Math Problem Statement

Plot the requested fraction on each number line: A) 22/9, B) 21/5, C) 5/8.

Solution

The image displays three tasks where you are asked to plot fractions on a number line. Here's how you can approach each one:

A) Plot the fraction: 229\frac{22}{9}

  • Convert 229\frac{22}{9} to a mixed number: 229=249\frac{22}{9} = 2 \frac{4}{9} This means the fraction lies between 2 and 3. On the number line, it should be plotted slightly less than halfway between 2 and 3 (since 49\frac{4}{9} is just under half of 9).

B) Plot the fraction: 215\frac{21}{5}

  • Convert 215\frac{21}{5} to a mixed number: 215=415\frac{21}{5} = 4 \frac{1}{5} This means the fraction is between 4 and 5. It should be plotted a bit past 4, closer to 4.2.

C) Plot the fraction: 58\frac{5}{8}

  • This fraction is less than 1. Specifically, it’s a little more than halfway between 0 and 1, because 58\frac{5}{8} is more than 12\frac{1}{2}.

By plotting these points accurately on the number line, you can graph these fractions correctly.

Would you like further clarification on any of these points?

Here are 5 related questions to expand on this:

  1. How do you convert improper fractions to mixed numbers?
  2. What is the process for converting fractions to decimals for easier plotting?
  3. How do you estimate fraction locations on a number line without converting them?
  4. How do number lines help in visualizing fractions and their relative sizes?
  5. How can you plot more complex fractions or mixed numbers on number lines?

Tip: To plot fractions precisely, it can be helpful to first convert them to decimals. For example, 2292.44\frac{22}{9} \approx 2.44.

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Math Problem Analysis

Mathematical Concepts

Fractions
Mixed Numbers
Number Lines

Formulas

Conversion of improper fractions to mixed numbers
Estimating fraction values on a number line

Theorems

None explicitly required, but involves understanding of basic fraction properties

Suitable Grade Level

Grades 6-8