Mrs.Hyatt went to the fabric store. She purchased 1 1/2 a yard of red material, 2 1/8 a yard of blue material and 3 3/4 a yard of green material. How many yards of material did she buy? A. 1 3/8 B. 6 3/8 C. 6 7/8 D. 7 3/8
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To find the total yards of material Mrs. Hyatt bought, we need to add up the measurements:
1 1/2 yard + 2 1/8 yards + 3 3/4 yards
First, let's convert all the fractions to have the same denominator:
1 1/2 yard is equal to 2/2 + 1/2 = 3/2 yards
2 1/8 yards stays as 2 1/8 yards
3 3/4 yards can be written as 3 * 4/4 + 3/4 = 12/4 + 3/4 = 15/4 yards
Now, we can add the converted fractions:
3/2 yards + 2 1/8 yards + 15/4 yards
Next, let's convert the mixed number 2 1/8 to an improper fraction:
First, multiply the whole number (2) by the denominator of the fraction (8):
2 * 8 = 16
Then, add the product to the numerator of the fraction (1):
16 + 1 = 17
So, 2 1/8 is equal to 17/8.
Now, we can rewrite the addition using the common denominator (8):
3/2 yards + 17/8 yards + 15/4 yards
Now, let's convert all the fractions to have the common denominator of 8:
3/2 yards can be written as 12/8 yards
17/8 yards stays as 17/8 yards
15/4 yards can be written as 30/8 yards
Now, we can add the fractions:
12/8 yards + 17/8 yards + 30/8 yards
Adding the numerators, we get:
12 + 17 + 30 = 59
So, the total yards of material Mrs. Hyatt bought is 59/8 yards.
To simplify the fraction, we can divide the numerator and denominator by the greatest common divisor, which is 8:
59/8 ÷ 8/8 = 59/8 ÷ 1 = 59/8
Therefore, Mrs. Hyatt bought 59/8 yards of material.
To express the answer as a mixed number, we can divide the numerator (59) by the denominator (8):
59 ÷ 8 = 7 remainder 3
So, Mrs. Hyatt bought 7 3/8 yards of material. Therefore, the answer is option D.
To find the total yards of material Mrs. Hyatt bought, we need to add up the lengths of each color of fabric she purchased.
For the red fabric, she bought 1 1/2 yards.
For the blue fabric, she bought 2 1/8 yards.
And for the green fabric, she bought 3 3/4 yards.
To add these fractions with different denominators, we need to find a common denominator. In this case, the common denominator is 8.
Converting the fractions to have a denominator of 8, we get:
- 1 1/2 yards is equal to 4/8 + 1/2 = 5/8 yards.
- 2 1/8 yards is equal to 8/8 + 1/8 = 9/8 yards.
- 3 3/4 yards is equal to 6/8 + 3/4 = 15/8 yards.
Now, let's add these fractions together:
5/8 + 9/8 + 15/8 = 29/8.
To express this fraction as a mixed number, we divide the numerator (29) by the denominator (8), resulting in 3, with a remainder of 5. So, the total is 3 5/8 yards.
Therefore, the answer is B. 6 3/8.
Aren't you just doing ...
1 1/2 + 2 1/8 + 2 3/4
step1: get rid of those silly and useless mixed fractions
1 1/2 + 2 1/8 + 2 3/4
= 3/2 + 17/8 + 11/4
your common denominator is obviously 8, so make the changes
take over, let me know what you get