Transcript The Distance Between two Rational Numbers

The Distance Between two Rational Numbers
Ms. McKeown
Aim: How can we find the distance between two rational
numbers?
• Do Now:
Which number in the pair is farther away from zero.
a) 4, -5
b) 2, 5
c) -1, -3
d) -12, 11
Aim: How can we find the distance between two rational
numbers?
• Use the number line to answer each of the following
questions?
• What is the distance between -3 and 5?
• What is the distance between 5 and -3?
Aim: How can we find the distance between two rational
numbers?
Formula for the Distance Between two Rational Numbers.
If p and q are rational numbers on number line,
then the distance between p and q is |p-q |. It
does not matter which endpoint we call p or which
endpoint we call q. Distance is always positive.
Find the Distance between -3 and 2
Using a formula:
|-3 – 2 | = |-3 + -2 | = |-5 | = 5 or
|2 – ( - 3 ) | = | 2 + 3 | = | 5| = 5
Aim: How can we find the distance between two rational
numbers?
• A hiker starts hiking at the beginning of a trail at a point which
is 200 feet below sea level. He hikes to a location on the trail
that is 580 feet above sea level and stops for lunch.
1. What is the vertical distance between 200 feet below sea
level and 580 feet above sea level?
2. How should we interpret 780 feet in the context of this
problem?
Aim: How can we find the distance between two rational
numbers?
Use the distance formula to find each answer. Support you
answer using a number line
a. Find the distance between -7 and -4
b. Find the change in temperature if the temperature rises
from -18 F to 15 F .
Aim: How can we find the distance between two rational
numbers?
Exit Ticket : Find the distance between -2 and -8
Homework:
Two 7th grade students, Emma and Anna, both solved the
following math problem:
If the temperature drops from 7 F to -17 F, by how much
did the temperature decrease?
The students came up with different answers. Emma said
the answer is 24 F, and Anna said the answer is 10 F.
Who is correct? Explain and support your written response
with the use of a formula and a number line.