Bill can ride his bike 7 1/2 miles in a hour. a. How far will he ride in 3 hours? b. How far will he ride in 1/3 of an hour? I think for a. the answer is multiply so it would be 22 1/2 miles and for b. it would be 2 1/2 miles. Is this correct?
Both of your answers are right.
To find the distances, you are correct that you need to multiply. Let's break it down step by step:
a. To find how far Bill will ride in 3 hours, you need to multiply the rate (7 1/2 miles per hour) by the time (3 hours):
Distance = Rate × Time
Distance = 7 1/2 miles/hour × 3 hours
To multiply a whole number by a fraction, multiply the whole number by the numerator and put that product over the denominator.
7 1/2 × 3 = (7 × 3) + (1/2 × 3) = 21 + 3/2 = 21 3/2 = 22 1/2 miles
So, you are correct. Bill will ride 22 1/2 miles in 3 hours.
b. To find how far Bill will ride in 1/3 of an hour, you once again need to multiply the rate by the time:
Distance = 7 1/2 miles/hour × 1/3 hour
To multiply a fraction by a whole number, multiply the numerators and multiply the denominators.
7 1/2 × 1/3 = (7/1 × 1/3) + (1/2 × 1/3) = 7/3 + 1/6 = 14/6 + 1/6 = 15/6 = 2 1/2 miles
Again, you are correct. Bill will ride 2 1/2 miles in 1/3 of an hour.
So, your answers are indeed correct. Well done!