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“Okay, listen up! Today’s lesson will be on adding fractions. Let’s start with an easy one like 1/3 + 1/6. The first step is to find a common numerator, which, in this example, we already have. This becomes the numerator of the sum so let’s write a 1 up there. The denominator is, of course, itself a fraction whose numerator is the product of the denominators and whose denominator is the sum of the denominators. This gives us 1/(18/9), or 1/2. Let’s kick it up a notch and try 2/3 + 1/4. Remember, the first step is to find the lowest common numerator, or LCN. You guys look a little puzzled. You remember learning this in grade 7, right? Since the LCN is 2, we have 2/3 + 2/8. Write a 2 up top. To determine the denominator, simply multiply and add to get 24/11. We have 2/(24/11). This is a tricky one since 24/11 doesn’t reduce nicely. Multiplying the common numerator by the denominator of the denominator gives us 22/24. One more thing… if you don’t reduce to lowest terms, I’ll have to deduct half a mark. 22/24 should be written as 11/12. I’ve typed up some notes. Take one sheet and pass the rest back.” I think Christopher (@Trianglemancsd) plays it straight when he shows his algorithm to pre-service teachers. I couldn’t pull this off – more of a tongue-in-cheek thing for me. This elicited some (nervous?) laughter as teachers put themselves in the role of their students learning about LCD’s.
These last two are connected… more on this later.
In order to continue enjoying our site, we ask that you confirm your identity as a human. Thank you very much for your cooperation. You might like to read Adding Fractions first. Step 1. The bottom numbers are already the same. Go straight to step 2. Step 2. Subtract the top numbers and put the answer over the same denominator: 3 4 − 1 4 = 3 − 1 4 = 2 4 2 4 = 1 2 (If you are unsure of the last step see Equivalent Fractions.)
Step 1. The bottom numbers are different. See how the slices are different sizes? We need to make them the same before we can continue, because we can't subtract them like this:
To make the bottom numbers the same, multiply the top and bottom of the first fraction (1/2) by 3 like this:
And now our question looks like this:
The bottom numbers (the denominators) are the same, so we can go to step 2. Step 2. Subtract the top numbers and put the answer over the same denominator: 3 6 − 1 6 = 3 − 1 6 = 2 6 In picture form it looks like this:
2 6 = 1 3 With Pen and PaperAnd here is how to do it with a pen and paper (press the play button):
Subtracting Mixed FractionsI have a special page on Adding and Subtracting Mixed Fractions. Making the Denominators the SameIn the previous example it was easy to make the denominators the same, but it can be harder ... so you may need to use either the
They both work, use which one you prefer!
Example: Cupcakes You want to sell cupcakes at a market: You get paid 2 5 of total sales But you have to pay 1 4 of total sales for the stall How much do you get?We need to subtract 1 4 from 2 5 2 5 − 1 4 = ? ? First make the bottom numbers (the denominators) the same. Multiply top and bottom of 2/5 by 4: 2 × 4 5 × 4 − 1 4 = ? ? And multiply top and bottom of 1/4 by 5: 2 × 4 5 × 4 − 1 × 5 4 × 5 = ? ? Now do the calculations: 8 20 − 5 20 = 8 − 5 20 = 3 20 Answer: you get to keep 3 20 of total sales. Copyright © 2020 MathsIsFun.com |
What is the first step when calculating the fraction 1 4 2 3?
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