4.1 Visualize fractions  (Page 7/11)

Order fractions and mixed numbers

We can use the inequality symbols to order fractions. Remember that $a>b$ means that $a$ is to the right of $b$ on the number line. As we move from left to right on a number line, the values increase.

Order each of the following pairs of numbers, using $<$ or $>:$

1. ⓐ $-\frac{2}{3}\_\_\_\_\mathrm{-1}$
2. ⓑ $\mathrm{-3}\frac{1}{2}\_\_\_\_\mathrm{-3}$
3. ⓒ $-\frac{3}{7}\_\_\_\_-\frac{3}{8}$
4. ⓓ $\mathrm{-2}\_\_\_\_\frac{\mathrm{-16}}{9}$

Solution

ⓐ $-\frac{2}{3}>\mathrm{-1}$

ⓑ $\mathrm{-3}\frac{1}{2}<\mathrm{-3}$

ⓒ $-\frac{3}{7}\text{<}-\frac{3}{8}$

ⓓ $\mathrm{-2}<\frac{\mathrm{-16}}{9}$

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Key concepts

• Property of One
  • Any number, except zero, divided by itself is one.
    $\frac{a}{a}=1$ , where $a\ne 0$ .
• Mixed Numbers
  • A mixed number consists of a whole number $a$ and a fraction $\frac{b}{c}$ where $c\ne 0$ .
  • It is written as follows: $a\frac{b}{c}c\ne 0$
• Proper and Improper Fractions
  • The fraction $ab$ is a proper fraction if $a<b$ and an improper fraction if $a\ge b$ .
• Convert an improper fraction to a mixed number.
  1. Divide the denominator into the numerator.
  2. Identify the quotient, remainder, and divisor.
  3. Write the mixed number as quotient $\frac{\text{remainder}}{\text{divisor}}$ .
• Convert a mixed number to an improper fraction.
  1. Multiply the whole number by the denominator.
  2. Add the numerator to the product found in Step 1.
  3. Write the final sum over the original denominator.
• Equivalent Fractions Property
  • If $\mathrm{a,\; b,}$ and $c$ are numbers where $b\ne 0$ , $c\ne 0$ , then $\frac{a}{b}=\frac{a\cdot c}{b\cdot c}$ .

Practice makes perfect

In the following exercises, name the fraction of each figure that is shaded.

1. ⓐ $\frac{1}{4}$
2. ⓑ $\frac{3}{4}$
3. ⓒ $\frac{3}{8}$
4. ⓓ $\frac{5}{9}$

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In the following exercises, shade parts of circles or squares to model the following fractions.

In the following exercises, use fraction circles to make wholes, if possible, with the following pieces.

In the following exercises, name the improper fractions. Then write each improper fraction as a mixed number.

1. ⓐ $\frac{5}{4}=1\frac{1}{4}$
2. ⓑ $\frac{7}{4}=1\frac{3}{4}$
3. ⓒ $\frac{11}{8}=1\frac{3}{8}$

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1. ⓐ $\frac{11}{4}=2\frac{3}{4}$
2. ⓑ $\frac{19}{8}=2\frac{3}{8}$

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In the following exercises, draw fraction circles to model the given fraction.

In the following exercises, rewrite the improper fraction as a mixed number.

In the following exercises, rewrite the mixed number as an improper fraction.

In the following exercises, use fraction tiles or draw a figure to find equivalent fractions.

In the following exercises, find three fractions equivalent to the given fraction. Show your work, using figures or algebra.

In the following exercises, plot the numbers on a number line.

In the following exercises, order each of the following pairs of numbers, using $<$ or $>.$

Everyday math

Writing exercises

Self check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

ⓑ If most of your checks were:

…confidently. Congratulations! You have achieved the objectives in this section. Reflect on the study skills you used so that you can continue to use them. What did you do to become confident of your ability to do these things? Be specific.

…with some help. This must be addressed quickly because topics you do not master become potholes in your road to success. In math, every topic builds upon previous work. It is important to make sure you have a strong foundation before you move on. Who can you ask for help? Your fellow classmates and instructor are good resources. Is there a place on campus where math tutors are available? Can your study skills be improved?

…no—I don’t get it! This is a warning sign and you must not ignore it. You should get help right away or you will quickly be overwhelmed. See your instructor as soon as you can to discuss your situation. Together you can come up with a plan to get you the help you need.