Question Video: Finding the Result of Adding Three Fractions with Different Denominators and Expressing It as a Mixed Number | Nagwa Question Video: Finding the Result of Adding Three Fractions with Different Denominators and Expressing It as a Mixed Number | Nagwa

# Question Video: Finding the Result of Adding Three Fractions with Different Denominators and Expressing It as a Mixed Number Mathematics

Calculate 1/6 + 5/8 + 1/2. Give your answer as a mixed number.

02:06

### Video Transcript

Calculate one-sixth plus five-eighths plus one-half. Give your answer as a mixed number.

To find the sum of these three fractions, we first need to find the least common denominator. In this case, that will be the smallest common multiple of six, eight, and two. We begin by listing a few multiples of six, which includes six, 12, 18, 24, and 30. When we do the same for eight and two, we find the least common multiple is 24.

We note that sometimes we need to create longer lists of multiples for smaller denominators before we can find something in common. Now we need to convert the fractions to equivalent fractions with denominator 24. We multiply the numerator and denominator of one-sixth by four. This shows that one-sixth is equivalent to four twenty-fourths. Next, we multiply the numerator and denominator of five-eighths by three. This shows that five-eighths is equivalent to fifteen twenty-fourths. Finally, we multiply the numerator and denominator of one-half by 12. Therefore, we know that one-half is equivalent to twelve twenty-fourths.

Now that we have equivalent fractions where the denominators are the same, we can simply add the numerators, four, 15, and 12, to get 31. Altogether, we have thirty-one twenty-fourths, which can be written as a mixed number. The whole number part, one, is equivalent to twenty-four twenty-fourths, so seven out of the 31 parts remain. So we write our mixed number answer as one and seven twenty-fourths. This is the sum of one-sixth plus five-eighths plus one-half.

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