Julianna has 22 1/2 yards of material. If it takes 3/4 yard of material to make 1 pair of shorts, can she make enough shorts for 30 children?
what is 22.5 ÷ .75 ??
To determine if Julianna has enough material to make shorts for 30 children, we need to find out how many pairs of shorts can be made from the available material.
First, we need to convert the mixed number of yards she has into an improper fraction. Julianna has 22 1/2 yards of material, which can be written as 45/2 yards.
Next, we divide the amount of material needed to make one pair of shorts (3/4 yard) into the total amount of material available (45/2 yards):
(45/2 yards) ÷ (3/4 yards) = (45/2 yards) × (4/3 yards)
To simplify this, we multiply the numerators (45 × 4) and the denominators (2 × 3):
(45/2 yards) × (4/3 yards) = (180/6) yards
Simplifying 180/6, we get:
180/6 = 30 yards
Thus, Julianna has enough material to make 30 yards of shorts.
However, to determine if she can make enough shorts for 30 children, we need to consider how many pairs of shorts can be made from 30 yards. Given that 1 pair of shorts requires 3/4 yards, we divide the total yards available (30) by the amount of material needed per pair (3/4):
(30 yards) ÷ (3/4 yards) = (30 yards) ÷ (3/4 yards)
To divide fractions, we multiply by the reciprocal of the second fraction:
(30 yards) ÷ (3/4 yards) = (30 yards) × (4/3 yards)
Multiplying the numerators (30 × 4) and denominators (1 × 3), we get:
(30 yards) × (4/3 yards) = (120/3) yards
Simplifying 120/3, we get:
120/3 = 40 yards
Therefore, Julianna can make enough shorts for 30 children, as she has 40 yards of material.