Fractions in mathematics

Question

Kerubo uses 1/2 of her shamba for grazing, 1/3 of the remainder is planted with maize. The rest of Kerubo's has equal portions for cabbages, potatoes, and beans. If the area planted with beans is 1/3, how big is Kerubo's shamba?

Answer 1

1/3 * 1/2 = 1/6 is planted with maize...

1/2 + 1/6 = 3/6 +1/6 = 4/6 = 2/3 is accounted and used...

so 1 - 2/3 = 1/3 remains

X is the amount altogether.

1/3 divided by 3 = 1/3 divided by 3/1 = 1/3 * 1/3 = 1/9 each for cabbage, potatoes, beans

1/9 of X = 1/3 unit

(1/9)X = 1/3

9*(1/9)X = 9*1/3

X = 3 units

The entire area is 3 units.

CHECK:

Half of that is 1.5 units used for grazing with 1.5 units remaining.

1/3 of 1.5 units = 1.5/3 = 0.5 units for maize, with 1.5-0.5 = 1 unit remaining.

1/3 unit each for cabbage, potato, and beans

THe entire area is 3 units