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Study Guides > Prealgebra

Introduction to Multiplying and Dividing Fractions

A large pizza sitting on a pizza riser on a table in a restaurant with red-checkered tablecloths What fraction of this pizza is left over after Karen and her roommates eat?
On Friday night, Karen and her roommates ordered a large pizza. After eating 1/2 of the pizza, they wrapped up the rest to save for later. The next day, Karen and her roommates finished 2/3 of the remaining pizza. What fraction of the original pizza is left? To figure this out, we can use mathematical operations with fractions. Multiplying and dividing fractions are skills that often come in handy in everyday situations like this one. Read on to find out how to do it!  

Learning Outcomes

By the end of this section, you will be able to:
  • Simplify fractions
  • Multiply fractions
  • Find reciprocals
  • Divide fractions
 

readiness quiz

Before you get started, take this readiness quiz. 1) [ohm_question]146554[/ohm_question] If you missed this problem, review the following video. https://youtu.be/2K5pBvb7Sss 2) Draw a model of the fraction [latex]\frac{6}{8}[/latex].

Answer:

If you missed this problem, review this example.
Shade [latex]\frac{3}{4}[/latex] of the circle. An image of a circle.

Answer:

Solution The denominator is [latex]<span id="MathJax-Element-22-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: inherit; padding: 1px 0px; margin: 0px; font-size: 17.44px; vertical-align: baseline; background: transparent; border: 0px; outline: 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; letter-spacing: normal; word-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn>"><span id="MJXc-Node-134" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-135" class="mjx-mrow"><span id="MJXc-Node-136" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R">4[/latex], so we divide the circle into four equal parts ⓐ. The numerator is [latex]3[/latex], so we shade three of the four parts ⓑ. In [latex]/frac{3}{4}[/latex] of the circle is shaded.

  3) Find two fractions equivalent to [latex]\frac{5}{6}[/latex].

Answer: Answers may vary. Acceptable answers include [latex]\frac{10}{12},\frac{15}{18},\frac{50}{60},\frac{100}{120}[/latex], etc.

If you missed this problem, review the following video. https://youtu.be/8gJS0kvtGFU
 

Licenses & Attributions

CC licensed content, Original

  • Question ID: 146554. Authored by: Alyson Day. License: CC BY: Attribution. License terms: IMathAS Community License CC-BY + GPL.

CC licensed content, Shared previously

  • Artichoke Pizza from Houston. Authored by: Patrick Feller. Located at: https://www.flickr.com/photos/nakrnsm/3980269048. License: CC BY: Attribution.
  • Ex 1: Prime Factorization. Authored by: James Sousa (Mathispower4u.com). License: CC BY: Attribution.
  • Ex: Determine Equivalent Fractions.. Authored by: James Sousa (Mathispower4u.com) . License: CC BY: Attribution.

CC licensed content, Specific attribution