A certain recipe requires 6 2/7 cups of flour and 7 2/9 cups of sugar.

A) if 6/5 of the recipe is to be made, how much sugar is needed? Write your answer as a proper or improper fraction:
B) if the above ingredients are required for one batch, find the amount of flour needed for a double batch. Write your answer as a proper or improper fraction.

A)

7 2 / 9 = 7 + 2 / 9 =

7 * 9 / 9 + 2 / 9 =

63 / 9 + 2 / 9 = 65 / 9

( 6 / 5 ) * ( 65 / 9 ) =

6 * 65 / ( 5 * 9 ) =

2 * 3 * 5 * 13 / ( 5 * 3 * 3 ) =

2 * 13 / 3 = 26 / 3

B)

6 2 / 7 = 6 + 2 / 7 =

6 * 7 / 7 + 2 / 7 =

42 / 7 + 2 / 7 = 44 / 7

2 * 44 / 7 = 88 / 7

A) To find out how much sugar is needed, we first need to calculate 6/5 of 7 2/9 cups.

Step 1: Convert the mixed number 7 2/9 to an improper fraction.
7 * 9 = 63
63 + 2 = 65
65/9 = 7 2/9

Step 2: Multiply the fraction 7 2/9 by 6/5.
(7 2/9) * (6/5)

To multiply mixed numbers, we need to convert them to improper fractions.
7 * 9 = 63
63 + 2 = 65
65/9

Now, multiply the fractions:
(65/9) * (6/5)

To multiply fractions, multiply the numerators and denominators:
(65 * 6) / (9 * 5)
(390) / (45)

Simplify the fraction:
390 ÷ 45 = 8 remainder 30
30/45 can be simplified to 2/3.

Therefore, 6/5 of 7 2/9 cups of sugar is 2 2/3 cups.

B) To find the amount of flour needed for a double batch, we need to multiply the amount required for one batch by 2.

The amount of flour needed for a double batch is:
(6 2/7) * 2

To multiply mixed numbers, convert them to improper fractions:
6 * 7 = 42
42 + 2 = 44
44/7

Now, multiply the fractions:
(44/7) * 2

To multiply fractions, multiply the numerators and denominators:
(44 * 2) / (7 * 1)
(88) / (7)

Simplify the fraction:
88 ÷ 7 = 12.

Therefore, the amount of flour needed for a double batch is 12 cups.