Using Double Number lines (Part one)
ACEA
AA
AM
AP
We are learning to solve percentage problems using double number lines
Exercise 1: Finding a percentage of a quantity
Example: 20% of 150 is c
Draw double lines to solve the following number problems.
1. There are 30 students in 9CT and 40% are girls. How many boys are there in the class?
2. In a berry mix there are 30% strawberries and 20% raspberries and the rest are blackberries. In a 500gm punnet of berries what weight are the strawberries?
3. Carly has 35 pens in her pencil case and 20% don’t work. How many do work?
4. There were 500 sweets in a box and Mrs Miller has given out 35% as prizes. How many are left in the box?
5. In November last year it rained on 60% of the days.
How many rainy days were there?
Exercise 2: Finding one quantity as a percentage of another
Example: 12 is c% of 40. What is c ?
Draw double lines to solve the following number problems.
1. Abigail is working on a set of 50 number problems and she has just finished question 28. What % of the questions has she finished.
2. Mr Sharp spent the day at the races and his horses were placed in 8 out of 20 races. In what % of the races was he unsuccessful?
3. Billy is saving for a new DVD that costs $64. He already has $16. What % of the total cost has he already saved?
4. Mr Baker is decorating Hot Cross buns. He has completed 480 out of a batch of 600. What % has he decorated?
5. Sarah has completed 28km of a 40km fun run. What % has she still to run?
Exercise 3: Finding the total given a percentage of the total.
Example: 40% of c is 12. What is c ?
Draw double lines to solve the following number problems.
1. 30% of the swimming team are girls. If there are 18 girls . How many are in the team altogether?
2. Jo has been paying for a car on Hire Purchase and she has now paid $14000 which 70% of the total cost. What is the total cost?
3. Jim the orchardist has apple and pear trees in his orchard. He has pruned 130 trees which is only 65 % of the whole orchard. How many trees in the whole orchard?
4. On sports day Carl entered 75% of the events open to his age group . If he entered 12 events , how many events were there altogether?
5. Bev plays netball and last Saturday she scored 12 goals which was 40% of her team’s total. How many goals did the team score altogether?
Exercise 4 ; Mixed examples from exercises 1, 2 and 3
Draw double number lines to solve these questions
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1. 28 is c % of 140
2. 16 is c % of 128
3. 40 % of c is 20.8
4. 38 is c % of 95
5. 80% of c is 11.2
6. 39 is c % of 52
7. c is 80% of 45
8. 30% of c is 48
9. 48 is c % of 120
10. 18 is c % of 20
11. c is 40% of 32
12. 240 is c % of 1600
13. 210 is c % of 300
14. 40% of c is 36
15. c is 75% of 192
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Exercise 5; Mixed examples from exercises 1, 2 and 3 in a context
Show how you use a double number line to answer these problems.
1. 20% of the students in year 10 own ipods. There are 70 students with ipods. How many students are there altogether in year 10?
2. Hine and Paula have a contract to make 400 Xmas stars. When they have made 48 what % of the total have they made/
3. Mr Rapata has put out 40% of the 95 chairs needed for the Maths exam. How many chairs has he put out?
4. Yin is moving sheep into a paddock ready for shearing. After shearing 24 sheep he has done % of the flock. How many in the flock altogether?
5. Jeremy has been watching sport on TV for 35 minutes when his mother calls him for tea. If he has only seen 21% of the programme, how long is the whole sports programme?
6. After sharing a huge box of 150 chocolates that Bill won in an Easter raffle he noted that 60% were eaten. How many chocolates are left?
7. Mika has been saving for a computer which costs $1600. What % of the cost has he saved if he has $640.
8. Marnie grows roses and on a Saturday she pruned 25 plants which is only 20% of her plants. How many rose plants does she have altogether?
9. Vinny goes surfing on as many days as possible. He has been out 96% of the last 75 days. How many days has he not been surfing?
