what is ratio and what is the definition of comparing quantities
Answers
Step-by-step explanation:
Comparing Quantities. A ratio is a comparison between two or more like quantities in the same units. This suggests that a ratio can be simplified by dividing its terms by the same number. Therefore: This suggests that the terms of a ratio can be multiplied by the same number.
Answer:
Comparing Quantities
A ratio is a comparison between two or more like quantities in the same units.
Compare AB to CD.
If we compare 5 cm with 10 cm as a ratio, we write 5 : 10 or 5/10. We call 5 and 10 the terms of the ratio.
We know that 5/10 = 1/2.
This suggests that a ratio can be simplified by dividing its terms by the same number. Therefore:
5 : 10 = 1 : 2
Also 1/2 = 5/10
This suggests that the terms of a ratio can be multiplied by the same number. Therefore:
1 : 2 = 5 : 10
Note:
The ratio 1 : 2 is read as '1 to 2' or '1 is to 2'.
Simplifying Ratios
A ratio a : b (or a/b) is said to be its simplest form if a : b (or a/b) has been reduced to its lowest terms. That is, a and b have no common factor.
Example 1
Express the ratio 8 : 12 in its simplest form.
Solution:
By dividing both terms by 4, we find 8 : 12 = 2 : 3
Note:
The ratio 2 : 3 is in its simplest form since the numbers 2 and 3 have no common factor.
Scale Factor
If the ratio is expressed in the form 1 : n, then n is called the scale factor.
E.g. 10 : 100 = 1 : 10
So, 10 is the scale factor.
Equivalent Ratios
Clearly, 5 : 20 = 1 : 4
We say that 5 : 20 and 1 : 4 are equivalent.