Michaela has 11/12 of a yard of orange cloth and 7/8 of a yard of green cloth. Use 1/2 of a yard of each color for your sewing project. About how much fabric will Michaela have left if she combines the two colors?
To find out how much fabric Michaela will have left after combining the two colors, we need to first calculate the total amount of fabric she has from each color.
Michaela has 11/12 of a yard of orange cloth and 7/8 of a yard of green cloth.
Next, we need to find the common denominator between 12 and 8. The least common multiple of 12 and 8 is 24.
Now, we can convert 11/12 and 7/8 to have a common denominator of 24.
To convert 11/12 to have a denominator of 24, we multiply the numerator and denominator by 2:
11/12 * 2/2 = 22/24.
To convert 7/8 to have a denominator of 24, we multiply the numerator and denominator by 3:
7/8 * 3/3 = 21/24.
So, Michaela has 22/24 of a yard of orange cloth and 21/24 of a yard of green cloth.
Now, we can calculate how much fabric she will use for her sewing project. The project requires 1/2 of a yard of each color.
For the orange cloth, she will use 1/2 * 22/24 = 11/24 of a yard.
For the green cloth, she will use 1/2 * 21/24 = 21/48 = 7/16 of a yard.
Now, we can calculate how much fabric she will have left by finding the difference between the initial amount of fabric and the amount used for the project.
For the orange cloth: 22/24 - 11/24 = 11/24 of a yard left.
For the green cloth: 21/24 - 7/16 = 42/48 - 21/48 = 21/48 = 7/16 of a yard left.
Combining the leftover fabric from both colors, Michaela will have 11/24 + 7/16 = 44/96 + 42/96 = 86/96 = 43/48 of a yard left.
Therefore, Michaela will have about 43/48 of a yard of fabric left if she combines the two colors.