Sean bought 3/7 of a pound of cherries and then he ate 1/4 of a pound of them. When he got home, he saw that he still had 2/3 of a pound of cherries in his cupboard. How many total pounds of cherries does he have? Give your answer as an exact simplified improper fraction, not as a mixed number. Do not include units.

Question

17-09-2022
Mathematics

Answered

Sean bought 3/7 of a pound of cherries and then he ate 1/4 of a pound of them. When he got home, he saw that he still had 2/3 of a pound of cherries in his cupboard. How many total pounds of cherries does he have? Give your answer as an exact simplified improper fraction, not as a mixed number. Do not include units.

Answer :

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tazkiayousuf29 tazkiayousuf29 · Answer 1 · 2022-09-17T21:24:15-04:00

Answer:

71 /84

answer is not in imporper fraction.

Step-by-step explanation:

fractions need to be changed or converted to equivalent fractions inorder to solve them.

1.Total amount of cherries he bought and he already had in cupboard= 3/7 + 2/3

convert them to equivalent fractions inorder to add them by using LCM of the denominators.Which in this case is 21 (LCM of 7 and 3 is 21)

2. Now the common denominator is 21

change 3/7 to a fraction with 21 as denominator by multiplying the numerator to 3 and denominator also by 3 which will give you 3×3=9/ 7×3=21 or 9/21

note: you have to multiply both numerator and denominator by the same number which is used to convert the denominator to the number given by LCM.

3)Now change the second fractions denominator to 21 by multiplying the denominator 3 by 7 and numerator 2 to 7 :

2×7/3×7 = 14/21

4) Now the fractions have same denominator which means they can be added or subtracted.

5) Total amount of cherries he had= 9/21+14/21 = 23/21

6) The amount of cherries he ate = 1/4

7) Amount of cherries he has now with him after he ate 1/4 from 23/21 = 23/21 - 1/4

8) Again the fractions need to be changed to equivalent fractions inorder to subtract them.So,Take the LCM of the denominators (LCM 21 and 4 is 84).Now change the denominator of each fraction to 84.

9) 23/21 becomes 23× 4/21×4 = 92/84

1/4 becomes 1×21/4×21 = 21/84

now subtract them

92/84 - 21/84 = 71/84

71/84 cannot be properly divided so, 71/84 is the answer.

He has 71/84 pounds of cherries with him.