Lowest Common Denominator

Numbers Part Two Lowest Common Denominator

What if we wanted to add these two fractions, $\frac{1}{2}$ and $\frac{3}{5}$ . How can we do that?

Look at the pictures below. Are these fractions the same as the ones above?

The shaded blue areas are the same sizes but there are more lines in the second group of circles. The circles have been divided up into more parts.

What are the numerators and denominators of the blue areas in the second two circles?

$\frac{5}{10}$ and $\frac{6}{10}$

Now can we add these two fractions?

Yes.

We get $\frac{11}{10}$

It looks like this:

It’s the same as $\frac{10}{10} + \frac{1}{10}$

This is the same as $1\frac{1}{10}$

So, what we have done here is convert the fractions $\frac{1}{2}$ and $\frac{3}{5}$ into the fractions $\frac{5}{10}$ and $\frac{6}{10}$ and then we’ve added these up to get $\frac{11}{10}$ .

That is how you add fractions with different denominators. You convert the denominators so that they are the same in both fractions. They need a common denominator (this just means that they need the same denominator). You convert the denominators into the lowest common denominator. In the case of the denominators two and five, the lowest common denominator is ten.

We could have changed both denominators to be 20. We could have converted the fractions $\frac{1}{2}$ and $\frac{3}{5}$ into the fractions $\frac{10}{20}$ and $\frac{12}{20}$ and we could have added them together to get $\frac{22}{20}$ . We wouldn’t have used the lowest common denominator though and we can see that we can divide the numerator and denominator of $\frac{22}{20}$ by 2 to get $\frac{11}{10}$ .

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