Jason took 3/4 of an hour to paint 27 1/3 square yards. How many square yards does he paint per hour?
To find out how many square yards Jason can paint per hour, we need to determine the number of square yards he painted in 1 hour.
Jason took 3/4 of an hour to paint 27 1/3 square yards. To find out how much he paints in 1 hour, we can divide the number of square yards he painted by the fraction of an hour he took.
First, let's convert 3/4 of an hour to a decimal. To do this, divide the numerator (3) by the denominator (4): 3 ÷ 4 = 0.75.
Now we divide the number of square yards he painted (27 1/3) by the amount of time it took (0.75 hours):
(27 1/3) ÷ 0.75
To divide a whole number mixed with a fraction, we need to convert the mixed number into an improper fraction. Multiply the whole number (27) by the denominator of the fraction (3) and add the numerator (1). Place the result over the original denominator:
27 × 3 + 1 = 82
-----
3
Now we can divide the improper fraction:
82/3 ÷ 0.75
To divide a fraction by a decimal, we can multiply the fraction by the reciprocal of the decimal.
So, multiply 82/3 by the reciprocal of 0.75, which is 4/3:
(82/3) × (4/3)
To multiply fractions, multiply the numerators (top numbers) together and the denominators (bottom numbers) together:
(82 × 4) / (3 × 3)
Simplifying the multiplication:
328 / 9
Therefore, Jason can paint approximately 36.44 square yards per hour.