What is the difference between percentages and fractions

Click on the four eighths under the highlighted two quarters. Again, this is the same size or amount as one half. We can say that. These three fractions are equivalent fractions; they all have the same value. The next bar has been divided into sixteen equal parts, or sixteenths.

Click on the sixteenth until the shaded area is equivalent to one half. You will see that the list of equivalent fractions in the right hand column now includes eight sixteenths. Understanding 2 Fractions are Numbers All numbers can be located on a number line. Think of the fractions wall as a number line below. Understanding 3 Fractions on a Number Line The number line below represents eighths, that is, fractions with a denominator of eight.

We can see that the fractions on the same point on the number line are equivalent fractions. Learning Activity 2 Battleships Number Line You can use the Battleship Number Line Game to practice and build your estimation and visualisation skills when placing fraction and decimal numbers on a number line.

For example: If placing on the number line it may be easier to visualise where the equivalent fraction would lie. If placing on the number line, it is a little further to the right than or.

If placing 0. Battleship Number Line Game Number lines can assist with addition, subtraction, multiplication and division of fractions also see Fractions as operators further down on this page.

Understanding 4 Fractions Greater than One The term improper fractions is used to describe fractions greater than one, such as ten quarters. We can clearly see that or is equivalent to The decimal notation for this is 2. Understanding 5 Fractions as measures Fractions are commonly used as measures. Fractions are often used to measure time, for example: The term half an hour is more commonly used than 30 minutes. Understanding 6 Fractions as Operators A fraction acts as an operator when it is applied to a number, set or quantity to find a certain proportion of that number, set or quantity.

Example 1 Find three quarters of twenty four. Understanding 7 Fractions as Division Fractions can be used as a representation of division. Numbers that can be expressed in this way As are known as rational numbers and can be derived from dividing the numerator by the denominator. Example 2 Three people have to share two choc bars. How much does each person get? Here is one way to visually represent this problem:. Understanding 8 Fractions as Ratios Fractions can be interpreted as ratios.

Example 1 In the pictures below there are 5 puppies, 3 females and 2 males. Image from Math is Fun. Practice Task 1 1. Starting at write a sequence of eight numbers counting by: a One half b One quarter c One tenth d One twelfth 2. Find equivalent fractions for: a b. Practice Task 2 Solve the following problems where fractions are used as operators. Genni was renovating her laundry. The total number of equal sized tiles on the floor was How many tiles had to be replaced?

Which is the larger, of 45 or of 40? We cannot assume that the second one is the largest just because is a larger fraction than , as they relate to different wholes. Practice Task 3 Draw a visual model to show how six pizzas can be equally shared among eight people if: The pizzas are cut into eighths The pizzas are cut into quarters Identify whether the following problems are Part-to-part or Part-to-whole representations and represent the answers using a ratio: Timber Town has a population of people, 40 of these being children.

Check your Understanding of Big Idea 1 The purpose of this module was to identify how: Fractions occur in a wide range of contexts. Fractions have many different interpretations. To demonstrate the following understandings: Fractions can be used to describe parts of a whole. To order, compare, add or subtract fractions, they must relate to the same unit or whole. This would not be the case if we were talking about of a small pizza and of a large pizza. Fractions can be used as numbers as placed on the number line.

The system of decimal numbers is an extension of the whole-number number system. Decimal numbers are one way of representing fractions, ratios and percents. Decimals are widely used today, especially in areas such as finances, commerce and science. They are also used when measurements require a given accuracy. Although decimal notation is often used to represent fractions, sometimes fraction notation is more appropriate. For example, it is much simpler to find one third of twenty four x 24 than to use the decimal equivalent of one third 0.

The threes in this decimal go on indefinitely. Learning Activity 1 Where do fractions and decimals fit into the base-ten number system? Watch the following video about the classification of numbers The video shows how fractions and decimals fit into our number system.

Example The fraction three quarters can be written as a decimal. The following link shows Pi to one million decimal places! Common Misconceptions about Decimals 1. Longer is larger A common misunderstanding when comparing numbers originates from the separation of decimal numbers into two whole numbers; that is, the sets of numbers on each side of the decimal point are treated as whole numbers.

The following examples show how this misunderstanding can go unrecognised because sometimes it results in a 'fluke' correct answer: Which is smaller? Incorrect reasoning Correct reasoning Correct answer 5. The seven hundredths are not relevant as they are smaller than tenths 5. They are both have the same value because 5 tenths is the same as 50 hundredths Both the same 2.

Shorter is larger This is another common misunderstanding when comparing numbers. The following examples show how this misunderstanding can go unrecognised, as sometimes it results in a 'fluke' correct answer: Which is smaller? Incorrect reasoning Correct reasoning Correct answer 7.

Write each of the following numbers as fractions and decimals. Sample answers have been given for the first number. Number Fraction Expressed as a Decimal One quarter 0. Practice Task 2 Write each of the following numbers in expanded notation, renaming in terms of the place value parts: a Check your Understanding of Big Idea 2 The purpose of this module was to identify how: fractions and decimals fit into our number system.

To demonstrate the following understandings: Each digit in a number has a place value depending on its position or place. Numbers can be partitioned and named renamed in terms of the position of each digit. The decimal point separates the whole number places from the decimal number places. Does this make sense to you now? Fractions, decimals and percentages are related and can be used to express the same number, or proportion in different ways.

By the end of this module you should be able to fill in a chart similar to this one. Number Fraction Decimal Percent five 5. Learning Activity 1 Relating Decimals, Fractions and Percent Please go to the link below and complete the activities suggested below.

