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Adding and Subtracting Fractions with Unlike Denominators

Learn how to add and subtract fractions with unlike denominators using visual representations and finding the lowest common multiple. Practice questions included.

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Adding and Subtracting Fractions with Unlike Denominators

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  1. Comparing Apples with Apples I am learning to add and subtract fractions with unlike denominators. + = ? - = ? Before starting this lesson you need to be able to find the lowest common multiple of two numbers.

  2. Below are two fifths of a chocolate bar and three tenths of a chocolate bar. How much chocolate is there in total? Let’s place the chocolate that we have together. You can see we have + = ? If I draw in some lines you can see that the two fifths are the same as having two tenths. We now have: + = ? We changed the fifths into tenths because this was the lowest common multiple of both numbers. X2 You can see that because the denominator became twice as big the numerator also became twice as big so that we still had an equivalent fraction. X2

  3. Now let’s try a question without the pictures. Imagine two thirds of a chocolate bar plus one ninth of a chocolate bar. We can’t add the fractions together because the denominators are different. + = ? The lowest common multiple of 3 and 9 is 9 so let’s change the thirds into ninths. Imagine cutting each third into three pieces. This is how we make ninths. X3 Now we can answer our question. You can see = + = ? X3

  4. Subtraction works the same way. First we must change the fractions so they have a common denominator. - = ? We need to change the thirds into sixths. X2 You can see = X2 Now we can answer our question. or - = ?

  5. Now let’s try and example where we have to change both denominators. We can’t change thirds into quarters so we need to find a common multiple of 3 and 4. + = ? 12 is the lowest common multiple of 3 and 4. Below are 2 thirds. Below are 3 quarters Imagine splitting the 3 thirds into twelfths. Imagine splitting the 4 quarters into twelfths. X3 X4 You can see = You can see = or + = ? X3 X4

  6. Now let’s try a subtraction example. We can’t change thirds into fifths so we need to find a common multiple of 3 and 5. - = ? 15 is the lowest common multiple of 3 and 5. Below are 4 fifths. Below is 1 third. Imagine splitting the 5 fifths into fifteenths. Imagine splitting the 3 thirds into fifteenths. X5 X3 You can see = You can see = - = ? X5 X3

  7. Now try these questions on your own. Click again when you have worked out all the percentages. 5) - = ? 1) + = ? 6) - = ? 2) + = ? 7) or - = ? 3) + = ? or 4) + = ? Need some more practise? Try pg40 & 41 of Teacher Tools Fractions, Decimals and Percentages Book Numeracy resources

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