What Is The Sum Of $3 / 8$ And $1 / 16$?A. \$4 / 24$[/tex\] B. $1 / 6$ C. $7 / 16$ D. \$1 / 4$[/tex\]
Introduction
Fractions are a fundamental concept in mathematics, and understanding how to add them is crucial for solving various mathematical problems. In this article, we will explore the concept of adding fractions, focusing on the sum of $3 / 8$ and $1 / 16$. We will break down the problem step by step, explaining the reasoning behind each calculation.
Understanding Fractions
Before we dive into the problem, let's quickly review what fractions are. A fraction is a way of expressing a part of a whole as a ratio of two numbers. It consists of a numerator (the top number) and a denominator (the bottom number). For example, in the fraction $3 / 8$, the numerator is 3, and the denominator is 8.
The Problem: Adding Fractions
Now, let's tackle the problem at hand: finding the sum of $3 / 8$ and $1 / 16$. To add fractions, we need to follow a specific set of rules.
Step 1: Find the Least Common Multiple (LCM)
The first step in adding fractions is to find the least common multiple (LCM) of the denominators. The LCM is the smallest number that both denominators can divide into evenly. In this case, the denominators are 8 and 16.
To find the LCM, we can list the multiples of each denominator:
- Multiples of 8: 8, 16, 24, 32, ...
- Multiples of 16: 16, 32, 48, 64, ...
The smallest number that appears in both lists is 16, so the LCM of 8 and 16 is 16.
Step 2: Convert Each Fraction to Have the LCM as the Denominator
Now that we have the LCM, we need to convert each fraction to have the LCM as the denominator. To do this, we multiply the numerator and denominator of each fraction by the necessary factor to get the LCM as the denominator.
For the first fraction, $3 / 8$, we need to multiply the numerator and denominator by 2 to get:
For the second fraction, $1 / 16$, we don't need to do anything since the denominator is already 16.
Step 3: Add the Fractions
Now that both fractions have the same denominator, we can add them by adding the numerators:
Conclusion
In conclusion, the sum of $3 / 8$ and $1 / 16$ is $7 / 16$. We achieved this by finding the least common multiple (LCM) of the denominators, converting each fraction to have the LCM as the denominator, and then adding the fractions.
Answer
The correct answer is:
- C. $7 / 16$
Why This Matters
Understanding how to add fractions is a crucial skill in mathematics, and it has numerous real-world applications. For example, in cooking, you may need to add fractions of ingredients to create a recipe. In science, you may need to add fractions of measurements to calculate the results of an experiment.
Final Thoughts
In this article, we explored the concept of adding fractions, focusing on the sum of $3 / 8$ and $1 / 16$. We broke down the problem step by step, explaining the reasoning behind each calculation. By following these steps, you can add fractions with confidence and tackle a wide range of mathematical problems.
Additional Resources
If you're looking for more practice problems or want to learn more about fractions, here are some additional resources:
- Khan Academy: Fractions
- Mathway: Adding Fractions
- IXL: Fractions
References
- "Mathematics for Dummies" by Mark Zegarelli
- "The Art of Mathematics" by Tom M. Apostol
About the Author
Q: What is the least common multiple (LCM) of two numbers?
A: The least common multiple (LCM) of two numbers is the smallest number that both numbers can divide into evenly. For example, the LCM of 8 and 16 is 16.
Q: How do I find the LCM of two numbers?
A: To find the LCM of two numbers, you can list the multiples of each number and find the smallest number that appears in both lists. Alternatively, you can use the following formula:
LCM(a, b) = (a × b) / GCD(a, b)
where GCD(a, b) is the greatest common divisor of a and b.
Q: What is the greatest common divisor (GCD) of two numbers?
A: The greatest common divisor (GCD) of two numbers is the largest number that both numbers can divide into evenly. For example, the GCD of 8 and 16 is 8.
Q: How do I add fractions with different denominators?
A: To add fractions with different denominators, you need to find the least common multiple (LCM) of the denominators and convert each fraction to have the LCM as the denominator. Then, you can add the fractions by adding the numerators.
Q: What if the denominators are not multiples of each other?
A: If the denominators are not multiples of each other, you can find the LCM by listing the multiples of each denominator and finding the smallest number that appears in both lists. Alternatively, you can use the formula:
LCM(a, b) = (a × b) / GCD(a, b)
Q: Can I add fractions with unlike denominators using a calculator?
A: Yes, you can add fractions with unlike denominators using a calculator. Most calculators have a built-in function for adding fractions, which will automatically find the LCM and convert the fractions to have the LCM as the denominator.
Q: What if I have a fraction with a negative numerator or denominator?
A: If you have a fraction with a negative numerator or denominator, you can simply change the sign of the numerator or denominator to make it positive. For example, the fraction -3/4 is equivalent to 3/(-4).
Q: Can I add fractions with different signs?
A: Yes, you can add fractions with different signs. When adding fractions with different signs, you need to subtract the numerators instead of adding them. For example, the sum of 3/4 and -2/4 is 1/4.
Q: What if I have a fraction with a decimal numerator or denominator?
A: If you have a fraction with a decimal numerator or denominator, you can convert it to a fraction by multiplying the numerator and denominator by the appropriate power of 10. For example, the fraction 0.5/2 is equivalent to 5/10.
Q: Can I add fractions with decimals using a calculator?
A: Yes, you can add fractions with decimals using a calculator. Most calculators have a built-in function for adding fractions, which will automatically convert the decimals to fractions and add them.
Q: What if I have a fraction with a mixed number?
A: If you have a fraction with a mixed number, you can convert it to an improper fraction by multiplying the whole number by the denominator and adding the numerator. For example, the mixed number 2 3/4 is equivalent to the improper fraction 11/4.
Q: Can I add fractions with mixed numbers using a calculator?
A: Yes, you can add fractions with mixed numbers using a calculator. Most calculators have a built-in function for adding fractions, which will automatically convert the mixed numbers to improper fractions and add them.
Conclusion
Adding fractions with unlike denominators can be a challenging task, but with the right techniques and tools, it can be done easily. By following the steps outlined in this article, you can add fractions with confidence and tackle a wide range of mathematical problems.