Mrs. Garcia's class is making a banner to hang in the school's display case. They started by sewing 7/8 of a yard of gold fabric at the top, 5/8 of a yard of black fabric in the center, and 7/8 of a yard of red fabric on the bottom of the banner.

How many yards of fabric did they use?
2 3/8

If the class adds 1 1/8 more yards of the black fabric as a border, how much black fabric will they use?
1 3/4

If there were 5/4 yards of black fabric left over after the class finished making the banner, how many yards of black fabric did they start with?
3

All of your answers are right. :-)

To find the total amount of fabric used, we need to add up the amounts used for each color. In this case, we have:

- Gold fabric: 7/8 of a yard
- Black fabric: 5/8 of a yard
- Red fabric: 7/8 of a yard

To add these fractions, we need to find a common denominator, which is 8 in this case. Now, we can simply add the numerators and keep the denominator the same:

7/8 + 5/8 + 7/8 = (7 + 5 + 7)/8 = 19/8

The result is 19/8. However, since we are dealing with fabric, it is more convenient to express this as a mixed number. A mixed number is a whole number combined with a proper fraction. To convert 19/8 to a mixed number, we divide the numerator (19) by the denominator (8):

19 ÷ 8 = 2 remainder 3

The quotient (2) becomes the whole number, and the remainder (3) becomes the new numerator. The denominator remains unchanged. So 19/8 can be expressed as 2 3/8.

Therefore, the class used a total of 2 3/8 yards of fabric.

Now, let's consider the additional fabric the class wants to use as a border. They plan to add 1 1/8 yards of black fabric. To find the total amount of black fabric used, we need to add the initial amount (5/8 yard) to the additional amount (1 1/8 yards).

To add these fractions, we need to find a common denominator, which is 8 in this case:

5/8 + 1 1/8 = 5/8 + 9/8 = (5 + 9)/8 = 14/8

Again, it is more convenient to express this as a mixed number. To do that, we divide the numerator (14) by the denominator (8):

14 ÷ 8 = 1 remainder 6

The quotient (1) becomes the whole number, and the remainder (6) becomes the new numerator. The denominator remains unchanged. So 14/8 can be expressed as 1 6/8.

Therefore, the class will use a total of 1 6/8 yards or 1 3/4 yards of black fabric.

Finally, let's calculate the amount of black fabric they started with, given that there were 5/4 yards left over.

Initially, they used 5/8 yard of black fabric and added 1 1/8 yards as a border. So the total amount of black fabric used is:

5/8 + 1 1/8 = 5/8 + 8/8 = (5 + 8)/8 = 13/8

To find the amount of black fabric they started with, we subtract the amount left over (5/4) from the total amount used (13/8):

13/8 - 5/4

Since the denominators are not the same, we need to find a common denominator. The least common multiple (LCM) of 8 and 4 is 8. Now, we can continue with the subtraction:

13/8 - 5/4 = (13/8) - (10/8) = 3/8

Therefore, the class started with 3/8 yards of black fabric.