Converting Mixed Numbers to Improper Fractions

Oct 13, 2025 by recoveryshake.com 130 views

In Questions 3-8, Without Multiplying, Decide Which Symbol Belongs in the Box

Understanding the Problem

In this article, we will delve into the world of mathematics and explore the concept of deciding which symbol belongs in the box without multiplying. We will examine questions 3-8 and determine the correct symbol to use in each case.

Question 3: $5 \frac{1}{3} \times 2.75 \, \boxed{\langle, \rangle, =} \, 5 \frac{1}{3}$

To solve this problem, we need to understand the concept of multiplying mixed numbers. A mixed number is a combination of a whole number and a fraction. In this case, we have $5 \frac{1}{3}$ , which is a mixed number. When we multiply a mixed number by a decimal, we need to convert the mixed number to an improper fraction first.

Converting Mixed Numbers to Improper Fractions

To convert a mixed number to an improper fraction, we need to multiply the whole number by the denominator and then add the numerator. In this case, we have $5 \frac{1}{3}$ . To convert this to an improper fraction, we multiply 5 by 3 and add 1, which gives us 16. So, $5 \frac{1}{3}$ is equal to $\frac{16}{3}$ .

Multiplying Improper Fractions

Now that we have converted the mixed number to an improper fraction, we can multiply it by the decimal. To multiply an improper fraction by a decimal, we can multiply the numerator by the decimal and then divide by the denominator.

In this case, we have $\frac{16}{3} \times 2.75$ . To multiply this, we can multiply 16 by 2.75, which gives us 44. So, $\frac{16}{3} \times 2.75 = \frac{44}{3}$ .

Simplifying the Result

Now that we have multiplied the improper fraction by the decimal, we need to simplify the result. To simplify a fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator and divide both numbers by the GCD.

In this case, we have $\frac{44}{3}$ . The GCD of 44 and 3 is 1, so we cannot simplify this fraction further.

Conclusion

In conclusion, the correct symbol to use in the box for question 3 is $\langle$ . This is because the result of multiplying $5 \frac{1}{3}$ by 2.75 is not equal to $5 \frac{1}{3}$ .

Question 4: $10 \frac{3}{4} \times 2.25 \, \boxed{\langle, \rangle, =} \, 10 \frac{3}{4}$

To solve this problem, we need to follow the same steps as question 3. We need to convert the mixed number to an improper fraction, multiply the improper fraction by the decimal, and then simplify the result.

Converting Mixed Numbers to Improper Fractions

To convert a mixed number to an improper fraction, we need to multiply the whole number by the denominator and then add the numerator. In this case, we have $10 \frac{3}{4}$ . To convert this to an improper fraction, we multiply 10 by 4 and add 3, which gives us 43. So, $10 \frac{3}{4}$ is equal to $\frac{43}{4}$ .

Multiplying Improper Fractions

In this case, we have $\frac{43}{4} \times 2.25$ . To multiply this, we can multiply 43 by 2.25, which gives us 96.75. So, $\frac{43}{4} \times 2.25 = \frac{96.75}{4}$ .

Simplifying the Result

In this case, we have $\frac{96.75}{4}$ . The GCD of 96.75 and 4 is 0.25, so we can simplify this fraction by dividing both numbers by 0.25. This gives us $\frac{387}{4}$ .

Conclusion

In conclusion, the correct symbol to use in the box for question 4 is $\langle$ . This is because the result of multiplying $10 \frac{3}{4}$ by 2.25 is not equal to $10 \frac{3}{4}$ .

Question 5: $7 \frac{2}{3} \times 3.5 \, \boxed{\langle, \rangle, =} \, 7 \frac{2}{3}$

Converting Mixed Numbers to Improper Fractions

To convert a mixed number to an improper fraction, we need to multiply the whole number by the denominator and then add the numerator. In this case, we have $7 \frac{2}{3}$ . To convert this to an improper fraction, we multiply 7 by 3 and add 2, which gives us 23. So, $7 \frac{2}{3}$ is equal to $\frac{23}{3}$ .

Multiplying Improper Fractions

In this case, we have $\frac{23}{3} \times 3.5$ . To multiply this, we can multiply 23 by 3.5, which gives us 80.5. So, $\frac{23}{3} \times 3.5 = \frac{80.5}{3}$ .

