Point is at on a number line. On the
same number line, point is the same
distance from 0 as point , but it has a
numerator of 8 . What is the denominator
of the fraction at point ? Draw a numbe
line to model the problem.
To solve the problem, let’s break it down step by step.
Problem Statement
Point is located at on a number line.
Point is the same distance from 0 as point but has a numerator of 8. We need to find the denominator of the fraction representing point .
Understanding the Problem
Distance from 0:
Point is at , which means it is units away from 0.
Since point is the same distance from 0 as , it can be either:
(same side as )
(opposite side of )
Fraction Representation for :
Given that the numerator of is 8, we represent as , where is the denominator we need to find.
Setting Up the Equation
Since is the same distance from 0 as :
This leads to two possibilities:
Solving for :
First Case:
Second Case:
Since denominators are typically positive in fraction representations, we take .
Conclusion
The denominator of the fraction at point is 12.
Number Line Representation
Below is a simple representation of the number line with points and :
<---|---------|---------|---------|---------|--->
-1 -2/3 0 2/3 1
Point Y at -2/3 (represented as 8/12)
Point X at 2/3
Point is at .
Point is at (which is equivalent to ).
This visual helps illustrate that is indeed the same distance from 0 as but on the opposite side of the number line.
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The Deep Dive
To find point , we first determine the distance from point to 0. Point at has a distance of from 0. Since point is the same distance from 0 but has a numerator of 8, we can set up the equation .
To find the denominator , we can cross-multiply: . This yields . Dividing both sides by 2 gives us . So, point is at .
Now time to visualize! On a number line, point 0 is at the start, can be marked approximately two-thirds along the line, and will be right at the same point as since they’re equivalent fractions!
However, if we adjust to keep it fun, let’s imagine our number line as a fun race track! Point is a speed racer halfway through, while point gets a slick upgrade to a new set of wheels (or fractions!), landing at but keeping pace!