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Math Lesson 4.1.3 - Finding the Fraction of One Quantity Out of the Total

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Welcome to our Math lesson on Finding the Fraction of One Quantity Out of the Total, this is the third lesson of our suite of math lessons covering the topic of Ratios, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.

Finding the Fraction of One Quantity Out of the Total

Sometimes, we need to calculate what part of the total is one component involved in the ratio. In these situations we first calculate in how many parts the total is made and then, we find the fraction that shows what part of the total is the quantity required.

Example 6

Three sisters: Stacy, Rebecca and Wendy share a certain amount of money in the ratio 2:5:7.

  1. What part of the total each sister share?
  2. How much money does each sister has if they own in total $630?

Solution 6

  1. First, we find the total number of shares. If we take only the first letter of each name, we have:
    S:R:W = 2:5:7
    We can write this ratio as
    S/2 = R/5 = W/7 = k
    Thus,
    S = 2k
    R = 5k
    W = 7k
    Therefore, the total number of shares is
    2k + 5k + 7k = 14k
    Hence, the part of money each sister owns is
    Stacy = 2k/14k = 2/14 = 1/7
    Rebecca = 5k/14k = 5/14
    Wendy = 7k/14k = 7/14 = 1/2
    of the total.
  2. From the above ratios, we can find how much money each sister owns as follows:
    Stacy = 1/7 of $630 = 1/7 × $630 = 1 × $630/7 = $90
    Rebecca = 5/14 of $630 = 5/14 × $630 = 5 × $630/14 = $225
    Wendy = 1/2 of $630 = 1/2 × $630 = 1 × $630/2 = $315
    The solution is correct as $90 + $225 + $315 = $630.

More Ratios Lessons and Learning Resources

Ratio and Proportion Learning Material
Tutorial IDMath Tutorial TitleTutorialVideo
Tutorial
Revision
Notes
Revision
Questions
4.1Ratios
Lesson IDMath Lesson TitleLessonVideo
Lesson
4.1.1Definition of a Ratio
4.1.2Ratio in a Number Line
4.1.3Finding the Fraction of One Quantity Out of the Total
4.1.4Part : Whole vs Part : Part Ratios
4.1.5Finding the New Ratio When One Quantity Changes
4.1.6Dividing a Given Ratio

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  2. Ratio and Proportion Math tutorial: Ratios. Read the Ratios math tutorial and build your math knowledge of Ratio and Proportion
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  4. Ratio and Proportion Revision Notes: Ratios. Print the notes so you can revise the key points covered in the math tutorial for Ratios
  5. Ratio and Proportion Practice Questions: Ratios. Test and improve your knowledge of Ratios with example questins and answers
  6. Check your calculations for Ratio and Proportion questions with our excellent Ratio and Proportion calculators which contain full equations and calculations clearly displayed line by line. See the Ratio and Proportion Calculators by iCalculator™ below.
  7. Continuing learning ratio and proportion - read our next math tutorial: Rates. Applications of Ratios and Rates in Practice

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