Math Is Fun Virtual Manipulative Activities to demonstrate the relationship between fractions, decimals and percents, and reinforce and extend your understandings of percents being another way to represent fractions: 1.

Understanding 2 Representing Decimals to Thousandths A one thousand grid can be used to represent one whole 1 , and to demonstrate decimals up to thousandths. The entire grid represents one 1 , or one whole. The following statements can be made: The red area is one tenth or zero point one 0.

The yellow area is one hundredth or zero point zero one 0. The blue area is one thousandth or zero point zero zero one 0. The shaded area of the grid is one hundred and eleven thousands of the grid, which can also be expressed as the decimal fraction zero point one one one 0. Learning Activity 2 One Thousand Grid: A visual model for decimal fractions 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.

This sets the numerator range at the bottom of the screen as 0 — , and the denominator range at 1 — The fractions will therefore be improper, or greater than 1, because the numerator will be greater than the denominator. Use the plus and minus tabs either side of the numerator and denominator settings to select a numerator of 5 and a denominator of 3.

You will see five thirds represented on the area model on the screen. Above this you will see how this number is expressed as a fraction or improper fraction , a mixed number , a decimal 1. Note that the decimal and percent have been rounded up; otherwise they would go on forever.

Look at the different models length, area, region, set. Try other numbers greater than one, looking at the different visual representations. Note how they are expressed in improper fractions, mixed numbers, decimals and percents. Understanding 3 Relating Decimals, Fractions and Percent using a Number Line 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: 0. Common Misconceptions for Ordering Fractions 1. The larger the denominator, the bigger the fraction This is true for unit fractions fractions with a numerator of one.

Practice Task 1 1 Complete the table so that the numbers in each row represented by fractions, decimals and percents are equivalent: Fraction Decimal Percent 1. Practice Task 2 1 Relating decimals, fractions and percent using a number line 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. Check your understanding of Big Idea 3 The purpose of this big idea was to demonstrate the following understandings; A number can be represented as a fraction or a decimal.

A percent is a fraction out of one hundred and are a very commonly used in everyday life. Percents can also be understood as hundredths Does this make sense to you now? An understanding of percent relationships helps us to compare and represent increasing and decreasing proportions. 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.

Understanding 2 Percent Decrease and Increase Example 1 Mathematical language and data presented in media is not always clear. Example 2. Image provided by: Mathematics Assessment Resource Service.

Note that 0. Look at the same paragraph as the previous section: Alarming figures show a Understanding 4 Using Percentages in Simple Interest Calculations 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. Practice task 1 You want to buy two T-shirts.

Which is the best buy, Shop A or Shop B? Shop A. Shop B. Practice Task 3 The staff of a company decreased from 55 to What was the percent decrease? Click here to check your answer. Check your Understanding of Big Idea 4 The previous module showed how percents are hundredths and as such are another way of representing rational numbers. Also, when you figure out your taxes or shop around for the best interest rate on a car loan, you use percentages.

Within the IT field, percentages are used to study how resources are being used on a computer or how much bandwidth is being consumed on a network based upon the maximum capacity of the network.

You will also need to be mindful of ratios and proportions used for the screen resolutions of mobile devices in order to properly design a mobile application. In this section, you will learn to convert between each of these formats decimals, percents, and fractions. A ratio is defined as the comparison of one size of a number to the size of another number. A most convenient number to use when comparing numbers is Ratios in which one number is compared to are called percents.

The word percent comes from the Latin word per centum. The word per means "for each" or "for every," and the word centum means "hundred. Notice that 50 of the squares in the grid below have been shaded green. Since a percent is a ratio a ratio can be written as a fraction, and a fraction can be written as a decimal.

This means any of these forms can be converted to any of the others. Look at the chart below for detailed information on how to make conversions between fractions, decimals, and percents. Reduce, if possible. Review the examples below which provide detailed steps for converting to fractions, decimals and percents. Convert to a decimal and to a percent. Watch the following Khan Academy video about decimals, percents, and fractions.

You will see additional examples that can help you better understand these new concepts. Representing a Number as a Decimal, Percent, and a Fraction.

Get your child to work out discounts in the sale on the go, or challenge them to work out fractions of amounts when weighing up your fruit and veg on a scale. Mix it up by throwing a decimal in there! Here are a few examples of what you could ask:. We only want half a kilo. How much will it be? How much would we be saving? This is a very simple activity but one that can help your child get to grips with all three formats using something they are already familiar with, namely money! Using the change in your pocket, you can get your child to:.

As has been touched upon earlier in the post, baking and cooking in general presents a great opportunity to practise fractions, decimals and percentages. Visual representation is a great tool to use when teaching children, and that is certainly true when it comes to decimals for kids. Place a number 1 on the right hand end of the stick and a 0 on the left hand end. Ask your child to place where 0. Learn more or request a personalised quote to speak to us about your needs and how we can help.

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Group Created with Sketch. Register for FREE now. Ellie Williams. What is a fraction? Understanding and Comparing Fractions Worksheets Download these FREE understanding and comparing fractions worksheets for Year 3 pupils, intended to help pupils independently practise what they've been learning.

Download Free Now! Ellie Williams Third Space Learning. With a love for all things KS2 maths, Ellie is a part of the content team that helps all of the Third Space Learning blogs and resources reach teachers! Related Articles. Understanding and Comparing Fractions Worksheets. We use essential and non-essential cookies to improve the experience on our website. Please read our Cookies Policy for information on how we use cookies and how to manage or change your cookie settings.