Simplify This Ratio And Leave Your Answer In The Form { A:b $}$: 136 : 30 136:30 136 : 30
Introduction
In mathematics, ratios are used to compare the size of two or more quantities. A ratio is a way of expressing the relationship between two numbers, often in the form of a fraction. Simplifying ratios is an essential skill in mathematics, as it helps us to express complex relationships in a more concise and manageable way. In this article, we will explore how to simplify the ratio 136:30 and leave the answer in the form [a:b].
Understanding Ratios
A ratio is a comparison of two or more numbers. It is often expressed as a fraction, with the first number being the numerator and the second number being the denominator. For example, the ratio 136:30 can be written as the fraction 136/30. Ratios can be used to compare different quantities, such as the number of apples to oranges, or the number of boys to girls in a class.
Simplifying Ratios
To simplify a ratio, we need to find the greatest common divisor (GCD) of the two numbers. The GCD is the largest number that divides both numbers without leaving a remainder. Once we have found the GCD, we can divide both numbers by the GCD to simplify the ratio.
Finding the Greatest Common Divisor (GCD)
The GCD of two numbers can be found using various methods, including the prime factorization method, the Euclidean algorithm, or the division method. In this case, we will use the division method to find the GCD of 136 and 30.
Step 1: Divide 136 by 30
To find the GCD of 136 and 30, we will divide 136 by 30. The result is 4 with a remainder of 16.
Step 2: Divide 30 by 16
Next, we will divide 30 by 16. The result is 1 with a remainder of 14.
Step 3: Divide 16 by 14
Now, we will divide 16 by 14. The result is 1 with a remainder of 2.
Step 4: Divide 14 by 2
Finally, we will divide 14 by 2. The result is 7 with a remainder of 0.
Conclusion
Since the remainder is 0, we have found the GCD of 136 and 30, which is 2. Now that we have found the GCD, we can simplify the ratio by dividing both numbers by the GCD.
Simplifying the Ratio
To simplify the ratio, we will divide both numbers by the GCD, which is 2. The simplified ratio is 68:15.
Conclusion
In conclusion, we have simplified the ratio 136:30 and left the answer in the form [a:b]. We found the GCD of 136 and 30 using the division method and then divided both numbers by the GCD to simplify the ratio. The simplified ratio is 68:15.
Frequently Asked Questions
- Q: What is a ratio? A: A ratio is a comparison of two or more numbers.
- 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 then divide both numbers by the GCD.
- Q: What is the greatest common divisor (GCD)? A: The GCD is the largest number that divides both numbers without leaving a remainder.
Final Answer
The final answer is: 68:15
Introduction
In our previous article, we explored how to simplify the ratio 136:30 and leave the answer in the form [a:b]. We found the greatest common divisor (GCD) of 136 and 30 using the division method and then divided both numbers by the GCD to simplify the ratio. The simplified ratio is 68:15. In this article, we will answer some frequently asked questions about simplifying ratios.
Q&A
Q: What is a ratio?
A: A ratio is a comparison of two or more numbers. 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 then divide both numbers by the GCD.
Q: What is the greatest common divisor (GCD)?
A: The GCD is the largest number that divides both numbers without leaving a remainder.
Q: How do I find the greatest common divisor (GCD) of two numbers?
A: There are several methods to find the GCD of two numbers, including the prime factorization method, the Euclidean algorithm, or the division method.
Q: What is the prime factorization method?
A: The prime factorization method involves breaking down each number into its prime factors and then finding the product of the common prime factors.
Q: What is the Euclidean algorithm?
A: The Euclidean algorithm is a step-by-step process for finding the GCD of two numbers. It involves repeatedly dividing the larger number by the smaller number and taking the remainder.
Q: What is the division method?
A: The division method involves dividing the larger number by the smaller number and taking the remainder. This process is repeated until the remainder is 0.
Q: How do I simplify a ratio with a variable?
A: To simplify a ratio with a variable, you need to find the GCD of the variable and the other number. Then, you can divide both numbers by the GCD to simplify the ratio.
Q: Can I simplify a ratio with a decimal?
A: Yes, you can simplify a ratio with a decimal by converting the decimal to a fraction and then finding the GCD of the fraction and the other number.
Q: What is the difference between simplifying a ratio and reducing a fraction?
A: Simplifying a ratio involves finding the GCD of the two numbers and then dividing both numbers by the GCD. Reducing a fraction involves dividing both the numerator and the denominator by their GCD.
Conclusion
In conclusion, we have answered some frequently asked questions about simplifying ratios. We have discussed the different methods for finding the greatest common divisor (GCD) of two numbers and how to simplify a ratio with a variable or a decimal. We have also explained the difference between simplifying a ratio and reducing a fraction.
Final Answer
The final answer is: 68:15