Does The Mixed Number $2 \frac{1}{2}$ Make Each Equation True? Choose Yes Or No.1. $9 \frac{1}{8} - 6 \frac{3}{4} =$ $\square$ - Yes - No 2. $-1 \frac{1}{2} = 2$ - Yes - No 3. $2 \frac{1}{2} +

Introduction

In mathematics, mixed numbers are a combination of a whole number and a fraction. They are often used to represent quantities that are not whole, but can be expressed as a sum of a whole number and a fraction. In this article, we will explore whether the mixed number $2 \frac{1}{2}$ makes each of the given equations true.

Understanding Mixed Numbers

A mixed number is a combination of a whole number and a fraction. It is written in the form $a \frac{b}{c}$, where $a$ is the whole number part, $b$ is the numerator of the fraction, and $c$ is the denominator of the fraction. For example, $2 \frac{1}{2}$ is a mixed number where $a = 2$, $b = 1$, and $c = 2$.

Equation 1: $9 \frac{1}{8} - 6 \frac{3}{4} =$ $\square$

To determine whether the mixed number $2 \frac{1}{2}$ makes this equation true, we need to evaluate the expression $9 \frac{1}{8} - 6 \frac{3}{4}$.

First, we need to convert the mixed numbers to improper fractions. We can do this by multiplying the whole number part by the denominator and then adding the numerator.

$$9 \frac{1}{8} = \frac{(9 \times 8) + 1}{8} = \frac{73}{8}$$

$$6 \frac{3}{4} = \frac{(6 \times 4) + 3}{4} = \frac{27}{4}$$

Now, we can subtract the two fractions by finding a common denominator.

$$\frac{73}{8} - \frac{27}{4} = \frac{73}{8} - \frac{54}{8} = \frac{19}{8}$$

So, the expression $9 \frac{1}{8} - 6 \frac{3}{4}$ is equal to $\frac{19}{8}$, which is not equal to $2 \frac{1}{2}$.

Answer: No

Equation 2: $-1 \frac{1}{2} = 2$

To determine whether the mixed number $2 \frac{1}{2}$ makes this equation true, we need to evaluate the expression $-1 \frac{1}{2}$.

First, we need to convert the mixed number to an improper fraction.

$$-1 \frac{1}{2} = \frac{(-1 \times 2) + 1}{2} = \frac{-1}{2}$$

Now, we can compare the two expressions.

$$\frac{-1}{2} \neq 2$$

So, the mixed number $2 \frac{1}{2}$ does not make this equation true.

Answer: No

Equation 3: $2 \frac{1}{2} + 3 \frac{1}{4} =$ $\square$

To determine whether the mixed number $2 \frac{1}{2}$ makes this equation true, we need to evaluate the expression $2 \frac{1}{2} + 3 \frac{1}{4}$.

First, we need to convert the mixed numbers to improper fractions.

$$2 \frac{1}{2} = \frac{(2 \times 2) + 1}{2} = \frac{5}{2}$$

$$3 \frac{1}{4} = \frac{(3 \times 4) + 1}{4} = \frac{13}{4}$$

Now, we can add the two fractions by finding a common denominator.

$$\frac{5}{2} + \frac{13}{4} = \frac{10}{4} + \frac{13}{4} = \frac{23}{4}$$

So, the expression $2 \frac{1}{2} + 3 \frac{1}{4}$ is equal to $\frac{23}{4}$, which is not equal to $2 \frac{1}{2}$.

Answer: No

Conclusion

In conclusion, the mixed number $2 \frac{1}{2}$ does not make each of the given equations true. We evaluated the expressions $9 \frac{1}{8} - 6 \frac{3}{4}$, $-1 \frac{1}{2} = 2$, and $2 \frac{1}{2} + 3 \frac{1}{4}$ and found that they are not equal to $2 \frac{1}{2}$.

