• Students recognize that the rules for adding and subtracting integers apply to rational numbers.
• Given a number line, students use arrows to model rational numbers where the length of the arrow is the absolute value of the rational number and the sign of the rational number is determined by the direction of the arrow with respect to the number line.
• Students locate the sum p + q of two rational numbers on a number line by placing the tail of the arrow for q at p and locating at the head of the arrow. They create an arrow for the difference p - q by first rewriting the difference as a sum, p + (-q), and then locating the sum.
• The rules for adding and subtracting integers apply to all rational numbers.
• The sum of two rational numbers (for example, -1 + 4.3) can be found on the number line by placing the tail of an arrow at -1 and locating the head of the arrow 4.3 units to the right to arrive at the sum, which is 3.3.
• To model the difference of two rational numbers on a number line (for example, -5.7 - 3), first rewrite the difference as a sum, -5.7 - (-3), and then follow the steps for locating a sum. Place a single arrow with its tail at -5.7 and the head of the arrow 3 units to the left to arrive at -8.7.
Suppose a 7th grader’s birthday is today, and she is 12 years old. How old was she 3 1/2 years ago? Write an equation and use a number line to model your answer.
Find the following sum using a number line diagram. -2 1/2 + 5
Example 2: Representing Differences of Rational Numbers on a Number Line
a. Rewrite the difference 1 - 2 1/4 as a sum:1 + (-2 1/4)
Now follow the steps to represent the sum:
b. Place the tail of the arrow on 1.
c. The length of the arrow is the absolute value of -2 1/4 ; |-2 1/4| = 2 1/4
d. The direction of the arrow is to the left since you are adding a negative number to .
Draw the number line model in the space below:
Find the following difference, and represent it on a number line. -5 1/2 - (-8)
Find the following sums and differences using a number line model.
a. -6 + 5 14
b. 7 - (-0.9)
c. 2.5 + (-1/2)
d. -1/4 + 4
e. 1/2 - (-3)
Create an equation and number line diagram to model each answer.
a. Samantha owes her farther $7.00. She just got paid $5.50 for babysitting. If she gives that money to her dad, how much will she still owe him?
b. At the start of a trip, a car’s gas tank contains 12 gallons of gasoline. During the trip, the car consumes 1 1/8 gallons of gasoline. How much gasoline is left in the tank?
Represent each of the following problems using both a number line diagram and an equation.
1. A bird that was perched atop a 15½-foot tree dives down six feet to a branch below. How far above the ground is the bird’s new location?
2. Mariah had owed her grandfather $2.25 but was recently able to pay him back $1.50. How much does Mariah currently owe her grandfather?
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