Big Ideas Math: Modeling Real Life, Grade 7
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Big Ideas Math: Modeling Real Life, Grade 7 View details
1. Rational Numbers
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Exercise 2 Page 7

A ratio is a comparative relation between two quantities.

4:6

Practice makes perfect
We want to find the ratio of bears to deer. Let's start by counting the number of bears and the number of deer in the given diagram!
bears and deer diagram
We can see in the diagram that there are 4 bears and 6 deer. Now, recall that a ratio is a comparison of two quantities by division. This means that to find the ratio of bears to deer, we can divide the number of bears, 4, by the number of deer, 6. Let's do it! 4/6 l← Number of bears ← Number of deer The ratio of bears to deer is 46, which can be also written as 4 to 6 or 4:6. We know that the ratio ab means that for every a units of one quantity, there are b units of another quantity. Therefore, the ratio of 46 means that for every 4 bears, there are 6 deer.

Extra

Simplify the Ratio

To simplify the ratio, we divide the numerator and the denominator by their greatest common factor (GCF). The first step in finding a GCF is to express each number as a product of its prime factors. Let's do it!

Given Number Prime Factorization Common Prime Factors
4 2* 2 2
6 3* 2 2
The only common prime factor for the given values is 2, so 2 is the GCF of 4 and 6. We can simplify our ratio by dividing the numerator and denominator by 2.
4/6
2/3
The ratio of bears to deer is 23, which can be also written as 2 to 3 or 2:3. Recall that the ratio 23 also means that for every 2 bears, there are 3 deer.