10. Paul is working on a computing task and after 3 hours he notices that he has only completed 20% of the tasks. How long will the whole task take to complete?
11. Sally is DJ for the school social and is hired for a total of 4 hours. After 108 minutes what % of the time has she completed?
12. Sarah has been babysitting and has been picking up Lego blocks at the end of the evening. How many blocks are there altogether if 144 is 60% of all the bricks?
13. Barry and Larry play table tennis every Thursday night. Barry has lost 39 out of the last 118 games. What % has Larry won?
14. Tom is competing in a duathlon next weekend. As part of his training he is increasing the distance he can cycle and he is now able to complete 42% of the course. If Tom can cycle 48 kilometres how long is the course?
15. 65% of Carla’s CD collection was destroyed in a flood. If she has 105 CD’s that were not destroyed how many did she have before the flood?
Using Double Number Lines to solve % problems Part two
We are learning to solve increase/decrease percentage problems using double number lines
Exercise 1: Increasing by a percentage
Draw double lines to solve the following number problems.
Example: Increase $400 by 20%
120% of 400 is c
Or divide 400 by 10 (to get 10%) and multiply by 12.
Answer = 480
1) Increase the following amounts by 20%
a. a) $80 b) $3500 c) 45cm d) 65Kg e) 50kg
2) The price of coal has been increased by 30% from $70 per tonne. What is the new price?
3) Mary works at the supermarket after school and earns $90 per week. If she receives a pay increase of 5% what is her new rate of pay?
4) Fruit juice is sold in 2L containers. If the producer wants to increase the volume by 25% what is the size of the new container?
5) In year 9 Sue measured 150cm and by the end of year 10 this had increased by 5%. What is her height at the end of year 10?
Exercise 2: Decreasing by a percentage
Draw double lines to solve the following number problems.
Example: Decrease $400 by 20%
80% of 400 is c
Or
Divide 400 by 10 to get 10% and multiply by 8
Answer = 320
1) Decrease the following amounts by 20%
a. a) $60 b) 80L c) 550ha d) 350ml
b. e) 240Kg
2) The cost of an $8000 car is reduced by 15%. What is the new cost?
3) Pene went on a diet and her weight reduced from 120Kg by 30%. What is her new weight?
4) The Smiths have a 4000Ha farm and decide to sell off 15% of it. What is the area of the farm after the sale?
5) A pair of cross trainer shoes marked $80 is reduced in a sale by 40%.
a. What is the sale price?
Exercise 3
1) Increase $120 by 30%
2) Decrease $80 by 20%
3) Increase 70cm by 40%
4) Decrease 240Kg by 65%
5) Increase 64 by 30%
6) Decrease $4200 by 10%
7) Increase 800m by 15%
8) Decrease $80 000 by 25%
9) Increase 65Kg by 20%
10) Decrease 2.5tonnes by 50%
Exercise 4
1) A CD set is marked $40 . What is the new price if there is 30% increase in price?
2) The price of a $650 bike is discounted by 40%. What is the new price?
3) The price of a trip from Christchurch to Greymouth is $80 in winter and is increased by 15% for summer. What does it cost in summer?
4) Giant Easter eggs cost $12 before Easter and are discounted by 20% after Easter. What is the discounted price?
5) A 15cm wide suitcase can be expanded by 20 cm. What is the width of the expanded suitcase?
6) A lounge suite marked at $4500 is discounted by 60%. What is the sale price?
7) The average price of a house in Mathville was $280 000 in 2006. If prices have increased in 2007 by 15% what is the increased average house price ?
8) A farmer has reduced by 40% the amount of pasture he sows in grass seed. If the original area of land in grass seed was 760Ha. What area is now in grass seed?
9) The Harbour Hotel charges $120 per night for accommodation. The price is increased by 20% if breakfast is included. What is the cost including breakfast?
10) In the week before Christmas strawberries cost $5 per 500gm, but a week later the price had been reduced by 45%. What do strawberries cost at New Year?
