When we add a positive number, we move to the right on a number line. On the other hand, when we add a negative number, we move to the left.
Example Addition Expression: - 25+1 Example Sum: 35
Practice makes perfect
Let's use 15 as the unit fraction to represent the space between the tick marks on the number line. We can start by looking at the diagram!
We want to write an addition expression represented by the number line. Let's do it!
?+?
Consider the bottom arrow.
Looking at the diagram, we can see that the bottom arrow starts at 0 and ends at - 25. This means that the arrow represents - 25, so the first addend is - 25.
- 2/5+?
Next, look at the top arrow on the given diagram.
Notice that the top arrow is 1 unit to the right of - 25. This means that the top arrow represents adding 1 to the first addend. Let's complete our addition expression!
- 2/5+1
Before we can evaluate the expression, we will rewrite 1 as a fraction with denominator 5.
- 2/5+1 ⇔ - 2/5+5/5
Notice that our addends have different signs. To find their sum, we will subtract the lesser absolute value from the greater absolute value. Then, we will use the sign of the number with the greater absolute value. Let's calculate the absolute value of the numbers!
| - 2/5|=2/5and
|5/5|=5/5
We know that the absolute value of 55 is greater than the absolute value of - 25. In this case, we will subtract 25 from 55.
55-2/5= 3/5
We know that the fraction with the greater absolute value, 55, has a positive sign. This means that our sum is equal to 35. Remember that we chose 15 as the unit fraction. Answers will vary depending on the chosen unit fraction.
Checking Our Answer
We want to check whether the sum of - 25 and 1 is equal to 35. Let's look at our number line.
We can see that the top arrow ends at 35. This confirms that the sum of - 25 and 1 is equal to 35.
