Last week, Emmy spent 3 1/5 hours watching television. Rhianna watched television for 1 4/5 times as many hours as Emmy did. How many hours did Rhianna spend watching television?
Simplify your answer and write it as a fraction or as a whole or mixed number.
hours
To find how many hours Rhianna watched, we need to multiply Emmy's time by 1 4/5:
1 4/5 × 3 1/5
To multiply mixed numbers, we usually convert them to improper fractions first:
1 4/5 = (5 × 1 + 4)/5 = 9/5
3 1/5 = (5 × 3 + 1)/5 = 16/5
Now we can multiply:
9/5 × 16/5 = (9 × 16)/(5 × 5) = 144/25
This is the amount of time Rhianna spent watching television, but we may want to simplify the fraction. We can divide the numerator and denominator by their greatest common factor, which is 1 in this case:
144/25 = (144 ÷ 1)/(25 ÷ 1) = 144/25
So Rhianna watched 144/25 hours of television, which is an improper fraction. To convert it to a mixed number, we can divide the numerator by the denominator and write the remainder as a fraction:
144 ÷ 25 = 5 remainder 19
The quotient is the whole number part of the mixed number, and the remainder is the numerator of the fractional part, which should be written over the same denominator as before:
144/25 = 5 19/25
Therefore, Rhianna spent 5 19/25 hours watching television.