6.2 Adding and Subtracting Fractions

In this section, we are going to look at how we add and subtract numbers that include fractions.

The chocolate bar pictured above has 24 pieces. Each piece is one divided by 24of the bar, so the whole bar is 24 divided by 24, or 1. There are four identical rows, so each row is one divided by four of the bar. There are also six identical columns, so each column is one divided by six of the bar.

Now, imagine that you eat one third of the chocolate bar. That is eight out of the 24 pieces (because equation left hand side one divided by three equals right hand side eight divided by 24). You are still feeling hungry five minutes later, so you decide to eat another five pieces. What fraction of the bar will you have eaten in total? What fraction of the bar is left?

The fraction eaten will be one divided by three plus five divided by 24, but it’s not easy to quickly determine what fraction this is because the two fractions are out of different numbers of parts. However, if you recall that eating one divided by three of the bar is the same as eating eight divided by 24, the fraction eaten is equation left hand side eight divided by 24 plus five divided by 24 equals right hand side 13 divided by 24. You can check this answer on the bar of chocolate: just count the number of squares that have been eaten!

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The fraction that is left will be one minus 13 divided by 24. So, thinking of the whole bar as 24 divided by 24, the calculation becomes equation left hand side 24 divided by 24 minus 13 divided by 24 equals right hand side 11 divided by 24. You can check this by counting the number of squares that are left.

This method of changing the fractions into the same kind using equivalent fractions can be used for adding and subtracting fractions in general.

If you need to add or subtract fractions, the first question you need to ask yourself is “Are these the same kind of fractions?” That is, are they divided into the same number of parts? If the answer is no, then you need to convert the fractions into equivalent fractions with the same denominator in order to add or subtract them.

6.1.11 Using the Calculator for Fractions

6.2.1 Adding and Subtracting Fractions with the Calculator