How does percentages relate to fractions

The grid can be divided into 10 equal parts, or tenths. One of these ten equal parts, or one tenth of the grid , is shaded in red. One tenth, the red portion, can be divided into ten equal parts the yellow section shows this. The yellow portion is a one hundredth as of these make the whole. A one hundredth , the yellow portion, can also be divided into ten equal parts the blue section shows this. The blue portion is represents one thousandths of the whole, as of these thousands makes the whole.

The following video uses a thousandths grid in a similar way, to demonstrate writing decimal fractions:. The second example in the video focuses on the shaded area being one thousandths of a whole comprising one thousandths. It is written as or 0. It is easy to see that this shaded area is one half of the whole grid. This shaded area can also be broken up into 50 hundredths. The fraction 50 hundredths is equivalent to thousandths.

Furthermore, the shaded area in the video can be broken up into five tenths. The fraction five tenths is equivalent to the fraction 50 hundredths and thousandths. All of these fractions have the same value of one half , and so they are equivalent fractions. The decimal notation does not require the zeros after the five. Unlike whole numbers, a zero on the end right hand side does not change the value of the decimal.

However, the zeros can sometimes assist when adding and subtracting decimals. Click on the following link from Illuminations Resources for Teaching Math:. The number line below is marked in increments of one hundredths from zero to 0. Notice where the following decimal numbers, all containing similar digits but in different places, are placed on the number line:. The decimal 0. It decimal 0. It also has 3 thousandths, so it is just past the 2 hundredths mark three tenths past the mark.

The decimal is 0. It is half way between the seven and eight tenths marks because it also has 5 thousandths. It has five hundredths, so it is about half way between 0. It also has 7 thousandths, so it is just past half way between 0. This time the three different representations of rational numbers, fractions, decimals and percents, have been placed on a blank number line. Examples of how percentages are used in real life Example 1. How much will you save by buying it now? The larger the denominator, the bigger the fraction.

This is true for unit fractions fractions with a numerator of one. There is an inverse relationship between the number of parts and the size of each part: The larger the number of parts the denominator , the smaller the size of each part the numerator. Unless the problem context indicates that two fractions relate to different wholes, we assume both relate to the same whole.

With this in mind, it makes sense that the more parts into which the whole is divided, the smaller they will be. Example: Compare one eighth to one fifth If we are referring to the same whole, such as a portion of a cake modelled below , we can see that the more parts into which it is divided, the smaller each part will be. In the visual representation, we can clearly see that is larger than.

Five people sharing above cake, so each. Eight people sharing same sized cake, so each. When we are comparing just one of each part, such as one eighth to one fifth , the bigger the denominator, the smaller each part will be. The numerator is one. This time, we will compare one fifth , and three eighths.

We know that eighths are smaller than fifths, but we must note that this time there are three eighths, not just one. In the diagram below, we can see that is a bigger portion than. Person A ate one fifth of the cake. Person B ate three eighths of the cake. If we cannot reliably compare the fractions with different denominators visually, as in the diagram above, we need to change one or both of the fractions into equivalent fractions for a common denominator.

It is easy to recognise that four fifths is greater than two fifths , because each of the parts fifths is the same size. Four is greater than two, so must be greater than. What about comparing four fifths and seven tenths , which have different denominators?

As was seen on the fraction wall , each fifth is equivalent to two tenths. This is demonstrated in the model below:. Changing four fifths to the equivalent fraction eight tenths makes it much easier to see that four fifths is greater than seven tenths.

Click on the link below and complete the activity by placing all of the fractions, decimals and percents on the number lines from ICT games. This is an activity that students could do as well. Using percent in to solve everyday problems requires proportional reasoning.

Proportion reasoning involves the consideration of number in relative terms,rather than absolute terms. For example, converting a fraction of five sixths to a percent is equivalent to finding what part of is equal to five parts out of six. In numerical notation this can be expressed as. One way to convert a fraction into a percent is to remember that any fraction can be interpreted as a quotient division see FDRP BI2 Fractions as division.

Remembering that percents are hundredths, this can be expressed as. Knowing this can make understanding of everyday maths language easier, such as in the following example of percent decrease. Mathematical language and data presented in media is not always clear. Being able to understand percent use and its relationship with fractions, decimals and proportional reasoning helps us to more easily interpret information about our world. So do you think that an increase in the number of deaths by drowning from 57 to 64 the following year is an alarming increase?

Alarming figures show a The The graph in the article shows the number of drowning for each age group, which totals , as mentioned in the article. The number of drowning in the 25 — 34 age group is the highest on the graph, and appears to be about 64 in number.

This number of 64 includes the Therefore the number 64 represents We can therefore workout that in the previous year 57 people x 0.

