| Percent - a special form of fraction | Percent Models | Ratios | | Relationships:decimal fractions, typical fractions, percent and also ratio | prices | fast quiz |
Percent - a special kind of fraction
0.25, 1/4, 25%
These expression tell united state what section of the square is coloured orange.
You are watching: What is the ratio of 25 to 40
The word percent come native the expression "per cent" and also literally way "a part of one hundred". A percent is a part, or fraction, out of 100. Because that example:
|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)|
We can see the to write a percent together a portion we to express the percent as a portion with a denominator the 100. We might then have the ability to simplify the fraction further.
For example, 75% = 75/100 = 3/4
To refer a fraction as a percent we must first convert the portion into hundredths (in an easy cases we can do this by using identical fractions) and then change "/100" through the percent "%" sign.
For example, 4/5 = 80/100 = 80%
We deserve to see that us express a percent as a decimal by splitting by 100.
|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|
To express a decimal as a percent us multiply the decimal number by 100.
|0.108 = 0.108 x 100 = 10.8%|
|0.75 = .75 x 100 = 75%|
|1.2 = 1.2 x 100 = 120%|
Some percents expressed as fractions and also decimals
|= 0.125 (decimal)|
| ||= 0.236 (decimal)|
|= 0.333 (decimal, rounded to 3 decimal places)|
|= 0.5 = 0.50 (decimal)|
|= 0.667 (decimal, rounded come 3 decimal places)|
|= 1.1 (decimal)|
|= 1.5 (decimal)|
Example 1: 30 out of 50 apologize in a box room too bruised come sell. What percent of apples cannot be sold?
| || |
30 the end of 50 apples space bruised. To stand for 30/50 as a percent we require to discover out how numerous apples out of 100 space bruised. By identical fractions we know that 30 out of 50 amounts to 60 the end of 100, for this reason 60% of the apples space bruised.
us could additionally say that, 3/5 of the apples are bruised 0.6 that the apples space bruised.
Example 2: Ryan invested 25 minutes in the bank, 11 minutes of i m sorry was spent waiting in a queue. What percent of time go he spend waiting in the queue?
| || |
Ryan spent 11 minutes the end of 25 minutes wait in a queue. To rotate this into a percent we room asking, 11 the end of 25 minutes amounts to how plenty of minutes out of 100 minutes?
We can see the 11 mins the end of 25 mins equals 44 mins the end of 100 mins by identical fractions (because we recognize 25 x 4 = 100) .
We have the right to say that Ryan spent 44%, 0.44 or 11/25 that his time in the bank waiting in a queue.
Example 3: What percent is 7 cm of 20 cm?
| || |
To uncover out what percent 7 out of 20 is, we have to ask: 7 the end of 20 is how numerous out that 100?
5 groups of 20 do 100, so 7 out of 20 is 35 the end of 100 (5 x 7 the end of 5 x 20).
Therefore 7/20 equates to 35%, or 0.35 if we represent it as a decimal.
Dual-scale number heat model
We deserve to use the dual-scale number line, likewise called the proportional number line, come illustrate example 1 native above.
|Recall example 1: 30 out of 50 apples in a box are too bruised to sell. What percent the apples cannot be sold?|
The left side of the number line listed below has a percent scale. The right side the the number line has actually a number scale. We deserve to label each scale using the details we are given in the problem.
We recognize that there space 50 to apologize in total, ie. 50 apples equates to 100% the the apples. We recognize that 30 the end of the 50 apples room bruised and we require to uncover what percent this is.
In more complicated problems this dual-scale number line is a great way the organising the information we are given and to work-related out what details we have to find.
Once we have represented the problem in this means we have the right to 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 simply noticed the it is a "multiply by 2" relationship, so 30 x 2 = 60)
Therefore 60% the apples room too bruised to sell.
The dual-scale number line design is debated further in the other pages of the Percent, Ratio and Rates topic.
Elastic tape measure model
The ice cream measure design is a good linear model of percent. Teachers can easily make these models making use of a ruler, such as a 1 metre ruler, and elastic. The elastic needs to be significant with a percent scale. It have the right to then be extended to the desired length.
See more: Good Girls Are Made Of Sugar And Spice, What Are Little Boys Made Of
For example, what is 60% the 50?
To uncover the answer we line up the zeros that the ruler and also the elastic. We then large the elastic so the 100% currently up with the entirety amount, i beg your pardon in this instance is 50. Us then look because that 60% on the elastic and read the equivalent amount ~ above the ruler. We have the right to see below that 60% the 50 is 30.
The intentionally is not to use this version accurately. That is a an excellent way of reflecting that percent constantly involves a proportional comparison of something to 100.
|1 metre ruler |
By manipulating the ice measure, this model have the right to be provided for the 3 varieties of percent problems, discussed in Percent Examples. Examples of i beg your pardon are,
What is 20% the 50? What percent is 10 the 50? 30% the what number is 15?
(Note: because that a lesson, a teacher will require elastics tape steps of assorted lengths, because the elastic have the right to only be extended - it can not be shrunk).