A fruit grower uses one-third of his land for bananas,three-eighth for pineapples,one-sixth for mangoes and the remainder for oranges.What fraction of his land is used for oranges?
Please I need the answer and solution.
1 = 1/3 + 3/8 + 1/6 + R
24/24 = 8/24 + 9/24 + 4/24 + 24 R/24
24 = 21 + 24 R
R = 3/24 = 1/8
1/3 +3/8 +1/6 +×=1 8+9+4+24×=1 21+24×/24 =21+24×=24 24×=24-21 =23"×3/24
October 7th
2022
To find the fraction of land used for oranges, we need to add up the fractions of land used for bananas, pineapples, and mangoes, and subtract this total from 1 (since the remaining fraction is used for oranges).
Let's calculate the fractions step by step:
1. Bananas: The grower uses one-third of his land for bananas, which is equivalent to the fraction 1/3.
2. Pineapples: The grower uses three-eighths of his land for pineapples, which is equivalent to the fraction 3/8.
3. Mangoes: The grower uses one-sixth of his land for mangoes, which is equivalent to the fraction 1/6.
Now, let's add up the fractions used for bananas, pineapples, and mangoes:
1/3 + 3/8 + 1/6
To add these fractions, we need to find a common denominator. The least common multiple (LCM) of 3, 8, and 6 is 24. Therefore, we convert each fraction to have a denominator of 24:
(8/8)(1/3) + (3/3)(3/8) + (4/4)(1/6)
8/24 + 9/24 + 4/24
Now, we can add the numerators:
(8 + 9 + 4)/24
21/24
So, the grower uses a fraction of 21/24 of his land for bananas, pineapples, and mangoes.
Finally, to find the fraction used for oranges, we subtract this fraction from 1:
1 - 21/24
To subtract fractions, we need a common denominator. In this case, the denominator is 24:
(24/24) - (21/24)
3/24
Simplifying this fraction, we get:
1/8
Therefore, one-eighth of the grower's land is used for oranges.
Answer: The fraction of land used for oranges is 1/8.