What Is The Ratio $15:75$ In Lowest Terms?A. $1:5$ B. \$2:5$[/tex\] C. $3:5$ D. $1:4$

Feb 26, 2025 by ADMIN 98 views

Understanding Ratios

A ratio is a way to compare two or more numbers by division. It is often expressed as a fraction, with the first number being the numerator and the second number being the denominator. In this case, we are given the ratio 15:75, and we need to simplify it to its lowest terms.

Simplifying Ratios

To simplify a ratio, we need to find the greatest common divisor (GCD) of the two numbers and divide both numbers by the GCD. The GCD is the largest number that divides both numbers without leaving a remainder.

Finding the Greatest Common Divisor (GCD)

To find the GCD of 15 and 75, we can list the factors of each number:

Factors of 15: 1, 3, 5, 15
Factors of 75: 1, 3, 5, 15, 25, 75

The greatest common divisor of 15 and 75 is 15.

Simplifying the Ratio

Now that we have found the GCD, we can simplify the ratio by dividing both numbers by the GCD:

15 ÷ 15 = 1 75 ÷ 15 = 5

So, the simplified ratio is 1:5.

Conclusion

The ratio 15:75 in lowest terms is 1:5.

Answer

The correct answer is A. 1:5.

Additional Information

Ratios can be used to compare quantities in various fields, such as mathematics, science, and engineering. Simplifying ratios is an important skill to have, as it allows us to compare quantities more easily and accurately.

Example Use Case

Suppose we have two groups of students, one with 15 students and the other with 75 students. We want to compare the number of students in each group. We can use the ratio 15:75 to compare the two groups. By simplifying the ratio to 1:5, we can see that the second group has 5 times as many students as the first group.

Tips and Tricks

When simplifying ratios, make sure to find the greatest common divisor (GCD) of the two numbers.
Use the GCD to divide both numbers and simplify the ratio.
Ratios can be used to compare quantities in various fields, such as mathematics, science, and engineering.
Simplifying ratios is an important skill to have, as it allows us to compare quantities more easily and accurately.

References

"Ratios and Proportions" by McGraw-Hill Education
"Simplifying Fractions" by Pearson Education
"Ratios and Proportions" by Cengage Learning

Q: What is a ratio?

A: A ratio is a way to compare two or more numbers by division. It is often expressed as a fraction, with the first number being the numerator and the second number being the denominator.

Q: How do I simplify a ratio?

A: To simplify a ratio, you need to find the greatest common divisor (GCD) of the two numbers and divide both numbers by the GCD.

Q: What is the greatest common divisor (GCD)?

A: The greatest common divisor (GCD) is the largest number that divides both numbers without leaving a remainder.

Q: How do I find the GCD of two numbers?

A: You can find the GCD of two numbers by listing the factors of each number and finding the largest number that is common to both lists.

Q: What is the difference between a ratio and a proportion?

A: A ratio is a comparison of two or more numbers, while a proportion is a statement that two ratios are equal.

Q: How do I convert a ratio to a proportion?

A: To convert a ratio to a proportion, you need to set up an equation where the two ratios are equal.

Q: What is the relationship between ratios and fractions?

A: Ratios and fractions are related in that a ratio can be expressed as a fraction, and a fraction can be expressed as a ratio.

Q: How do I simplify a complex ratio?

A: To simplify a complex ratio, you need to find the GCD of the two numbers and divide both numbers by the GCD.

Q: What is the importance of simplifying ratios?

A: Simplifying ratios is important because it allows us to compare quantities more easily and accurately.

Q: How do I use ratios in real-life situations?

A: Ratios are used in various fields, such as mathematics, science, and engineering, to compare quantities and make decisions.

Q: What are some common mistakes to avoid when simplifying ratios?

A: Some common mistakes to avoid when simplifying ratios include not finding the GCD, not dividing both numbers by the GCD, and not checking for errors.

Q: How do I check my work when simplifying ratios?

A: To check your work when simplifying ratios, you need to make sure that you have found the GCD and divided both numbers by the GCD.

Q: What are some real-life examples of ratios?

A: Some real-life examples of ratios include the ratio of the number of boys to girls in a class, the ratio of the number of apples to oranges in a basket, and the ratio of the number of miles to hours in a car trip.

Q: How do I use ratios to solve problems?

A: To use ratios to solve problems, you need to identify the ratio, simplify it if necessary, and then use it to make decisions or comparisons.

Q: What are some common applications of ratios?

A: Some common applications of ratios include finance, science, engineering, and sports.

Q: How do I use ratios to compare quantities?

A: To use ratios to compare quantities, you need to identify the ratio, simplify it if necessary, and then use it to make comparisons.

Q: What are some common mistakes to avoid when using ratios?

A: Some common mistakes to avoid when using ratios include not identifying the ratio, not simplifying the ratio if necessary, and not using the ratio to make comparisons.

Q: How do I check my work when using ratios?

