A meteorologist found that the rainfall in Castroville during the first half of the month was 7/8 of an inch. At the end of the month, he found that the total rainfall for the month was 2 3/4 inches. How much did it rain in the second half of the month?

Question

Write your answer as a fraction or as a whole or mixed number

Answer 1

To find the amount of rainfall in the second half of the month, we need to subtract the rainfall from the first half of the month from the total rainfall for the month.

First, convert the total rainfall of 2 3/4 inches into an improper fraction:

$$2\frac{3}{4}=\frac{2\times 4+3}{4}=\frac{8+3}{4}=\frac{11}{4}$$

Now we can express the rainfall in the first half of the month (7/8 inches) as a fraction:

$$\text{Rainfall in first half}=\frac{7}{8}$$

Next, we will find the rainfall in the second half of the month by subtracting the first half's rainfall from the total rainfall:

$$\text{Rainfall in second half}=\text{Total rainfall}-\text{Rainfall in first half}$$

Substituting the values we have:

$$\text{Rainfall in second half}=\frac{11}{4}-\frac{7}{8}$$

To perform this subtraction, we need a common denominator. The least common multiple of 4 and 8 is 8. We will convert $\frac{11}{4}$ to have a denominator of 8:

$$\frac{11}{4}=\frac{11\times 2}{4\times 2}=\frac{22}{8}$$

Now we can perform the subtraction:

$$\text{Rainfall in second half}=\frac{22}{8}-\frac{7}{8}=\frac{22-7}{8}=\frac{15}{8}$$

Finally, we can convert $\frac{15}{8}$ into a mixed number:

$$\frac{15}{8}=1\frac{7}{8}$$

So, the amount it rained in the second half of the month is:

$$\boxed{{\displaystyle 1\frac{7}{8}}}$$