In today’s post we are going to work with **proportions**. Today, we’ll start by looking at problems with **proportional** **numbers**.

In order to solve problems with proportional numbers, the first step is to know the *concepts of ratio and proportion. *

##### Ratio

A **ratio** is the quotient of two numbers or quantities that are being compared to each other and it is expressed as a fraction. In other words, if we have number A and number B, their ratio is expressed in fraction a/b.

Let’s check out some examples:

The ratio between 6 and 2 is 3 because 6/2 = 3

The ratio between 1 and 0.2 is 5 because 1/0.2 = 5

The ratio between 100 and 10 is 10 because 100/10 = 10

If you want to **practice**, you can apply the ratio concept to following exercises:

- What is the ratio between the numbers 3 and 81?
- How many times bigger is the number 224 than 16?
- How many times smaller is the number 3 than 17?
- What is x’s value if the ratio between 8 and x is 1.6?
- What are two numbers that have a ratio of 11?

##### Proportion

But…Can we find different number pairs that have the same ratio between them?

Of course we can! There are an infinite number of number pairs than meet this condition. For example, we are going to think of different number pairs that have **2.5 as their ratio:**

5 and 2; 10 and 4; 100 and 40; 2,5 and 1…

We can represent these by doing the following:

5/2= 10/4 = 100/40 = 2.5/1 =2.5

**All of these number pairs are proportional to each other.**

So, we say that the numbers a, b, c and d are proportions if the ratio between a and b is the same as the ratio between c and d. This written as:

a/b=c/d

It’s read: a is to b as c is to d

In this proportion, a and d are extremes, and b and c are means. In proportions*, the product of the means needs to be equal to the product of the extremes*.

So, we do this by a x d = b x c

##### Proportional Numbers Problems

You can practice some proportional number exercises, for example:

*Are the following ratios proportional to another?*

- 30/20 and 200/110
- 800/50 and 4/0.25
- 3/4 and 15/75

*What does x’s value need to be so that the following number pairs can be proportional to each other?*

- 6/15 and x/10
- 0.15/x and 4/6
- x/10 and 19/15

What did you think about this post? We hope that it helped you understand proportional numbers problems!

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### Learn More:

- Ratio and Proportion: Concept and Some Examples
- Proportional Relationship and Examples in Everyday Life
- Direct Proportions: What Are They? What Are They Used For?
- Let’s Learn about Ratios with Singaporean Bar Models
- Rule of 3: Direct and Inverse