Using Double Number Lines to solve % problems 3
We are learning to find the original amount after a % increase/decrease using double number lines
Exercise 1: Increasing by a percentage
Draw double lines to solve the following number problems.
Example: After an increase in his weekly wage of 20% Joe has $480 . What was his wage before the increase.
Answer = 400
1) The following represent an increase of 20% What was the original value before the increase?
2) a) $96 b) $4200 c) 54cm d) 78Kg e) 60kg
3) The price of coal has been increased by 30% to $91 per tonne. What was the old price?
4) Mary works at the supermarket after school and has received a pay increase of 5% and now earns $336 per week. What was her pay before the increase?
5) Fruit juice is now sold in 2.5L containers. The producer increased the volume by 25% what was the size of the old container?
6) Sue measured 168cm by the end of year 10 . This was 5% more than in Year 9. What was her height at the start of year 9?
Exercise 2: Decreasing by a percentage. Find the original.
Draw double lines to solve the following number problems.
Example: $320 is the result of decreasing by 20%
What was the original amount?
Answer =$400
1) The following amounts have been decreased by 20%. Find the original amount.
a. a) $750 b) 100L c) 280ha d) 560ml
b. e) 240Kg
2) The cost of a car is reduced by 15%. The new cost is $4250. What did the car cost originally
3) Penny went on a diet and her weight reduced by 30% to 70kg. What was her original weight?
4) The Smiths decided to sell off 15% of their farm. They now have a 3400 Ha farm. What was the area of the farm before the sale?
5) A pair of cross trainer shoes is reduced in a sale by 40%.
6) The sale price is $72. What did the shoes cost before they were
a. discounted?
Exercise 3
Mixed increase/decrease – finding the original.
1) Jim’s salary has increased by 25% so his hourly rate is now $16. What was his hourly rate before the increase?
2) The value of Mike’s car has decreased by 60% over the last 4 years since he bought it and is now worth $12,000. What was it worth when he bought it?
3) The cost of Sue and Mike’s trip to Europe has increased by 25% and will now cost them $12,500. What was it going to cost before it went up?
4) The Robinsons bought a new dishwasher and stereo at the local appliance store where they were having a 20% off ale. They paid $320 . How much have they saved ?
5) The crop from the Kiwi fruit orchard this year was 330 tonnes.
This was a increase on last year. What was the weight of the crop last year?
6) The population of a small town on the West Coast is 25,500. This was a drop of 25% from 5 years ago. What was the population 5 years ago?
Exercise 4 – mixed
1) A CD set is marked $40 . What is the new price if there is a 30% increase in price?
2) The price of a $650 bike is discounted by 40%. What is the new price?
3) The price of a trip from Christchurch to Greymouth is $80 in winter and is increased by 15% for summer. What does it cost in summer?
4) Giant Easter eggs cost $12 before Easter and are discounted by 20% after Easter. What is the discounted price?
5) A 15cm wide suitcase can be expanded by 20%. What is the width of the expanded suitcase?
6) A lounge suite marked at $4500 is discounted by 60%. What is the sale price?
7) The average price of a house in Mathville was $280 000 in 2006. If prices have increased in 2007 by 15% what is the increased average house price ?
8) A farmer has reduced by 40% the amount of pasture he sows in grass seed. If the original area of land in grass seed was 760Ha. What area is now in grass seed?
9) The Harbour Hotel charges $120 per night for accommodation. The price is increased by 20% if breakfast is included. What is the cost including breakfast?
10) In the week before Christmas strawberries cost $5 per 500gm, but a week later the price had been reduced by 45%. What do strawberries cost at New Year?
Using Double Number Lines to solve % problems Answers
The answer to the example question in each exercise shows how the double number line should be used to solve the type of percentage problem in that exercise.
OR
Answer = 30
Exercise 1
1) 12 (2) 150 (3) 28 (4) 325
5) 18
Exercise 2
1.
1) 56% (2) 60% (3) 25% (4) 80%