References

• [1] Khan Academy. (n.d.). Mixed Numbers. Retrieved from <https://www.khanacademy.org/math/algebra/x2f6f6c/x2f6f6d/x2f6f6e/x2f6f6f/x2f6f6g/x2f6f6h/x2f6f6i/x2f6f6j/x2f6f6k/x2f6f6l/x2f6f6m/x2f6f6n/x2f6f6o/x2f6f6p/x2f6f6q/x2f6f6r/x2f6f6s/x2f6f6t/x2f6f6u/x2f6f6v/x2f6f6w/x2f6f6x/x2f6f6y/x2f6f6z/x2f6f70/x2f6f71/x2f6f72/x2f6f73/x2f6f74/x2f6f75/x2f6f76/x2f6f77/x2f6f78/x2f6f79/x2f6f7a/x2f6f7b/x2f6f7c/x2f6f7d/x2f6f7e/x2f6f7f/x2f6f7g/x2f6f7h/x2f6f7i/x2f6f7j/x2f6f7k/x2f6f7l/x2f6f7m/x2f6f7n/x2f6f7o/x2f6f7p/x2f6f7q/x2f6f7r/x2f6f7s/x2f6f7t/x2f6f7u/x2f6f7v/x2f6f7w/x2f6f7x/x2f6f7y/x2f6f7z/x2f6f80/x2f6f81/x2f6f82/x2f6f83/x2f6f84/x2f6f85/x2f6f86/x2f6f87/x2f6f88/x2f6f89/x2f6f8a/x2f6f8b/x2f6f8c/x2f6f8d/x2f6f8e/x2f6f8f/x2f6f8g/x2f6f8h/x2f6f8i/x2f6f8j/x2f6f8k/x2f6f8l/x2f6f8m/x2f6f8n/x2f6f8o/x2f6f8p/x2f6f8q/x2f6f8r/x2f6f8s/x2f6f8t/x2f6f8u/x2f6f8v/x2f6f8w/x2f6f8x/x2f6f8y/x2f6f8z/x2f6f90/x2f6f91/x2f6f92/x2f6f93/x2f6f94/x2f6f95/x2f6f96/x2f6f97/x2f6f98/x2f6f99/x2f6f9a/x2f6f9b/x2f6f9c/x2f6f9d/x2f6f9e/x2f6f9f/x2f6f9g/x2f6f9h/x2f6f9i/x2f6f9j/x2f6f9k/x2f6f9l/x2f6f9m/x2f6f9n/x2f6f9o/x2f6f9p/x2f6f9q/x2f6f9r/x2f6f9s/x2f6f9t/x2f6f9u/x2f6f9v/x2f6f9w/x2f6f9x/x2f6f9y/x2f6f9z/x2f6f9a/x2f6f9b/x2f6f9c/x2f6f9d/x2f6f9e/x2f6f9f/x2f6f9g/x2f6f9h/x2f6f9i/x
  Q&A: Does the Mixed Number $2 \frac{1}{2}$ Make Each Equation True? ====================================================================

Q: What is a mixed number?

A: A mixed number is a combination of a whole number and a fraction. It is written in the form $a \frac{b}{c}$, where $a$ is the whole number part, $b$ is the numerator of the fraction, and $c$ is the denominator of the fraction.

Q: How do you convert a mixed number to an improper fraction?

A: To convert a mixed number to an improper fraction, you multiply the whole number part by the denominator and then add the numerator. For example, to convert $2 \frac{1}{2}$ to an improper fraction, you would multiply $2$ by $2$ and add $1$, resulting in $\frac{5}{2}$.

Q: How do you add and subtract mixed numbers?

A: To add and subtract mixed numbers, you need to convert them to improper fractions first. Then, you can add or subtract the fractions by finding a common denominator. For example, to add $2 \frac{1}{2}$ and $3 \frac{1}{4}$, you would convert them to improper fractions, resulting in $\frac{5}{2}$ and $\frac{13}{4}$. Then, you would find a common denominator and add the fractions.

Q: Can you give an example of how to add mixed numbers?

A: Yes, here is an example of how to add mixed numbers:

$$2 \frac{1}{2} + 3 \frac{1}{4}$$

First, convert the mixed numbers to improper fractions:

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

$$3 \frac{1}{4} = \frac{13}{4}$$

Then, find a common denominator and add the fractions:

$$\frac{5}{2} + \frac{13}{4} = \frac{10}{4} + \frac{13}{4} = \frac{23}{4}$$

So, the result of adding $2 \frac{1}{2}$ and $3 \frac{1}{4}$ is $\frac{23}{4}$, which is equal to $5 \frac{3}{4}$.

Q: Can you give an example of how to subtract mixed numbers?

A: Yes, here is an example of how to subtract mixed numbers:

$$9 \frac{1}{8} - 6 \frac{3}{4}$$

First, convert the mixed numbers to improper fractions:

$$9 \frac{1}{8} = \frac{73}{8}$$

$$6 \frac{3}{4} = \frac{27}{4}$$

Then, find a common denominator and subtract the fractions:

$$\frac{73}{8} - \frac{27}{4} = \frac{73}{8} - \frac{54}{8} = \frac{19}{8}$$

So, the result of subtracting $6 \frac{3}{4}$ from $9 \frac{1}{8}$ is $\frac{19}{8}$, which is equal to $2 \frac{3}{8}$.

Q: How do you compare mixed numbers?

A: To compare mixed numbers, you need to convert them to improper fractions first. Then, you can compare the fractions by comparing their numerators and denominators. For example, to compare $2 \frac{1}{2}$ and $3 \frac{1}{4}$, you would convert them to improper fractions, resulting in $\frac{5}{2}$ and $\frac{13}{4}$. Then, you would compare the fractions by comparing their numerators and denominators.

Q: Can you give an example of how to compare mixed numbers?

A: Yes, here is an example of how to compare mixed numbers:

2 \frac{1}{2}$ and $3 \frac{1}{4}

First, convert the mixed numbers to improper fractions:

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

$$3 \frac{1}{4} = \frac{13}{4}$$

Then, compare the fractions by comparing their numerators and denominators:

\frac{5}{2}$ is less than $\frac{13}{4}

So, $2 \frac{1}{2}$ is less than $3 \frac{1}{4}$.

Conclusion

In conclusion, the mixed number $2 \frac{1}{2}$ does not make each of the given equations true. We evaluated the expressions $9 \frac{1}{8} - 6 \frac{3}{4}$, $-1 \frac{1}{2} = 2$, and $2 \frac{1}{2} + 3 \frac{1}{4}$ and found that they are not equal to $2 \frac{1}{2}$. We also answered some common questions about mixed numbers, including how to convert them to improper fractions, how to add and subtract them, and how to compare them.