Angela is crocheting scarfs for seniors at the nursing home. She needs 20 ¼ yards of yarn for each scarf. If she is given 324 yards of yarn by the craft shop, how many scarves can she crochet?
16 scarves?
Yes, Angela can crochet a total of 16 scarves with the given amount of yarn.
She can crochet 324/20 ¼ = <<324/20+1/4=16>>16 scarfs. Answer: \boxed{16}.
To determine how many scarves Angela can crochet, divide the total yards of yarn she has by the yards needed for each scarf.
Total yards of yarn ÷ yards needed per scarf = number of scarves
324 yards ÷ 20 ¼ yards = number of scarves
To divide a mixed number by a whole number, you need to convert the mixed number to an improper fraction.
20 ¼ yards can be converted to an improper fraction as follows:
20 × 4 = 80
80 + 1 = 81
So, 20 ¼ yards is equivalent to 81/4 yards.
Now let's plug in the appropriate values into the formula:
324 yards ÷ 81/4 yards = number of scarves
To divide by a fraction, you can multiply by its reciprocal.
324 yards × 4/81 yards = number of scarves
Cancel out any common factors:
324 ÷ 9 = 36
81 ÷ 9 = 9
36 × 4 = 144
9 × 1 = 9
144 ÷ 9 = 16
So, Angela can crochet 16 scarves with the given yardage of yarn.
To find out how many scarves Angela can crochet, we need to divide the total number of yards of yarn she has by the amount of yarn she needs for each scarf.
Given that she needs 20 ¼ yards of yarn for each scarf, and she has 324 yards of yarn, we can use division to solve the problem.
Dividing 324 by 20 ¼ can be a bit complicated since the value contains a fraction. To simplify the calculation, we can convert both numbers to the same format. Let's convert 20 ¼ yards to an improper fraction:
20 ¼ = (20 * 4 + 1) / 4 = 81 / 4
Now that we have the same format, we can divide 324 by 81/4. Division of fractions is the same as multiplying by the reciprocal, so we can rewrite the division as a multiplication:
324 ÷ (81 / 4) = 324 * (4 / 81)
To multiply fractions, we multiply the numerators and denominators separately:
324 * 4 = 1296 (numerator)
81 * 1 = 81 (denominator)
Thus, 324 ÷ (81 / 4) = 1296 / 81.
Now we can divide both the numerator and denominator of the fraction by their greatest common divisor to simplify the fraction. The greatest common divisor of 1296 and 81 is 81:
1296 ÷ 81 = 16 (numerator)
81 ÷ 81 = 1 (denominator)
The simplified fraction is 16/1, which is equivalent to the whole number 16.
So, Angela can crochet 16 scarves with the given amount of yarn.