Note that in a context like this in which the numbers calculated are numbers of people, rounding to the nearest whole number is appropriate. It is important to consider that a change in percent is always considered in relation to the original amount.

From our previous calculation, we know that is. We can see that the actual decrease is a considerable drop in tax. Look at the same paragraph as the previous section:. As well as the mention of a In the previous section we calculated the number of deaths for two consecutive years, being 57 and Using knowledge of percent or fractions in this case hundredths as an operator see FDRP BI2 Fractions as operators , we can work out the numbers of males and females for a clearer understanding of the data.

Again, in this context where the numbers calculated are numbers of people, rounding to the nearest whole number is appropriate. The actual numbers of male and females who drowned, rather than using percents, may send a clearer message than percents about the difference between male and female drownings.

When money is borrowed or invested for a fixed time at a fixed interest rate and the interest rate is calculated only on the initial investment , simple interest sometimes known as flat interest is calculated.

Note: that simple interest is not the only way that interest can be calculated. Note also that in an algebraic formula like this we do not need to put in the multiplication symbol. What was the percent increase?

What is the best two-year deal, A or B? In the original survey, the number of smokers was What was the number of smokers after 2 years? What was the actual price of the car before sales tax? The previous module showed how percents are hundredths and as such are another way of representing rational numbers.

However, learning with relation to percent cannot be limited to this understanding, but must also be linked with proportional reasoning as well as decimals and fractions. Percents are frequently used in real life situations such as when working with interest rates, discounts and price changes. Percents are also often used to compare two quantities. The purpose of this module was to further develop your knowledge of the meaning of percent by exploring how percents can be used in real life contexts.

If you have completed all the Big Ideas and feel you have a good understanding of each Big Idea, then test yourself with the module Quiz for the Relationships between Fractions, Decimals, Ratios and Percentages. Click here to take the Quiz. Search UTAS. Mathematics Pathways. Quick Links Community and industry. Fractions are commonly used in everyday life as well as in mathematics.

In the case of the fraction three fifths the numerator is three 3 and the denominator is five 5. Example 2 A class of sixty 60 students is comprised of thirty six 36 females and twenty four 24 males. This part-whole concept can be represented in a diagram:. It demonstrates two important understandings; Fraction Wall 1. Click on the top bar to highlight.

This bar represents one whole. The bar underneath is the same size, but is divided into two equal parts. Click on one of the two equal parts. The symbol for this one half is , the numerator 1 showing the number of parts, and the denominator 2 showing the number of equal parts into which the one whole is divided.

When you click on the second half you will notice that the total of the two halves is one whole the number 1 appears in the final column The next bar is divided into four equal parts, or quarters. As you click on each quarter watch the right hand column to see how the sum of the shaded area changes.

The whole is divided into four equal parts, not two as in the previous bar. There are more parts, but the whole is the same, so each part or fraction must be smaller. In fact, you will notice that each green quarter is half the size of each yellow half.

You will also notice that as the parts get smaller, the denominator gets bigger more parts. Look at the next bar which is divided into eighths. You will see that each eighth is half the size of a quarter. Notice the relationship between halves, quarters and eighths. As the number of parts doubles the size of each part halves. The term hundredths can be replaced with percent to be Further explanations of the decimal point in naming decimals can be found in the information on the Decimal Number System.

Percents can be represented pictorially in the same way as tenths and hundredths using base-ten models such as 10 x 10 grids and circular disks marked around the edge. Place value columns can also show the term percent. To solve problems it is helpful for students to be able to interchange between fractions and decimal units.

Use the resource finder. Big Idea Decimals, fractions and percentages are closely related. Background Points for teaching: Decimals are another way of writing fractions. Percentages are another way of writing hundredths. Now you get a chance to work some problems. You may use a calculator if you would like. Study each of these problems carefully; you will see similar problems on the lesson knowledge check. Select the following link to complete the practice activity.

You will need to get out a piece of paper and a pencil to complete the practice problems. Converting between Fractions, Decimals, and Percents.

Once you complete the practice activity, check to see how well you did by selecting the following link:. Solutions: Converting between Fractions, Decimals, and Percents.

Percents are a common way to represent decimal or fractional amounts. Any number that can be written as a decimal, fraction, or percent can also be written using the other two representations. Now that you have finished Lesson 1 in this module, you are encouraged to conduct additional research into how these topics pertain to your particular area of study within the IT world.

You probably don't have to look much farther than your computer screen. Most computers have the ability to zoom in or out. This zoom feature is typically characterized with a percentage. With this simple computer feature, you can zoom out to see the whole world on Google Earth or zoom in to see your personal vehicle sitting in your drive way. Now that you have read over the lesson carefully and attempted the practice exercises, it is time for a knowledge check.

Please note that this is a graded part of this lesson so be sure you have prepared yourself before starting. Additional Attributions. Course Home Lessons.