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Unformatted text preview: Percentages www.mathsrevision.com Revision of Level E Appreciation / Depreciation Expressing "A" as a percentage of "B"
Finding Initial Value after increase or decrease 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Starter Questions
Q1. 34.5 + 0.6 + 5 www.mathsrevision.com Q2. 6 w 4 r + 4 w + 9 r Tidyup the expression Find y wh e n 3 y + 6 = 3 3 Q3.
Q4. I f p = 4 , q = 5 , r = 3 Find
13 Feb 2012 pq  r 2
Created by Mr. Lafferty Maths Dept. Percentages
Revision of Level E
Learning Intention Success Criteria 1. Convert percentages to fractions and decimals. 2. Change fraction to percentages. 3. Find percentage values. www.mathsrevision.com 1. To summarise Level E work using Mind Map. 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Percentages
Revision of Level E
Put over 100 0.3
3 10 3.0 www.mathsrevision.com 30%
Put over 100 30 3 = 100 10
0.7
7 10 7.0 0. 3 70%
13 Feb 2012 70 7 = 100 10
Created by Mr. Lafferty Maths Dept. 0.7 What simple % is missing
Pe r c e nt ag e 50 4 80% = Percentages 5 Revision of Level E
25 75 33 www.mathsrevision.com Fr ac t io n 1 2 1 4 3 4 2 1 66 3 3 1 2 3 3 20 40 60 10 30 70 90 1 5 2 5 3 5 1 10 3 10 7 10 9 10 Example : Find 20% of 450 20 1 = 10 0 5
13 Feb 2012 1 o f 4 5 0 = 4 5 0 5 = 9 0 5
Created by Mr. Lafferty Maths Dept. S3 How to find % of a quantity using a calculator
Find 50% of 300 example
50 1 = = 0. 5 100 2 www.mathsrevision.com Step 1 : Convert % to a decimal 0. 5 of 300
Step 2 : 0. 5 300 of means x Step 3 : Do sum 0. 5 300 = 150
Calculator Keys 5
13 Feb 2012 0 1 0 0 x 3 0 0 = 150 Created by Mr. Lafferty Maths Dept. S3 How to find % of a quantity using a calculator
Find 40% of 480 example
40 4 = = 0. 4 100 10 www.mathsrevision.com Step 1 : Convert % to a decimal 0. 4 of 480
Step 2 : 0. 4 480 of means x Step 3 : Do sum 0. 4 480 = 192
Calculator Keys 4
13 Feb 2012 0 1 0 0 x 4 8 0 = 192 Created by Mr. Lafferty Maths Dept. Percentages
Revision of Level E www.mathsrevision.com Now try Exercise 1 Ch19 (page 92) 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Starter Questions
Q 1. W r it e t h e s e pe r e c e nt ag e s as d e c im a ls . www.mathsrevision.com (a) 5 0 % (b ) 2 5 % (c ) 6 0 % Q 2 . Find 4 0 % o f 4 0 0 . Q 3 . Find t h e ar e a o f t h e s h ape . 5cm 13 Feb 2012 Created by Mr. Lafferty Maths Dept. 6cm Calculating Percentages
Appreciation & Depreciation
Learning Intention Success Criteria 1. To know the terms appreciation and depreciation. 2. Show appropriate working when solving problems containing appreciation and depreciation. www.mathsrevision.com 1. To understand the terms appreciation and depreciation. 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Calculating Percentages
Appreciation & Depreciation www.mathsrevision.com Appreciation / Depreciation
Appreciation : Going up in value e.g. House value Depreciation : Going down in value e.g. car value 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Average house price in Glasgow has appreciated by 50% over the past 10 years. If you bought the house for 80 000 in 1994 how much would the house be worth now ? Appreciation = 50% x 80 000 = 0.50 x 80 000 = 40 000 Just working out percentages New value = Old Value + Appreciation = 80 000 + 40 000 = 120 000
13 Feb 2012 Created by Mr. Lafferty Maths Dept. Calculating Percentages
Appreciation & Depreciation A Mini Cooper cost 15 000 in 2005 At the end 2006 it will have depreciated by 20% What will the mini cooper worth at end 2006? End 2006 Depreciation = 20% x 15 000 = 0.2 x 15 000 = 3 000 New value = Old value Depreciation = 15 000 3000 = 12 000 13 Feb 2012 Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Calculating Percentages
Appreciation & Depreciation
