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.
