a gift store owner used 9 rolls of wrapping paper to wrap his customers' gifts last week. each roll was 58 1/3 inches long. how many gifts did he wrap if a 8 1/3 inch long piece of wrapping paper was used to wrap each gift?
yes
Vvb
To find out how many gifts the store owner wrapped, we need to determine the total length of the wrapping paper used and then divide it by the length of paper used for each gift.
First, let's calculate the total length of the wrapping paper used. We know that the store owner used 9 rolls of wrapping paper, and each roll was 58 1/3 inches long. To find the total length, multiply the length of one roll by the number of rolls:
Total length of wrapping paper = Length per roll × Number of rolls
Total length of wrapping paper = (58 1/3 inches) × (9 rolls)
To perform the calculation, we need to convert the mixed number (58 1/3) into an improper fraction. The formula for converting a mixed number to an improper fraction is:
improper fraction = (whole number × denominator) + numerator / denominator
Converting 58 1/3 to an improper fraction:
58 1/3 = (58 × 3 + 1) / 3 = 175 / 3
Plugging in the values:
Total length of wrapping paper = (175 / 3 inches) × (9 rolls)
Now, let's multiply the fractions:
Total length of wrapping paper = (175 × 9) / (3) inches
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 175 and 3 is 1:
Total length of wrapping paper = 175 × 9 / 3 inches
Total length of wrapping paper = 1575 / 3 inches
Next, let's calculate how many gifts can be wrapped using an 8 1/3 inch piece of wrapping paper. Like before, we'll convert 8 1/3 into an improper fraction:
8 1/3 = (8 × 3 + 1) / 3 = 25 / 3
Now, we'll divide the total length of wrapping paper by the length used per gift to find the number of gifts wrapped:
Number of gifts = Total length of wrapping paper / Length used per gift
Number of gifts = (1575 / 3 inches) / (25 / 3 inches)
By simplifying the expression, the inches in the numerator and denominator cancel out:
Number of gifts = 1575 / 25
Let's perform the division:
Number of gifts = 63
Therefore, the gift store owner wrapped 63 gifts.