Math Lesson 4.1.2 - Ratio in a Number Line

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Welcome to our Math lesson on Ratio in a Number Line, this is the second 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.

Ratio in a Number Line

Number lines can help us express ratios. We need at least two number lines to represent each quantity involved in a ratio. The units are not the same but they correspond to the quantities they represent when viewed vertically. This allows us to very easily find other equivalent ratios, not only the one expressed in the simplest terms. In addition, expressing ratios in a number line allows us identify smaller groups of elements formed, based on their given relationship. Let's see an example to clarify this point.

Example 4

The ratio between the number of workers in a factory and the T-shirts they can produce in one day is shown in the figure below.

$Math Tutorials: Ratios Example$

Calculate the daily production of T-shirts in the factory if 150 workers are employed in it.

Solution 4

The numbers written in the same position of units are helpful in determining the ratio R, which in this case represents the daily production of a single worker. (We call this type of ratio the "rate", we will discuss this type of ratio in the next tutorial). Thus, we have

R = Daily production of a single worker = No.of T-shirts produced/No.of workers hired in the factory
= 80/5 = 160/10 = 240/15 = ⋯ = 16 (T-shirts)/day

Therefore, following this rule, we can work out the daily production if 150 workers are hired in the factory. Thus,

R = No.of T-shirts produced/No.of workers hired in the factory

Hence,

No.of T-shirts produced = R × No.of workers hired in the factory
= 16 (T-shirts)/day × 150 workers
= 2,400 T-shirts

Ratios Expressed in the Form 1:R

Practical situations as the one described in the question above may be also reconsidered, in order to express them as ratios of type 1:R. In other words, we may want to calculate how much from the quantity b is needed for every a. We silently did this in the above example, where we didn't start calculating the ratio from the first quantity (quantity a) but from the quantity b instead. This is because it is not very suitable to calculate how many workers are needed to produce one T-shirt in a day, as the result of ratio will be a decimal (5/80 = 1/16 = 0.0625 T-shirts/worker). Hence, we inverted the fraction derived from the ratio and instead of calculating the ratio R, we calculated its inverse, 1/R instead, this is purely for convenience.

Example 5

Most modern bronze is made with 88% copper and 12% tin. This means that in 100 g bronze, for every 12 g tin there are 88 g copper. How many grams of copper are needed for every kilogram of tin?

Solution 5

The tin : copper ratio for 100 g bronze is

R = 12 g tin/88 g copper = 0.136

Since this value is not suitable because it is very small, we deal with the inverse ratio. Hence, the inverse ratio 1/R which shows how much copper is needed for every kilogram of tin is

1/R = 88/12 = 7.3

This result means we need 7.333 kg of copper for every kg of tin to produce modern bronze.

More Ratios Lessons and Learning Resources

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

Whats next?

Enjoy the "Ratio in a Number Line" math lesson? People who liked the "Ratios lesson found the following resources useful:

Number Line Feedback. Helps other - Leave a rating for this number line (see below)
Ratio and Proportion Math tutorial: Ratios. Read the Ratios math tutorial and build your math knowledge of Ratio and Proportion
Ratio and Proportion Video tutorial: Ratios. Watch or listen to the Ratios video tutorial, a useful way to help you revise when travelling to and from school/college
Ratio and Proportion Revision Notes: Ratios. Print the notes so you can revise the key points covered in the math tutorial for Ratios
Ratio and Proportion Practice Questions: Ratios. Test and improve your knowledge of Ratios with example questins and answers
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.
Continuing learning ratio and proportion - read our next math tutorial: Rates. Applications of Ratios and Rates in Practice

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