James uses 1/3 of his land for growing durians, 1/4 for guavas, 3/8 for bananas and 9 hectares for mangoes. what is the total area?
To find the total area of James' land, we need to add up the portions of land used for growing each fruit.
Using fractions, James uses 1/3 of his land for growing durians, 1/4 for guavas, and 3/8 for bananas.
To calculate, we need to find a common denominator for 3, 4, and 8. The least common multiple (LCM) of these numbers is 24.
1/3 can be expressed as 8/24 (multiplying both numerator and denominator by 8), since 8 is the equivalent fraction that has 24 as the denominator.
1/4 can be expressed as 6/24 (multiplying both numerator and denominator by 6), since 6 is the equivalent fraction that has 24 as the denominator.
3/8 remains as 3/8 since it already has 8 as the denominator.
Now, we can add up the fractions:
8/24 + 6/24 + 3/8 = (8 + 6 + 6)/24 = 20/24
Therefore, James uses 20/24 of his land for growing fruits.
Given that 9 hectares are used for mangoes, we need to determine the value of 20/24 hectares in terms of an actual measurement.
To do this, we need to find the equivalent fraction for 20/24 with 9 as the numerator. We can establish a ratio and cross-multiply:
20/24 = 9/x
Cross-multiplying gives us:
20x = 24 * 9
Simplifying:
20x = 216
Dividing both sides by 20 gives us:
x = 216/20
x = 10.8
Therefore, 20/24 hectares is equivalent to 10.8 hectares.
Finally, to find the total area of James' land, we add the 9 hectares used for mangoes:
Total area = 10.8 hectares + 9 hectares = 19.8 hectares
Hence, the total area of James' land is 19.8 hectares.
1/3 + 1/4 + 3/8 = 23/24
so, 9 hectares is 1/24 of the total...