Translate each ratio into a fraction in simplest form. 45 people to 30 people
The Correct Answer and Explanation is:
Ratio to Fraction (Simplest Form)
Given Ratio: 45 people to 30 people
Step 1: Write the ratio as a fraction4530\frac{45}{30}3045
Step 2: Simplify the fraction by dividing both the numerator and denominator by their greatest common factor (GCF)
- The GCF of 45 and 30 is 15
45÷1530÷15=32\frac{45 ÷ 15}{30 ÷ 15} = \frac{3}{2}30÷1545÷15=23
Final Answer:32\boxed{\frac{3}{2}}23
Explanation
A ratio is a comparison between two quantities. When we say 45 people to 30 people, we are comparing one group of 45 people to another group of 30. Ratios can be written in three different forms: 45 to 30, 45:30, or as a fraction, 45/30. To solve this problem, we will translate the ratio into a fraction and then simplify it.
The first step is to express the ratio 45 to 30 as a fraction: 45 over 30, or 45/30. This fraction represents how many times 45 contains 30 when compared. However, this is not in its simplest form. To simplify a fraction, we need to find the greatest common factor, or GCF, of the numerator and the denominator. The GCF is the largest number that divides both numbers evenly.
The factors of 45 are 1, 3, 5, 9, 15, and 45. The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. The largest common factor between them is 15. We divide both 45 and 30 by 15:
45 ÷ 15 = 3
30 ÷ 15 = 2
So the simplified fraction is 3/2.
This tells us that for every 3 people in the first group, there are 2 people in the second group. This type of simplification is important in mathematics because it makes numbers easier to understand and compare. Whether dealing with people, objects, or measurements, simplifying ratios to fractions in lowest terms helps us see relationships more clearly. The simplified form of 3/2 also shows that the first group is one and a half times larger than the second.
