Write each ratio as a fraction in simplest form. See Example
The Correct Answer and Explanation is:
Examples:
- Ratio: 8 to 12
Fraction in simplest form: 812=23\frac{8}{12} = \frac{2}{3}128=32 - Ratio: 15:25
Fraction in simplest form: 1525=35\frac{15}{25} = \frac{3}{5}2515=53 - Ratio: 36 to 48
Fraction in simplest form: 3648=34\frac{36}{48} = \frac{3}{4}4836=43 - Ratio: 50:10
Fraction in simplest form: 5010=51\frac{50}{10} = \frac{5}{1}1050=15
Explanation
A ratio is a comparison of two numbers. It tells us how much of one thing there is compared to another. Ratios can be written in three forms: using the word “to”, with a colon, or as a fraction. For example, the ratio 8 to 12 can be written as 8:12 or 8/12. To express a ratio as a fraction in simplest form, we follow a few easy steps.
First, write the ratio as a fraction. If the ratio is given as “a to b”, we write it as a/b. This step helps to see the relationship in fraction form.
Second, simplify the fraction. To simplify a fraction, divide both the numerator and the denominator by their greatest common factor (GCF). The GCF is the largest number that divides evenly into both numbers. For instance, in the ratio 8 to 12, the GCF of 8 and 12 is 4. Dividing both 8 and 12 by 4 gives 2 and 3. So, 8/12 simplifies to 2/3.
Why is simplification important? Simplifying a fraction gives the most reduced form of the ratio. This makes it easier to understand and compare with other ratios. It also shows the proportional relationship in the clearest way.
If the GCF is 1, then the fraction is already in simplest form. For example, 3/5 cannot be simplified further because 3 and 5 have no common factors other than 1.
Understanding how to write and simplify ratios is a fundamental math skill. It helps in everyday situations such as cooking, comparing prices, and analyzing data. By following these steps, you can confidently work with ratios and present them in their most useful form.
