Final Answer:
If she has to use 3/4 yards of fabric for each scarf, how many scarves will she be able to make 5 scarves.
Step-by-step explanation:
To determine how many scarves Sarah can make with the fabric she has, we need to figure out how many times 3/4 yards of fabric can be subtracted from 4 1/6 yards. Here's how you'd solve this step-by-step:
1. Convert 4 1/6 yards to an improper fraction to make the division easier. To do this, multiply the whole number part by the denominator of the fraction part and add the numerator:
4 * 6 + 1 = 24 + 1 = 25
So, 4 1/6 yards is the same as25/6 yards when expressed as an improper fraction.
2. Now, divide 25/6 yards of fabric by 3/4 yards per scarf to find out how many scarves can be made:
25/6 ÷ 3/4
To divide by a fraction, we multiply by its reciprocal. The reciprocal of 3/4 is 4/3, so the equation becomes:
25/6 * 4/3
3. Multiply the numerators together and the denominators together:
Numerator: 25 * 4 = 100
Denominator: 6 * 3 = 18
So the fraction representing the number of scarves is 100/18.
4. Simplify the fraction. Both the numerator and the denominator are divisible by 2:
100 ÷ 2 / 18 ÷ 2 = 50/9
5. Now, we want to convert the improper fraction back to a mixed number to make it easier to understand.
To do this, divide the numerator by the denominator:
50 ÷ 9 = 5 with a remainder of 5.
Thus, 50/9 is equivalent to 5 and 5/9 as a mixed number.
This means Sarah can make 5 whole scarves. However, since we cannot make a fraction of a scarf (assuming she wants to make full scarves), we can only count the whole number.
So, Sarah can make 5 scarves with 4 1/6 yards of fabric, and she will have some fabric left over.