| Percent - a special type of fraction | Percent Models | Ratios |
| Relationships:decimal fractions, common fractions, percent and ratio | Rates | Quick quiz |
0.25, 1/4, 25% These expressions tell us what portion of the square is coloured orange. |
100% | =100/100 | =1 | = 1.0 (decimal) | |
50% | = 50/100 | = 5/10 | = 1/2 | = 0.5 = 0.50 (decimal) |
25% | = 25/100 | = 5/20 | = 1/4 | = 0.25 (decimal) |
40% | = 40/100 | = 4/10 | = 2/5 | = 0.4 (decimal) |
5% | = 5/100 | = 1/20 | = 0.05 (decimal) | |
0.5% | = 5/1000 | = 1/200 | = 0.005 (decimal) |
25% = 25/100 = 0.25 (twenty-five hundredths) |
47.3 % = 47.3/100 = 0.473 (forty seven hundredths and 3 thousandths) |
200% = 200/100 = 2 |
0.108 = 0.108 x 100 = 10.8% |
0.75 = .75 x 100 = 75% |
1.2 = 1.2 x 100 = 120% |
= 0.125 (decimal) | |
= 0.236 (decimal) | |
= 0.333 (decimal, rounded to 3 decimal places) | |
= 0.5 = 0.50 (decimal) | |
= 0.667 (decimal, rounded to 3 decimal places) | |
= 1.1 (decimal) | |
= 1.5 (decimal) | |
=2.0 (decimal) |
Working Out | Thinking |
30 out of 50 apples are bruised. To represent 30/50 as a percent we need to find out how many apples out of 100 are bruised. By equivalent fractions we know that 30 out of 50 equals 60 out of 100, so 60% of the apples are bruised. We could also say that, 3/5 of the apples are bruised 0.6 of the apples are bruised. |
Working Out | Thinking |
Ryan spent 11 minutes out of 25 minutes waiting in a queue. To turn this into a percent we are asking, 11 out of 25 minutes equals how many minutes out of 100 minutes? We can see that 11 mins out of 25 mins equals 44 mins out of 100 mins by equivalent fractions (because we know 25 x 4 = 100) . We can say that Ryan spent 44%, 0.44 or 11/25 of his time in the bank waiting in a queue. |
Working Out | Thinking |
To find out what percent 7 out of 20 is, we need to ask: 7 out of 20 is how many out of 100? 5 groups of 20 make 100, so 7 out of 20 is 35 out of 100 (5 x 7 out of 5 x 20). Therefore 7/20 equals 35%, or 0.35 if we represent it as a decimal. |
Recall example 1: 30 out of 50 apples in a box are too bruised to sell. What percent of apples cannot be sold? | |
Thinking | |
The left side of the number line below has a percent scale. The right side of the number line has a number scale. We can label each scale using the information we are given in the problem. | We know that there are 50 apples in total, ie. 50 apples equals 100% of the apples. We know that 30 out of the 50 apples are bruised and we need to find what percent this is. In more complicated problems this dual-scale number line is a good way of organising the information we are given and to work out what information we need to find. Once we have represented the problem in this way we can write a proportion equation directly from the number line. 30/50 = ?/100 By equivalent fractions we know that 30/50 = 60/100. (Or we might have just noticed that it is a 'multiply by 2' relationship, so 30 x 2 = 60) Therefore 60% of apples are too bruised to sell. |
1 metre ruler Elastic |
The ratio of 1 : 3 tells us the ratio of shaded : unshaded The ratio of 3 : 1 tells us the ratio of unshaded : shaded The ratio of 1 : 4 tells us the ratio of shaded : whole |
scale on a map (every 1 cm on the map represents 10000 cm on the ground, every inch on the map represents 10000 inches on the ground) | ratio of blue to white paint is 1 : 4
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ratio of gears on a bicycle 8 : 16 : 24 Macbooster 3 1 5.
