Locating and Ordering Fractions and Mixed Numbers on the Number Line
Learning Outcomes
- Locate and label improper and proper fractions on a number line
- Order fractions and mixed numbers on a number line
- Use inequality symbols to compare fractions and mixed numbers
Example
Locate and label the following on a number line: [latex]\frac{3}{4},\frac{4}{3},\frac{5}{3},4\frac{1}{5}[/latex], and [latex]\frac{7}{2}[/latex]. Solution: Start by locating the proper fraction [latex]\frac{3}{4}[/latex]. It is between [latex]0[/latex] and [latex]1[/latex]. To do this, divide the distance between [latex]0[/latex] and [latex]1[/latex] into four equal parts. Then plot [latex]\frac{3}{4}[/latex]. Next, locate the mixed number [latex]4\frac{1}{5}[/latex]. It is between [latex]4[/latex] and [latex]5[/latex] on the number line. Divide the number line between [latex]4[/latex] and [latex]5[/latex] into five equal parts, and then plot [latex]4\frac{1}{5}[/latex] one-fifth of the way between [latex]4[/latex] and [latex]5[/latex] . Now locate the improper fractions [latex]\frac{4}{3}[/latex] and [latex]\frac{5}{3}[/latex] . It is easier to plot them if we convert them to mixed numbers first. [latex-display]\frac{4}{3}=1\frac{1}{3},\frac{5}{3}=1\frac{2}{3}[/latex-display] Divide the distance between [latex]1[/latex] and [latex]2[/latex] into thirds. Next let us plot [latex]\frac{7}{2}[/latex]. We write it as a mixed number, [latex]\frac{7}{2}=3\frac{1}{2}[/latex] . Plot it between [latex]3[/latex] and [latex]4[/latex]. The number line shows all the numbers located on the number line.try it
#146007 [ohm_question height="270"]146007[/ohm_question] #146008 [ohm_question height="270"]146008[/ohm_question]Example
Locate and label the following on the number line: [latex]\frac{1}{4},-\frac{1}{4},1\frac{1}{3},-1\frac{1}{3},\frac{5}{2}[/latex], and [latex]-\frac{5}{2}[/latex].Answer: Solution: Draw a number line. Mark [latex]0[/latex] in the middle and then mark several units to the left and right. To locate [latex]\frac{1}{4}[/latex], divide the interval between [latex]0[/latex] and [latex]1[/latex] into four equal parts. Each part represents one-quarter of the distance. So plot [latex]\frac{1}{4}[/latex] at the first mark. To locate [latex]-\frac{1}{4}[/latex], divide the interval between [latex]0[/latex] and [latex]-1[/latex] into four equal parts. Plot [latex]-\frac{1}{4}[/latex] at the first mark to the left of [latex]0[/latex]. Since [latex]1\frac{1}{3}[/latex] is between [latex]1[/latex] and [latex]2[/latex], divide the interval between [latex]1[/latex] and [latex]2[/latex] into three equal parts. Plot [latex]1\frac{1}{3}[/latex] at the first mark to the right of [latex]1[/latex]. Then since [latex]-1\frac{1}{3}[/latex] is the opposite of [latex]1\frac{1}{3}[/latex] it is between [latex]-1[/latex] and [latex]-2[/latex]. Divide the interval between [latex]-1[/latex] and [latex]-2[/latex] into three equal parts. Plot [latex]-1\frac{1}{3}[/latex] at the first mark to the left of [latex]-1[/latex]. To locate [latex]\frac{5}{2}[/latex] and [latex]-\frac{5}{2}[/latex], it may be helpful to rewrite them as the mixed numbers [latex]2\frac{1}{2}[/latex] and [latex]-2\frac{1}{2}[/latex]. Since [latex]2\frac{1}{2}[/latex] is between [latex]2[/latex] and [latex]3[/latex], divide the interval between [latex]2[/latex] and [latex]3[/latex] into two equal parts. Plot [latex]\frac{5}{2}[/latex] at the mark. Then since [latex]-2\frac{1}{2}[/latex] is between [latex]-2[/latex] and [latex]-3[/latex], divide the interval between [latex]-2[/latex] and [latex]-3[/latex] into two equal parts. Plot [latex]-\frac{5}{2}[/latex] at the mark.
Try it
#146009 [ohm_question height="270"]146009[/ohm_question] #146011 [ohm_question height="270"]146011[/ohm_question]Order Fractions and Mixed Numbers
We can use the inequality symbols to order fractions. Remember that [latex]a>b[/latex] means that [latex]a[/latex] is to the right of [latex]b[/latex] on the number line. As we move from left to right on a number line, the values increase.Example
Order each of the following pairs of numbers, using [latex]<[/latex]; or [latex]>:[/latex]- [latex]-\frac{2}{3}[/latex] __ [latex]- 1[/latex]
- [latex]-3\frac{1}{2}[/latex] __ [latex]- 3[/latex]
- [latex]-\frac{3}{7}-[/latex] __ [latex]\frac{3}{8}[/latex]
- [latex]-2[/latex] __ [latex]\frac{-16}{9}[/latex]
Answer: Solution: 1. [latex]-\frac{2}{3}>-1[/latex] 2. [latex]-3\frac{1}{2}<-3[/latex] 3. [latex]-\frac{3}{7}\text{<}-\frac{3}{8}[/latex] 4. [latex]-2<\frac{-16}{9}[/latex]
Try it
#146013 [ohm_question height="270"]146013[/ohm_question] #146012 [ohm_question height="270"]146012[/ohm_question]Licenses & Attributions
CC licensed content, Original
- Question ID: 146007, 146008, 146009, 146011, 146012, 146013. Authored by: Alyson Day. License: CC BY: Attribution. License terms: IMathAS Community License CC-BY + GPL.
CC licensed content, Shared previously
- Ex: Identify a Fraction on a Number Line. Authored by: James Sousa (Mathispower4u.com). License: CC BY: Attribution.
- Determine Negative Proper and Improper Fractions on the Number Line. Authored by: James Sousa (Mathispower4u.com). License: CC BY: Attribution.
CC licensed content, Specific attribution
- Prealgebra. Provided by: OpenStax License: CC BY: Attribution. License terms: Download for free at http://cnx.org/contents/[email protected].