0.46 inches greater than the yearly average, see solution.
We can start by looking at the given table.
October
November
December
- 0.86
2.56
- 1.24
Looking at the table, we can see the amount of rainfall in inches for three months compared to the yearly average. We want to check whether the total rainfall for the three-month period is greater than or less than the yearly average. To do so, we will add the change of the water level for October, November and December. Let's do it!
- 0.86+ 2.56+( - 1.24)We can simplify the expression using the Commutative Property of Addition and the Associative Property of Addition. Let's do it!
Add the absolute values of the rational numbers. Then use the common, negative, sign.
- 2+(- 5)=- 7
We will use the rule for adding negative rational numbers to simplify the expression in the brackets. We can start by calculating the sum of the absolute values of - 0.86 and - 1.24.
| - 0.86|+| - 1.24|&=0.86+1.24
&=2.1
The sum of | 0.86| and | 1.24| is 2.1. We know that the sum of two negative numbers will have a negative sign, so the sum of - 0.86 and - 1.24 is equal to - 2.1. We can use this information to simplify our expression.
[ - 0.86+( - 1.24)]+ 2.56 [0.3em]
⇕ [0.3em]
- 2.1+ 2.56
Now, - 2.1 is negative and 2.56 is positive. To find the sum of two numbers with different signs, we subtract the lesser absolute value from the greater absolute value. Let's start by calculating the absolute values!
| - 2.1|=2.1and| 2.56|=2.56
The absolute value of 2.56 is greater than the absolute value of - 2.1. This means that we should subtract | - 2.1| from | 2.56|.
| 2.56|-| - 2.1|&=2.56-2.1
&=0.46
Since the number with the greater absolute value, 2.56, has a positive sign, the sum of - 2.1 and 2.56 is a positive number, 0.46. This means that the total rainfall for the three-month period is 0.46 inches greater than the yearly average.
