In the last post about Equivalent Fractions we had the story of me, you, pizza and cake. There’s less food in this one, but you should be able to analyse and pick out fractions that share the same value by the end of these two posts and I’ve thrown in a little quiz for good measure.
When we’re looking for fractions that are equal, or equivalent, to each other we often need to think about simplifying the one with the biggest numbers in it. That means dividing top and bottom by the same number until we can’t divide any more.
So, if we we had eight (8) jars of pasta sauce and four (4) of them had mushrooms in we’d say that 4/8 were mushroom sauce. If we’d be asked to get half mushroom, and half plain that’s 1/2 of each. So how do we make sure that 4/8 is the same as 1/2?
One way is to simplify 4/8 so that we get the smallest number on top and bottom. We can try dividing by 2 or 4. Which do you think is better? If you’ve got a bigger number, you could try 5 or 10.
We’ll start with 4 because it looks like it might fit, it’s the higher number and we’re aiming for a unit fraction (one that has 1 on the top). Whatever we do to the numerator (top) we must also do to the denominator (bottom) to keep the fraction the same.
Now try the quizzes below. Match each numbered fraction on the left to the equivalent marked with a letter on the right. Click ‘Show Answers’ to see the solution. Don’t worry if you get some wrong, it just means you need a bit more information, or to change the way you’re thinking about it. Think about where you went wrong and see if you can work out a better way to do it next time. Let me know where you got to in the comments below or on twitter EveryDMaths
Quiz 1 – Equivalent Fractions
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Answers to Quiz: 1c, 2a, 3d, 4b.
Got them right? Excellent. Got it wrong? Excellent*, you’ve just grown a few more synapses in your brain. Remember you need to divide the top and bottom by the same number to simplify it down.
Quiz 2 – Equivalent Fractions
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1b, 2d, 3a, 4c
Got them right? Excellent! Got them wrong? Excellent! These ones were a bit more tricky so I’ve done some worked answers below.
If you worked them out a different way – I’d love to see it. Tweet me a photo to EveryDMaths.
Look at the diagram or picture. How many parts are highlighted? That’s your numerator (top number). How many parts are there in total? This is your denominator (bottom number)
So in Quiz 2, Question (1) we have 2 parts shaded out of a total of 6. So this is 2/6. So we know this is answer (b).
If we take Question (4) we can see we have 5 parts shaded out of 6. 5/6. Which of the remaining answers do you think it will match? Remember, you can take a guess and test it. You don’t have to be right first time.
So let’s try (d) 6/8. If we divide top and bottom by 2 (6 divided by 2 = 3 and 8 divided by 2 = 4) and we get 3/4. That’s no good. Let’s try 10/12 instead. 10 divided by 2 = 5 and 12 divided by 2 is 6. 5/6 BINGO!
I hope you had fun exploring equivalent fractions with me. See you in the next post.
*This attitude reflects something called the Growth Mindset. In short, this is the belief that no one is born with a ‘maths brain’, everyone can develop and improve their maths ability. That we should praise effort not talent. That mistakes are opportunities to learn. (After all, if you know all the answers, you’re not learning are you?) It can take a bit of getting used to, especially for if you’ve spent 10 or 20 years thinking that you’re ‘not a maths person’, but in the end it can make learning more successful, long-lasting and enjoyable.