Choose Yes Or No To Tell If The Statement Is Correct.1. The Sum Of $\frac{1}{2}$ And $\frac{1}{5}$ Is Between $ 1 2 \frac{1}{2} 2 1 ​ [/tex] And 1. □ \square □ Choose: Yes / No2. The Difference Of

Introduction

Fractions and decimals are two fundamental concepts in mathematics that help us represent and compare quantities. In this article, we will explore the concept of fractions and decimals, and how to add and subtract them. We will also discuss the difference between fractions and decimals, and how to convert between the two.

What are Fractions and Decimals?

Fractions are a way of representing a part of a whole as a ratio of two numbers. For example, the fraction 1/2 represents one half of a whole. Decimals, on the other hand, are a way of representing a fraction as a decimal number. For example, the decimal 0.5 represents the same value as the fraction 1/2.

Adding and Subtracting Fractions

When adding or subtracting fractions, we need to have the same denominator. The denominator is the number that is being divided into equal parts. For example, if we have the fractions 1/2 and 1/4, we can add them by finding a common denominator, which is 4. We can then add the numerators (the numbers on top) and keep the denominator the same.

Example 1: Adding Fractions

Let's add the fractions 1/2 and 1/5.

$$\frac{1}{2} + \frac{1}{5} = ?$$

To add these fractions, we need to find a common denominator, which is 10. We can then add the numerators and keep the denominator the same.

$$\frac{1}{2} = \frac{5}{10}$$

$$\frac{1}{5} = \frac{2}{10}$$

$$\frac{5}{10} + \frac{2}{10} = \frac{7}{10}$$

Therefore, the sum of 1/2 and 1/5 is 7/10.

Example 2: Subtracting Fractions

Let's subtract the fractions 1/2 and 1/5.

$$\frac{1}{2} - \frac{1}{5} = ?$$

To subtract these fractions, we need to find a common denominator, which is 10. We can then subtract the numerators and keep the denominator the same.

$$\frac{1}{2} = \frac{5}{10}$$

$$\frac{1}{5} = \frac{2}{10}$$

$$\frac{5}{10} - \frac{2}{10} = \frac{3}{10}$$

Therefore, the difference of 1/2 and 1/5 is 3/10.

Is the Statement Correct?

Now that we have added and subtracted fractions, let's go back to the original statement.

1. The sum of $\frac{1}{2}$ and $\frac{1}{5}$ is between $\frac{1}{2}$ and 1.

Is the statement correct? Yes or No?

Answer

The statement is correct. The sum of 1/2 and 1/5 is 7/10, which is between 1/2 and 1.

Conclusion

In this article, we have explored the concept of fractions and decimals, and how to add and subtract them. We have also discussed the difference between fractions and decimals, and how to convert between the two. We have used examples to illustrate the concept of adding and subtracting fractions, and have determined whether the original statement is correct.

Choose Yes or No

1. The sum of $\frac{1}{2}$ and $\frac{1}{5}$ is between $\frac{1}{2}$ and 1. $\square$ Choose: Yes / No

2. The difference of $\frac{1}{2}$ and $\frac{1}{5}$ is between $\frac{1}{2}$ and 1. $\square$ Choose: Yes / No

Answer Key

1. Yes
2. No

Discussion

The difference of 1/2 and 1/5 is 3/10, which is not between 1/2 and 1. Therefore, the statement is incorrect.

Conclusion

Q1: What is the difference between a fraction and a decimal?

A1: A fraction is a way of representing a part of a whole as a ratio of two numbers. For example, the fraction 1/2 represents one half of a whole. A decimal, on the other hand, is a way of representing a fraction as a decimal number. For example, the decimal 0.5 represents the same value as the fraction 1/2.

Q2: How do I add fractions with different denominators?

A2: To add fractions with different denominators, you need to find a common denominator. The common denominator is the smallest number that both denominators can divide into evenly. Once you have found the common denominator, you can add the numerators (the numbers on top) and keep the denominator the same.

Q3: How do I subtract fractions with different denominators?

A3: To subtract fractions with different denominators, you need to find a common denominator. The common denominator is the smallest number that both denominators can divide into evenly. Once you have found the common denominator, you can subtract the numerators (the numbers on top) and keep the denominator the same.

Q4: What is the rule for adding and subtracting fractions?

A4: The rule for adding and subtracting fractions is to have the same denominator. If the denominators are different, you need to find a common denominator before adding or subtracting the fractions.

Q5: How do I convert a fraction to a decimal?

A5: To convert a fraction to a decimal, you need to divide the numerator (the number on top) by the denominator (the number on the bottom). For example, to convert the fraction 1/2 to a decimal, you would divide 1 by 2, which equals 0.5.

Q6: How do I convert a decimal to a fraction?

A6: To convert a decimal to a fraction, you need to find the equivalent fraction. For example, to convert the decimal 0.5 to a fraction, you would find the equivalent fraction 1/2.

Q7: What is the difference between a proper fraction and an improper fraction?

A7: A proper fraction is a fraction where the numerator (the number on top) is less than the denominator (the number on the bottom). For example, the fraction 1/2 is a proper fraction. An improper fraction is a fraction where the numerator is greater than or equal to the denominator. For example, the fraction 3/2 is an improper fraction.

Q8: How do I simplify a fraction?

A8: To simplify a fraction, you need to find the greatest common divisor (GCD) of the numerator and the denominator. Once you have found the GCD, you can divide both the numerator and the denominator by the GCD to simplify the fraction.

Q9: What is the rule for multiplying and dividing fractions?

A9: The rule for multiplying and dividing fractions is to multiply or divide the numerators (the numbers on top) and multiply or divide the denominators (the numbers on the bottom).

Q10: How do I find the least common multiple (LCM) of two numbers?

A10: To find the LCM of two numbers, you need to list the multiples of each number and find the smallest number that is common to both lists.

Conclusion

In this article, we have answered some common questions about fractions and decimals. We have discussed the difference between fractions and decimals, how to add and subtract fractions with different denominators, how to convert fractions to decimals and vice versa, and how to simplify fractions. We have also discussed the rules for multiplying and dividing fractions and how to find the least common multiple (LCM) of two numbers.