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In this lesson, we will try to find out why and how a fraction is equivalent to another fraction, how to order fractions, and how to compare fractions.
See the fact file below for more information on the Fraction Equivalence and Ordering or alternatively, you can download our 33-page Fraction Equivalence and Ordering worksheet pack to utilise within the classroom or home environment.
Key Facts & Information
- By this time, you now have a basic understanding of fractions.
- Fraction is a part of a whole.
- But how do we recognize equivalent fractions? And what are equivalent fractions?
- How do we compare fractions with different numerators and denominators?
- Let’s have a short review.
- Numerator: How many parts you have
- Denominator: How many equal parts there are
- Before we go to fractions of different numerators and denominators, what if we have two fractions of the same denominator?
- 1/3 and 2/3
- Since we have two fractions of the same denominator, we can conclude that we have three equal parts.
- Thus, if we look at their numerators, 1 is less than 2, therefore we can say that ⅓ is less than ⅔.
- 1/3 > 2/3
- But what if we have two fractions of different denominators and different numerators?
- Our given fractions are ½ and ¾.
- Following the shaded regions, we can conclude that ¾ occupies a larger section compared to ½.
- Therefore, we can say that ¾ is larger than ½.
- Another method is to make their denominators equivalent.
- 1/2 and 3/4
- We know that if we multiply 2 by 2, we will get 4, which will give us
the denominator of the second fraction.
- Therefore, to make ½ have the same denominator as ¾, we will multiply it by 2.
- 2 x 1/2 and 3/4
- Note that if we multiply ½ by 2, this would mean that we will multiply both the numerator and the denominator by 2.
- 1 x 2 = 2 / 2 x 2 = 4
- Thus, the resulting fraction is now 2/4. This fraction has the same denominator as ¾, which means that we can already use the first method of just looking at their numerators.
- 2/4 < 3/4
- Therefore, ¾ is greater than 2/4 because 3 is greater than 2.
- Now, what if multiplying just one fraction to a number is not enough to find the common denominator between two fractions? Then, what we can do is to multiply both fractions by a certain number to find their common denominator.
- For example, if we have ⅔ and ¾, we cannot just multiply 3 by a certain number to get 4. Therefore, we have to find their least common denominator or LCD.
- LCD – Least common denominator is the lowest common multiple of the denominators.
- How do we find the LCD?
- Easiest way is to list down their multiples, since LCD is the lowest common multiple of these numbers.
- 3 6 9 12 15
- 4 8 12
- From the lists we made, the lowest common multiple of 3 and 4 is 12.
- Therefore, our aim is to make the denominator of the two fractions equal to 12.
- Now, because we already have a goal in mind, we need to find the numbers wherein if we multiply the fractions with these numbers, we will get 12 as their denominator.
- We know that if we multiply 3 and 4 we will get 12, and vice versa. Therefore, we have to multiply ⅔ by 4 and ¾ by 3.
- 2 x 4 = 8 / 3 x 4 = 12
- 3 x 3 = 9 / 4 x 3 = 12
- Therefore, our new fractions are 8/12 and 9/12.
- Comparing their numerators, we can conclude that 9/12 is greater than 8/12.
- Lastly, there is another way to compare fractions of different denominators.
- We can do cross multiplication.
- This method is called cross multiplication as we multiply the numerator of the first fraction by the denominator of the second fraction, and the denominator of the first fraction by the numerator of the second fraction.
- We know that if we multiply 2 and 4, we will get 8.
- We also know that if we multiply 3 and 3, we will get 9.
- Write the products on top of the numerators.
- 8 and 9 will serve as the “values” of the fractions they were written on top of.
- Then, we will compare 8 and 9. We know that 9 is greater than 8, and we also know that 9 represents ¾, therefore we can say that ¾ is greater than ⅔.
Fraction Equivalence and Ordering Worksheets
This is a fantastic bundle which includes everything you need to know about the Fraction Equivalence and Ordering across 33 in-depth pages. These are ready-to-use Fraction Equivalence and Ordering worksheets that are perfect for teaching students to find out why and how a fraction is equivalent to another fraction, how to order fractions, and how to compare fractions.
Complete List Of Included Worksheets
- Lesson Plan
- Fraction Equivalence and Ordering
- Connect Them
- Make It
- What Number?
- Cross X
- Find Out
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Use With Any Curriculum
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