Menu

Math Lesson 3.2.7 - Applications of Improper Fractions and Mixed Numbers in Practice

Please provide a rating, it takes seconds and helps us to keep this resource free for all to use

[ No Votes ]

Welcome to our Math lesson on Applications of Improper Fractions and Mixed Numbers in Practice, this is the seventh lesson of our suite of math lessons covering the topic of Proper and Improper Fractions. Mixed Numbers, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.

Applications of Improper Fractions and Mixed Numbers in Practice

Fractions have a lot of applications in practice. For example, we can express the part of a whole or of more than one whole by expressing fractions as in the example below.

Example 6

Laura had to solve 210 question from a math textbook in a week. She solved 235 questions in total. What part of the questions expressed in fraction and mixed number did Laura solve?

Solution 6

Laura has solved more questions than needed, so the corresponding fraction expressing this amount is an improper one, as it must represent more than a whole. Obviously, we must also check for any possible simplification for the fraction obtained. Therefore, we can write the part of questions solved
Part of questions solved = 235/210
= (235 ÷ 5)/(210 ÷ 5)
= 47/42 of total questions
When this amount is expressed as a mixed number, we obtain
Part of questions solved = 47/42 of total
= 1 5/42 of total
This is because 47 ÷ 42 = 1 (5). Let's consider another example of the use of improper fractions and mixed numbers in practice.

Example 7

One kilogram of peaches contains seven peaches on average. We have to insert them in 5 kg packs. How many packs do we need to insert 142 peaches?

Solution 7

First, we have to calculate the number of peaches contained in one pack. We have 5 kg/pack × 7 peaches/kg = 35 peaches/pack.

Now, let's express the total amount as a mixed number to identify the number of whole packs needed. We have
142/35 = 142 ÷ 35 = 4 2/35
Hence, we need five packs: four of them are full, while the fifth one is not full; it contains only 2 peaches.

More Proper and Improper Fractions. Mixed Numbers Lessons and Learning Resources

Fractions Learning Material
Tutorial IDMath Tutorial TitleTutorialVideo
Tutorial
Revision
Notes
Revision
Questions
3.2Proper and Improper Fractions. Mixed Numbers
Lesson IDMath Lesson TitleLessonVideo
Lesson
3.2.1Proper Fractions
3.2.2Improper Fractions
3.2.3Mixed Numbers
3.2.4How to Convert an Improper Fraction into Mixed Number
3.2.5How to Avoid the Confusion between Improper Fractions and Integers Expressed as Fractions
3.2.6How to Convert a Mixed Number into Improper Fraction
3.2.7Applications of Improper Fractions and Mixed Numbers in Practice

Whats next?

Enjoy the "Applications of Improper Fractions and Mixed Numbers in Practice" math lesson? People who liked the "Proper and Improper Fractions. Mixed Numbers lesson found the following resources useful:

  1. Applications Feedback. Helps other - Leave a rating for this applications (see below)
  2. Fractions Math tutorial: Proper and Improper Fractions. Mixed Numbers. Read the Proper and Improper Fractions. Mixed Numbers math tutorial and build your math knowledge of Fractions
  3. Fractions Video tutorial: Proper and Improper Fractions. Mixed Numbers. Watch or listen to the Proper and Improper Fractions. Mixed Numbers video tutorial, a useful way to help you revise when travelling to and from school/college
  4. Fractions Revision Notes: Proper and Improper Fractions. Mixed Numbers. Print the notes so you can revise the key points covered in the math tutorial for Proper and Improper Fractions. Mixed Numbers
  5. Fractions Practice Questions: Proper and Improper Fractions. Mixed Numbers. Test and improve your knowledge of Proper and Improper Fractions. Mixed Numbers with example questins and answers
  6. Check your calculations for Fractions questions with our excellent Fractions calculators which contain full equations and calculations clearly displayed line by line. See the Fractions Calculators by iCalculator™ below.
  7. Continuing learning fractions - read our next math tutorial: Comparing Fractions. Ordering Fractions

Help others Learning Math just like you

Please provide a rating, it takes seconds and helps us to keep this resource free for all to use

[ No Votes ]

We hope you found this Math tutorial "Proper and Improper Fractions. Mixed Numbers" useful. If you did it would be great if you could spare the time to rate this math tutorial (simply click on the number of stars that match your assessment of this math learning aide) and/or share on social media, this helps us identify popular tutorials and calculators and expand our free learning resources to support our users around the world have free access to expand their knowledge of math and other disciplines.

Fractions Calculators by iCalculator™