A valuable piece of jewellery appreciated by 10% in the 1st year and by 20 % in the 2nd Year. If its initial value was 1 000, what is its value now ? 1st Year Appreciation = 10% x 1 000 = 0.1 x 1 000 = 100 New Value = 1 000 + 100 = 1 100 2nd Year Appreciation = 20% x 1 100 = 0.2 x 1 100 = 220 New Value = 1 100 + 220 = 1320
Created by Mr. Lafferty Maths Dept. 13 Feb 2012 Calculating Percentages
Appreciation & Depreciation www.mathsrevision.com Now try Exercise 2 Ch19 (page 94) 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Starter Questions
Q 1. W r it e t h e s e pe r e c e nt ag e s as d e c im a ls . www.mathsrevision.com (a) 7 5 % (b ) 12 .5 % (c ) 6 0 % Q 2 . Find 3 0 % o f 4 0 0 . Q 3 . Find t h e ar e a o f t h e s h ape . 10cm 13 Feb 2012 Created by Mr. Lafferty Maths Dept. 8cm Calculating Percentages
Expressing "A" as a percentage of "B"
Learning Intention Success Criteria 1. To understand how to express "A" as a percentage of "B". 2. Solve problems in context. www.mathsrevision.com 1. To understand how to express "A" as a percentage of "B". 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Calculating Percentages
Expressing "A" as a percentage of "B" Example 1 : Frances scored 13 out of 20 in a Maths test. What was her percentage score? A % mark = B www.mathsrevision.com 13 13 = 10 0 20 20 =65% 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Calculating Percentages
Expressing "A" as a percentage of "B" Example 2 : Daniel was paid 20 per week. He got a wage rise to 22 per week. What was his percentage increase in pay ? A Actual Increase = 22 20 = 2 inc r e as e 2 = 10 0 % increase = o r ig inal pay 2 0 B
13 Feb 2012 Created by Mr. Lafferty Maths Dept. = 10 % Calculating Percentages
Expressing "A" as a percentage of "B" Example 3 : A house in Barlanark bought for 40 000 in 2001 was sold last week for 50 000. Calculate the percentage appreciation in value? A Actual Increase = 50 000 40 000 = 10 000 inc r e as e 10 0 0 0 = 10 0 % increase = o r ig inal pr ic e 4 0 0 0 0
13 Feb 2012 B =25% Created by Mr. Lafferty Maths Dept. Calculating Percentages
Expressing "A" as a percentage of "B" www.mathsrevision.com Now try Exercise 3 Ch19 (page 97) 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Starter Questions
1. 99. 6 + 7. 27 www.mathsrevision.com 2 . C a lc ula t e 7 0 % o f 8 4 3. 4. 40% of 160p Round t o 1 decimal place
(a) 6. 67 (b) 5. 54 (c) 7. 9 9 5. Find t he value of x 5x +25 = 105
Created by Mr. Lafferty Maths Dept. 13 Feb 2012 Finding initial value after an increase or decrease
Learning Intention Success Criteria 1. To understand the process of finding the initial value. 2. To solve problems using this process. Percentages www.mathsrevision.com 1. To explain how to find the initial value after an increase or decrease. 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Calculating Percentages
Finding initial value after an increase or decrease Example 1
www.mathsrevision.com
After a 10% increase the price of a house is 88 000. What was the price before the increase. Deduce from question : We have : 100 % + 10 % = 88 000 110 % = 88 000 1 % : 88 000 Price before is 100% : 13 Feb 2012 Created by Mr. Lafferty Maths Dept. 110 = 800 800 x 100 = 80 000 Calculating Percentages
Finding initial value after an increase or decrease Example 2
www.mathsrevision.com
The value of a car depreciated by 15%. It is now valued at 2550. What was it's original price. Deduce from question : We have : 1 % : 13 Feb 2012 100 %  15 % = 2 550 85 % = 2 550 2 550 85 = 30 Price before is 100% : Created by Mr. Lafferty Maths Dept. 30 x 100 = 3 000 Calculating Percentages
Finding initial value after an increase or decrease www.mathsrevision.com Now try Exercise 4 Ch19 (page 98) 13 Feb 2012 Created by Mr. Lafferty Maths Dept. ...
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