| ratio of number of girls to number of boys in class is 5 : 2
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We must always talk about ratios in context. To say or write 5 : 2, for example, has no meaning on its own. |
1 blue : 4 white |
1 : 4 | 1 : 4 | 1 : 4 |
x 2 | x 3 | x4 |
2 : 8 | 3 : 12 | 4 : 20 |
Working Out | Thinking | |||||||||||
| The ratio of 2 : 2 : 1 means that the inheritance is divided into 5 portions - two people each receive 2 portions and one person receives 1 portion. $15000 divided by 5 - each portion is worth $3000 |
Person 2 | ||
ratio | 2 : (2 x $3000) | 1 (1 x $3000) |
common fraction | (of $15000) | |
decimal fraction | 0.4 (of $15000) | 0.2 (of $15000) |
percent | 40 % (of $15000) |
Thinking |
The ratio of cordial to water is 250 : 750 or 1 : 3. One part cordial to 3 parts water. In fraction terms, the 1000 mls of mixed cordial is 250/1000 (1/4) cordial and 750/1000 (3/4) water. We talk about the ratio of cordial to water in many different ways: For every cup of cordial there are 3 cups of water. There is 3 times as much water as cordial. 1 out of every 4 parts of the mixed cordial is cordial. Can you think of any more ways? |
Thinking |
The ratio of males to females is 60 : 40 or 6 : 4. This means that overall there is a higher proportion of males in the group, and for every 6 males there are 4 females. In fraction terms, where we are talking about the group of 100 people, 60/100 (6/10) are male and 40/100 (4/10) are female. So we can also say that 6 out of every 10 people are males and 4 out of every 10 people are females. Whereas fractions only enable us to represent the part to whole relationship (in this case, males/people and females/people), different aspects of the relationships between quantities (people) can be shown using ratios. For example, The 3 ratios that represent the relationships of males and females in this group of people are: - the ratio of 6 males to 10 people can be represented as 6 : 10 - the ratio of 4 females to 10 people can be represented as 4 : 10 - for every 6 males there are 4 females can be represented as 6 : 4 Which ratio we choose depends on we want to say. The number of males to the number of females is 6 : 4 The number of males to the number of people is 6 : 10 The number of females to the number of people is 4 : 10 |
km/h | kilometres per hour |
c/L | cents per litre |
$/m | dollars per minute |
c/m | cents per minute |
Working Out | Thinking |
100 litres/1 hour = ? litres /2 hours 200 litres will run in 2 hours. | We know that 100 litres runs in 1 hour and we need to find out how many litres runs in 2 hours. We can write this as litres/hour because this is what we are trying to find out. By equivalent fractions we know that 100/1 = 200/2. Therefore 200 litres will run in 2 hours. |
Working Out | Thinking |
100 litres/1 hour = 350 litres /? hours 350 litres/ ? hours = 100 litres /1 hour 350 litres/3.5 hours = 100 litres/1 hour | We know that 100 litres runs in 1 hour and we need to know how long it takes to run 350 litres. 350 litres is 3.5 times 100 litres, so it takes 3.5 times as long i.e. 3.5 hours. Therefore 350 litres will run in 3.5 hours. |
1. | Express the following percents as fractions and decimals: | ||||
a) | 95% | ||||
b) | 13.5% | ||||
c) | 42% | ||||
d) | 1% | ||||
e) | 0.1% | ||||
2. | Express the following fractions as percents: | ||||
a) | 37/100 | ||||
b) | 164/100 | ||||
c) | 25/50 | ||||
d) | 14/20 | ||||
e) | 16/25 | ||||
3. | Express the following decimals as percents: | ||||
a) | 0.01 | ||||
b) | 0.83 | ||||
c) | 0.005 | ||||
d) | 1.10 | ||||
e) | 0.2 | ||||
4. | Express the following quantities as ratios: | ||||
a) | There were 3 boys for every 5 girls at school assembly. | ||||
b) | Nine people out of every ten watch television every night. | ||||
c) | In a class of 25 students 3 are left handed and 22 are right handed. | ||||
d) | To cook rice you need 1 cup of rice to 2 cups of water. | ||||
e) | To make ANZAC biscuits, you add the same amount of flour to sugar. | ||||
5. | The following ratios of pets owned have been obtained from surveys of 5 local neighbourhoods. Find at least one equivalent ratio for each of the following: | ||||
a) | dogs : cats = 10 : 20 | ||||
b) | cats : dogs = 30 : 50 | ||||
c) | dogs : cats = 100 : 100 | ||||
d) | dogs : cats : guinea pigs = 6 : 4 : 2 | ||||
e) | fish : turtles = 75 : 25 | ||||
6. | Express each part-to-part ratio below as a common fraction, decimal fraction and a percent of the whole: | ||||
a) | men : women : children = 3 : 3 : 4 | ||||
b) | men : women : children = 11 : 4 : 5 | ||||
c) | adults : children = 4 : 1 | ||||
d) | men : women : children : pets = 5 : 3 : 6 : 1 | ||||
7. | Write each of these sentences as a rate: | ||||
a) | She ran 100 metres in 15 seconds. | ||||
b) | The bus travelled 850 kilometres in 10 hours. | ||||
c) | Ilana can type 160 words in 2 minutes. | ||||
d) | The factory packaged 600 packets of biscuits in 5 minutes. |
Percentage | Common Fraction | Decimal Fraction |
32% | ||
0.06 |