be written as a percent. Mr.Motut gave him a decimal showing how many holes he won and how many Mr.Motut won.

Mr.Shinkaruk: .75
Mr.Motut: .25
.75 multiplied by 100 equals 75%
.25 multiplied by 100 equals 25%

Mr.Shinkaruk won 75% of the holes and Mr.Motut won 25% of the holes. Mr.Shinkaruk needs you to write each fraction as a decimal and as a percent.

a) 2/10 b) 3/50 c) 4/25 d) 13/20


Answers:
a) 2/10 = 0.2 = 20%

b) 3/50 = .06 = 6%

c) 4/25 = 0.16 = 16%

d) 13/20 = 0.65 = 65% Example 1 Example 2 Juli had .84 on a test and her friend Jane got 82%
on the test which of them got the higher mark?


Answer: Juli did because .84 multiplied by 100 equals 84% so juli got a higher mark by 2%. Example 3 Write each percent as a fraction and
a decimal.

a) 2% b) 9% c) 28% d) 95%


a) 2% = 2. divided by 100 = 0.02
0.02 = 2/100 to make it a smaller number
we divide by 2.
2 divided by 2 = 1 100 divided by 2 = 50
= 1/50 = 0.02 = 2%

b) 9% = 9 divide by 100 = 0.09
0.09 = 9/100 We cant make this a smaller
number because its not even.
0.09 = 9/100 = 9%
c) 28% = 0.28 = 28/100 divided by 2

28 divided by 2 = 14 100 = 50
= 14/50 = 0.28 = 28%

d) 95% = 0.95 = 95/100 100/100 0/0 25/100 75/100 1.0 0.25 0.75 100% 0% 25% 75% 0.0 3.8
Solving Percent Problems It is useful to calculate the percent, to find the sale price and final price and the discount to see which of the two items is a better deal. Say a jacket was $48.00 and it was 25% off. To find the sale price, make 25% a decimal then multiply it by the cost of the jacket.
48 x 0.25 = 12.00.
12.00 is the discount so to find the sale price, subtract the discount from $48.00
48-12= 36
sale price= $36.00 The sale price doesn't include
GST. The final price does, GST is always 1.05 So to get the final price multiply the sale price by 1.05. 36 x 1.05 = 37.80. So the final price is $37.80. If a question says find the sale price of 55% off of $90 you still multiply 0.55x 90. Then subtract the saved money (discount) to from the normal price. Help Mr. Shinkaruk calculate.
a) 10% of $30 b) 20% of $50 c)18% of $36
Answers:
a) 3 b) 10 c) 6.48 Example 1 Example 2 Find the tip left by each customer.
a) Mr. Shinkaruk: 15% of $24.20 b) Mr. Motut: 20% of $56.50 c) Mr. Christianson: 10% of $32.70
Answers:
a) $3.63 b) $11.30 c) $3.27 Example 3 There are 641 First Nations bands in Canada.
About 30% of these bands are in British Columbia . About how many are in British Columbia?

Answer
641 x .30 = 192



After a while of keeping track of the golf balls he hit, these were the results. Help Mr. Shinkaruk and change the fractions to decimals.
a) 4/5 b) 9/10 c) 3/6

Answers:
a) 0.8 b) 0.9 c) 0.5 Example 1

Then you move on to the first digit in the number which is 2. First you add a 0 then you multiply the 2 by the 6 then the 2 by the 3.
2x6=12
2x3=6
Add a zero Unit Quiz 3.1
1. Write each decimal as a fraction.
a) 0.26 b) 0.45 c) 0.01
3.2
2. In this set, identify which number has been misplaced.
29/5, 6 2/10, 6.25, 6 2/20
3.3
3. Estimate then calculate the sum.
46.71+3.9+0.875
3.4
4. Multiply.
a)2.7 x 4.786 b) 12.52 x 13.923
3.5
5.The area of a rectangle is 22.32m and the width is 0.8. What is the length?
3.6
6. Evaluate:
(46.78 - 23.58) x 2.5
3.7
7. Write each percent as a decimal.
a) 2% b) 9% c) 28% d) 95%
3.8
8. The regular price of a golf club is $60. Find the sale price of the club before taxes when the club is on sale for:
a) 25% off b) 30% off c) 40% off
3.1
1. a) 26/100 b) 9/20 c) 1/100
3.2
2. 6 2/20 should be after 29/5
3.3
3. Estimate= 47+4+1= 52
3.4
4. a) 12.922 2 b) 174.315 96
3.5
5. 27.9m
3.6
6. 58
3.7
7.a) 0.02 b) 0.09 c) 0.28 d) 0.95
3.8
8. a) $45.00 b) $42.00 c) $33.00 Then put the number you want to multiply. For example: 3.6x2.1 2 0.1


3 0.6






The last step is to add up all the answers on the grid and you will have your answer. Answers
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