Question Video: Adding two Fractions with Unlike Denominators | Nagwa Question Video: Adding two Fractions with Unlike Denominators | Nagwa

# Question Video: Adding two Fractions with Unlike Denominators Mathematics

Mia is designing a flag. She colors 4/6 of the flag yellow and 2/9 of the flag blue. She leaves the rest of the flag white. What fraction of the flag does Mia color altogether?

03:45

### Video Transcript

Mia is designing a flag. She colors four-sixths of the flag yellow and two-ninths of the flag blue. She leaves the rest of the flag white. What fraction of the flag does Mia color altogether?

Let’s quickly sketch what is happening. Mia is designing a flag. She colors four-sixths yellow and two-ninths blue. We need to find the fraction of the flag that is colored altogether. This means we need to add the fractions.

We know that to add two fractions, we count the number of equal parts. However, in this case, we do not have equal parts. Fractions with equal parts have the same denominator, but these fractions have different denominators: six and nine. So we need to find a common denominator, which is a common multiple of six and nine.

The product of six and nine in this case is certainly a multiple of six and a multiple of nine. But this method does not always lead to the least common denominator. 54 is quite a large number. And because six and nine both have three as a factor, it is likely not the least common denominator.

To find the least common denominator, we will begin by listing the multiples of both six and nine then select the smallest multiple they have in common. The first six multiples of six are six, 12, 18, 24, 30, and 36. The smallest multiple of six that is also a multiple of nine will be our least common denominator. The first four multiples of nine are nine, 18, 27, and 36. Which multiples do they have in common? 18 and 36. Since we want the least common denominator, we select 18.

Now we are ready to create equivalent fractions with our new common denominator. To find the fraction equivalent to four-sixths, we must think of the number we multiply by six to get 18. We know that six multiplied by three equals 18. So we multiply the numerator by three as well. The result is the equivalent fraction twelve eighteenths. Then we do the same for two-ninths. But in this case, we multiply the denominator nine by two to get 18. So we also multiply the numerator by two to find our equivalent fraction. And we find that two-ninths equals four-eighteenths.

Now that we have rewritten our fractions with a common denominator, we can add the parts of equal size together. Twelve eighteenths plus four-eighteenths equals sixteen eighteenths altogether. This means four-sixths plus two-ninths is equivalent to twelve eighteenths plus four-eighteenths, which equals sixteen eighteenths, which is the fraction of the flag Mia colored.

We should check whether our answer can be simplified. In this case, it can, as the numerator and denominator are both divisible by two. So the simplified answer is eight-ninths.

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