Alana bought 3/8 pound of swiss cheese and 1/4 pound of American Cheese. Which pair of fractions cannot be used to find how many pounds of cheese she bought in all
a)6/16 and 4/16
b)9/24 and 6/24
c)24/64 and 8/64
d)15/40 and 10/40
3/8 * 3/3 = 9/24
1/4 * 6/6 = 6/24
Answer A
To find the total amount of cheese Alana bought, we need to add together the amounts of Swiss cheese and American cheese.
Swiss cheese: 3/8 pound
American cheese: 1/4 pound
To add fractions together, they must have the same denominator. Let's find the fractions that have the same denominators as the given pairs:
a) 6/16 and 4/16
b) 9/24 and 6/24
c) 24/64 and 8/64
d) 15/40 and 10/40
Comparing the denominators of the given fractions, we can see that option c) has the correct denominator for both fractions, 64/64.
Therefore, the pair of fractions that cannot be used to find the total amount of cheese Alana bought is c) 24/64 and 8/64.
To find the total amount of cheese Alana bought, we need to add the fractions representing the amounts of Swiss cheese and American cheese.
The denominators (the bottom numbers) of both fractions represent the number of equal parts into which the whole is divided. In this case, it represents pounds of cheese.
To add fractions, we need a common denominator. The common denominator is the least common multiple (LCM) of the given denominators.
Now let's look at each pair of fractions:
a) 6/16 and 4/16:
The common denominator is 16. Adding the fractions gives us (6+4)/16 = 10/16.
b) 9/24 and 6/24:
The common denominator is 24. Adding the fractions gives us (9+6)/24 = 15/24.
c) 24/64 and 8/64:
The common denominator is 64. Adding the fractions gives us (24+8)/64 = 32/64.
d) 15/40 and 10/40:
The common denominator is 40. Adding the fractions gives us (15+10)/40 = 25/40.
Now, we need to compare each fraction to the original problem's fractions:
3/8 + 1/4 = 6/16 + 4/16 = 10/16.
Comparing 10/16 to the given answer choices:
a) 10/16 matches 6/16 and 4/16, so it can be used.
b) 10/16 does not match 9/24 and 6/24.
c) 10/16 does not match 24/64 and 8/64.
d) 10/16 matches 15/40 and 10/40, so it can be used.
Hence, the pair of fractions that cannot be used to find how many pounds of cheese she bought in all is:
b) 9/24 and 6/24.