1. Percent
Grade 6

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Warm up
1. Express the ratio in their simplest form.
a)35 : 50 Answer: a) 7 : 10
2. Fill in the gaps in each ratio, so that it becomes
3: 5when simplified.
a) __ : 10 b) 18 : __ Answer: a) b) 30
3. Express the following ratios as fractions.
1) 3 : ) 0.5 : 1 ½ Answer: a) 1/7 b) 1/3
In a test containing 20 questions of 3 marks each and 15 questions of 2 mark each and 10 questions of 1 mark each, Susan got 65marks. Compare her marks with the total marks. Answer: 13: 20
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Lets review what we have learned in the last leson
1. Ratio of two numbers X & Y(< >0) is X/Y (proper or improper fraction) written as X:Y.
A ratio should be expressed in its lowest form
2. In the ratio X : Y, the term X is called the antecedent and the term Y is called the consequent
3. All equivalent ratios can be expressed in one common ratio in its lowest form
4. Ratios are said to be in proportion when they are equivalent
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Recap
5. In the proportion p:q =r:s, p & s are
extremes and q & r are means and p*s=q*r
6. Two quantities are said to be in direct variation if they are related in such a way that when one increases(or decreases), the other also increases (or decreases) in such a manner that the ratio of the two remains the same.
7. The method of finding values by , first finding the value of one unit by division and then the value of the required number of units by multiplication is called the unitary method.
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Let’s get started
A percent is a ratio of a number to 100. A percent can be expressed using the percent symbol %.
y% = y
100 45
100
Example : 45% =
Note: 45% can be expressed as the ratio 45:100
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6. There are two main types of problems dealing with percents
1. The first type of problem is when the percent is given.
2.The second type of problem is when you are looking for the percent.
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Percent is given
In these problems, you must change the percent to a decimal
To change a percent to a decimal, divide the number by 100
This will move the decimal point two places to the left
Example: Find 7% of 250.
(Remember 7% = 0.07)
Let x = the answer
0.07 (250) = x
17.5 = x
Remember that the word "of" means to multiply”
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Example
30 is 15% of what number?
(Remember 15%=0.15)
Let n = the answer
30 = 0.15 n
n = 200
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Looking for a percent
In these problems, you should put a variable over a 100.
Example: 4 is what percent of 12?
Let x = the percent.
Writing this problem literally we would get:
4 = x% of 12.
4 = x/100 x 12
4/1 = 12x/100
12x = 4 x 100
x = 33 1/3%
To change a percent to a decimal, divide the number by 100.
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1) Find 14% of 150
Solution:
14% can be expresses as
The word “of” means multiply.
so, you can write x 150 = 21
14% of 150 = 21 14
100 14
100
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2) 46 is 20% of what number?
Solution:
Let x be the number.
46 is 20% of what number can be written as
= 20% * x Solve for x
46 = 20/100 * x
X = 230
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3) 30 is what percent of 50?
Let x be the percent.
Writing the problem as equation of
30 = x% of 50
30 = x 50
= solve for x
50x = 30 * multiply 100 on both sides
50x = Divide by 50 on both sides
x = 60 % x
100
50x
100
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13. Percent Increase and Decrease
In order to solve problems with percentage of increase of decrease you need to use the formula shown below:
= % increase or decrease
Amount of increase or decrease
Original amount
Note: Multiply the fraction by 100 to get % increase or decrease
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14. Example Amount of increase or decrease Original amount 60 500 60 500
Maria's rent went up from $500 to $560. What is
the difference of percent?
Solution:
Difference between the rent = $560 - $500
= $ 60
Use the formula, =
= 100 x
So, the difference of percent = 12%
Amount of increase or decrease
Original amount 60
500 60
500
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Time for a break!!!
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Your Turn
1) Convert 45% to decimal
2) Write the equivalent percent of %
3) Write the fraction of 15% /20
4) Convert fraction to percent: ½ %
5) If the price of a computer was decreased from $1000 to $750, by what percent was the price decreased? 25%
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Your Turn
6) Convert 68% to decimal 0.68
7) Change the decimal to percent : %
8) Write the fraction of 47% 47/100
9) What is the percent of 1/25 ? %
10) A collectors' comic book is worth $120 in 1994, and in 1995 its value is $132. Find the percent increase? 10%
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19. Lets review what we have learned in our lesson
Convert from Percent to Decimal:
To convert a percent to decimal, divide by 100. It means moving the decimal point two places to the left.
Example : 56%
56% = = 0.56
56% is equivalent to the decimal 0.56. 56
100
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20. Convert from Decimal to Percent
To convert a decimal to a percent, multiply
by 100. It means moving the decimal point
two places to the right.
Example: 0.34
0.34 x 100 = 34 %
0.34 is equivalent to 34%
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21. Percent increase or decrease
To find percent increase or decrease, use the formula
= % increase or decrease
Amount of increase or decrease
Original amount
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You did great today !
Be sure to practice what you have learned today!
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