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Maths Help: Equivalent Fractions. Fractions the same as each other, Numerator, Denominator, half ,quarter, third, tenth

Updated on October 27, 2013

Equivalent Fractions

So, what are we talking about here?

We are talking about fractions that have the same value, even if they look different.

For example;

1 = 2 = 4
2 . 4 . 8

What is the maths behind this? (Why are they the same?)

Because when you multiply or divide both the top and bottom by the same number, the fraction keeps it's value.

Lets put the theory to the test;

Multiplying

 . (x2) (x2) 
 .1 = 2 = 4
 .2 . 4 . 8
 . (x2) (x2)


Dividing

Here are some more equivalent fractions, this time by dividing:

 . (÷3) (÷3) 
 .18 = 6 = 1
 .36 . 12 .2
 . (÷3) (÷3)


If we keep dividing until we can't go any further, then we have simplified the fraction (made it as simple as possible).

The biggest rule to remember when it comes to fractions is;

Whatever you do to the numerator you have to do the same to the denominator.

Put in simplier terms;

Whatever you do to the top number you must do to the bottom number.



Children need to see it before they believe it!

A fraction wall is a great way to see how equivalent fractions work. It is an easy way to compare different fractions and an activity I find is good for them to make one themselves.

Fraction wall

I find if children can play around with a fraction wall they find it easier to picture and use fractions. They certainly find it easier to see equivalent fractions and why they are equivalent. There are plenty of website out there that will help you and the students to do this with great success.

Lesson idea 1 :

I do find though, that they enjoy making it themselves and then moving it around in order to find the equivalent fractions.

  • Strips of paper are given to the children all of the same length. This will depend on what fractions you want to do and how old the students are.
  • Next they are to work out a half by measuring the paper and dividing that by two. They then measure, mark off and cut this to create two equal halves. This way should be modelled to show the children how to do the other fractions instead of taking an easy option of folding the paper in half and then cutting it. I tell them that I use this as a check to see if my measuring skills are good enough.
  • This is repeated for 1/3, 1/4, 1/5. 1/6 etc.
  • Once this measuring is done, then stop the class and ask a few questions like if I had already cut out the 1/3's then how would this help me with the 1/6's? If I had already cut out the 1/4's then how would this help me with the 1/8's and so on and so on. (They should know that if a 1/3 is halved it would generate a 1/6. If a 1/4 is halved then it will generate an 1/8th. If not then it is a concept you have introduced which can only benefit their development.
  • Now they are all cut they can move them around and see what is equivalent with what. This can then be stuck onto a large piece of paper and used for a display - that way the children remember more about it and as it is their work be more proud and hopefully look at it more when they need help because they should rememeber doing it.

Lesson idea 2:

  • I have used the fraction wall but I didn't put all fractions on them. It was apart of a revision exercise where they were given part of a fraction wall with either a fraction, percentage or a decimal on each strip of paper.
  • They were not allowed to move these strips of paper to start with. They were there for a visual representation.
  • The idea was to find the equivalents by working out the equivalent fraction, percentage or decimal.
  • Then they were allowed the strips of paper to check their work and then they had to write down the equivalent fraction, decimal and percentage on the strip.
  • This was then used for a display - again with the same idea as above.

Lesson idea 3:

  • Children were given a strip of paper with 6-10 fractions on them on a number line.
  • It was a revision exercise so they had to find the equivalent percentage and decimal and write those under each other.
  • Then we discussed what each group had - it turned out that each group had equivalent fractions and then we discussed how we would be able to check that each fraction was indeed equivalent.

KS3 help with adding fractions - Lowest common multiple (LCM)

The least common denominator is the smallest whole number that is divisible by each of the denominators.

If we were to add two fractions then we need to make sure that we can compare the two sizes of the fractions. The ONLY way we can do this is to make sure the denominators are the same. Then all you need to do is add the numerators up.

Example 1:

To find the least common multiple, simply list the multiples of each denominator (multiply by 2,3,4 etc.) then look for the smallest number that appears in both lists. You should do about 6-10 multiples should do it.

If we had the fractions 1/5 and 1/6 then lets see

5 : 5, 10 ,15, 20, 25, 30, 35

6: 6, 12, 18, 24, 30, 36

LCM = 30.

So we can convert 1/5 and 1/6 to fractions over 30.

  • Multiply both the numerator and denominator of 1/5 by 6. So we have a fraction of 6/30
  • Multiply both the numerator and denominator of 1/6 by 5. So we have a fraction of 5/30.

So 1/5 + 1/6 = 6/30 + 5/30 = 11/30

Example 2:

3/7 + 6/10 =

7: 7,14,21,28,35,42,49,56,63,70,77

10:10,20,30,40,50,60,70,80

LCM = 70

  • multiply both the numerator and denominator of 3/7 by 10. So we have a fraction of 30/70
  • Multiply both the numerator and denominator of 6/10 by 7. So we have a fraction of 42/70

So 3/7 +6/10 = 30/70 + 42/70 = 72/70 = 1 and 2/70 = 1 and 1/35


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      ignugent17 3 years ago

      Thanks for sharing your ideas. :-)

    • profile image

      niculasdutch 13 months ago

      Thank you for the great list! This is incredibly helpful, especially with school out for the summer. I have saved this article to my favorites.

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