A: To check your work when using ratios, you need to make sure that you have identified the ratio, simplified it if necessary, and used it to make comparisons.

Q: What are some real-life examples of using ratios?

A: Some real-life examples of using ratios include comparing the number of boys to girls in a class, comparing the number of apples to oranges in a basket, and comparing the number of miles to hours in a car trip.

Q: How do I use ratios to make decisions?

A: To use ratios to make decisions, you need to identify the ratio, simplify it if necessary, and then use it to make comparisons and make decisions.

Q: What are some common applications of using ratios to make decisions?

A: Some common applications of using ratios to make decisions include finance, science, engineering, and sports.

Q: How do I use ratios to compare quantities in different units?

A: To use ratios to compare quantities in different units, you need to convert the quantities to the same unit and then use the ratio to make comparisons.

Q: What are some common mistakes to avoid when using ratios to compare quantities in different units?

A: Some common mistakes to avoid when using ratios to compare quantities in different units include not converting the quantities to the same unit, not using the ratio to make comparisons, and not checking for errors.

Q: How do I check my work when using ratios to compare quantities in different units?

A: To check your work when using ratios to compare quantities in different units, you need to make sure that you have converted the quantities to the same unit and used the ratio to make comparisons.

Q: What are some real-life examples of using ratios to compare quantities in different units?

A: Some real-life examples of using ratios to compare quantities in different units include comparing the number of miles to hours in a car trip, comparing the number of liters to gallons in a container, and comparing the number of pounds to kilograms in a weight.

Q: How do I use ratios to solve problems in finance?

A: To use ratios to solve problems in finance, you need to identify the ratio, simplify it if necessary, and then use it to make comparisons and make decisions.

Q: What are some common applications of using ratios to solve problems in finance?

A: Some common applications of using ratios to solve problems in finance include comparing the return on investment (ROI) of different investments, comparing the debt-to-equity ratio of different companies, and comparing the price-to-earnings ratio of different stocks.

Q: How do I use ratios to solve problems in science?

A: To use ratios to solve problems in science, you need to identify the ratio, simplify it if necessary, and then use it to make comparisons and make decisions.

Q: What are some common applications of using ratios to solve problems in science?

A: Some common applications of using ratios to solve problems in science include comparing the concentration of different substances, comparing the rate of reaction of different chemicals, and comparing the density of different materials.

Q: How do I use ratios to solve problems in engineering?

A: To use ratios to solve problems in engineering, you need to identify the ratio, simplify it if necessary, and then use it to make comparisons and make decisions.

Q: What are some common applications of using ratios to solve problems in engineering?

A: Some common applications of using ratios to solve problems in engineering include comparing the strength-to-weight ratio of different materials, comparing the efficiency of different engines, and comparing the speed of different vehicles.

Q: How do I use ratios to solve problems in sports?

A: To use ratios to solve problems in sports, you need to identify the ratio, simplify it if necessary, and then use it to make comparisons and make decisions.

Q: What are some common applications of using ratios to solve problems in sports?

A: Some common applications of using ratios to solve problems in sports include comparing the speed-to-agility ratio of different athletes, comparing the strength-to-power ratio of different teams, and comparing the endurance-to-speed ratio of different runners.

Q: How do I use ratios to compare quantities in different contexts?

A: To use ratios to compare quantities in different contexts, you need to identify the ratio, simplify it if necessary, and then use it to make comparisons and make decisions.

Q: What are some common applications of using ratios to compare quantities in different contexts?

A: Some common applications of using ratios to compare quantities in different contexts include comparing the number of boys to girls in a class, comparing the number of apples to oranges in a basket, and comparing the number of miles to hours in a car trip.

Q: How do I use ratios to make decisions in different contexts?

A: To use ratios to make decisions in different contexts, you need to identify the ratio, simplify it if necessary, and then use it to make comparisons and make decisions.

Q: What are some common applications of using ratios to make decisions in different contexts?

A: Some common applications of using ratios to make decisions in different contexts include finance, science, engineering, and sports.

Q: How do I use ratios to compare quantities in different units in different contexts?

A: To use ratios to compare quantities in different units in different contexts, you need to convert the quantities to the same unit and then use the ratio to make comparisons.

Q: What are some common applications of using ratios to compare quantities in different units in different contexts?

A: Some common applications of using ratios to compare quantities in different units in different contexts include finance, science, engineering, and sports.

Q: How do I use ratios to solve problems in different contexts?

A: To use ratios to solve problems in different contexts, you need to identify the ratio, simplify it if necessary, and then use it to make comparisons and make decisions.

Q: What are some common applications of using ratios to solve problems in different contexts?

A: Some common applications of using ratios to solve problems in different contexts include finance, science, engineering, and sports.

Q: How do I use ratios to compare quantities in different contexts in finance?

A: To use ratios to compare quantities in different contexts in finance, you need to identify the ratio, simplify it if necessary, and then use it to make comparisons and make decisions.