Simplifying the Result

In this case, we have $\frac{80.5}{3}$ . The GCD of 80.5 and 3 is 0.5, so we can simplify this fraction by dividing both numbers by 0.5. This gives us $\frac{161}{3}$ .

Conclusion

In conclusion, the correct symbol to use in the box for question 5 is $\langle$ . This is because the result of multiplying $7 \frac{2}{3}$ by 3.5 is not equal to $7 \frac{2}{3}$ .

Question 6: $4 \frac{1}{2} \times 2.25 \, \boxed{\langle, \rangle, =} \, 4 \frac{1}{2}$

Converting Mixed Numbers to Improper Fractions

To convert a mixed number to an improper fraction, we need to multiply the whole number by the denominator and then add the numerator. In this case, we have $4 \frac{1}{2}$ . To convert this to an improper fraction, we multiply 4 by 2 and add 1, which gives us 9. So, $4 \frac{1}{2}$ is equal to $\frac{9}{2}$ .

Multiplying Improper Fractions

In this case, we have $\frac{9}{2} \times 2.25$ . To multiply this, we can multiply 9 by 2.25, which gives us 20.25. So, $\frac{9}{2} \times 2.25 = \frac{20.25}{2}$ .

Simplifying the Result

In this case, we have $\frac{20.25}{2}$ . The GCD of 20.25 and 2 is 0.25, so we can simplify this fraction by dividing both numbers by 0.25. This gives us $\frac{81}{2}$ .

Conclusion

In conclusion, the correct symbol to use in the box for question 6 is $\langle$ . This is because the result of multiplying $4 \frac{1}{2}$ by 2.25 is not equal to $4 \frac{1}{2}$ .

**Question 7: $3 \frac{1}{4} \times 2.5 , \boxed{\langle, \rangle, =} <br/> In Questions 3-8, Without Multiplying, Decide Which Symbol Belongs in the Box

Q&A: Deciding Which Symbol Belongs in the Box

Q: What is the correct symbol to use in the box for question 3?

A: The correct symbol to use in the box for question 3 is $\langle$ . This is because the result of multiplying $5 \frac{1}{3}$ by 2.75 is not equal to $5 \frac{1}{3}$ .

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

A: To convert a mixed number to an improper fraction, you need to multiply the whole number by the denominator and then add the numerator. For example, to convert $5 \frac{1}{3}$ to an improper fraction, you would multiply 5 by 3 and add 1, which gives you 16. So, $5 \frac{1}{3}$ is equal to $\frac{16}{3}$ .

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 divides both numbers without leaving a remainder. For example, the GCD of 16 and 3 is 1, so we cannot simplify the fraction $\frac{16}{3}$ further.

Q: How do I simplify a fraction?

A: To simplify a fraction, you need to find the greatest common divisor (GCD) of the numerator and the denominator and divide both numbers by the GCD. For example, to simplify the fraction $\frac{96.75}{4}$ , you would find the GCD of 96.75 and 4, which is 0.25, and then divide both numbers by 0.25. This gives you $\frac{387}{4}$ .

Q: What is the correct symbol to use in the box for question 4?

A: The correct symbol to use in the box for question 4 is $\langle$ . This is because the result of multiplying $10 \frac{3}{4}$ by 2.25 is not equal to $10 \frac{3}{4}$ .

Q: How do I multiply an improper fraction by a decimal?

A: To multiply an improper fraction by a decimal, you can multiply the numerator by the decimal and then divide by the denominator. For example, to multiply $\frac{23}{3}$ by 3.5, you would multiply 23 by 3.5, which gives you 80.5. So, $\frac{23}{3} \times 3.5 = \frac{80.5}{3}$ .

Q: What is the correct symbol to use in the box for question 5?

A: The correct symbol to use in the box for question 5 is $\langle$ . This is because the result of multiplying $7 \frac{2}{3}$ by 3.5 is not equal to $7 \frac{2}{3}$ .

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

A: To convert a mixed number to an improper fraction, you need to multiply the whole number by the denominator and then add the numerator. For example, to convert $7 \frac{2}{3}$ to an improper fraction, you would multiply 7 by 3 and add 2, which gives you 23. So, $7 \frac{2}{3}$ is equal to $\frac{23}{3}$ .

Q: What is the correct symbol to use in the box for question 6?

A: The correct symbol to use in the box for question 6 is $\langle$ . This is because the result of multiplying $4 \frac{1}{2}$ by 2.25 is not equal to $4 \frac{1}{2}$ .

Q: How do I multiply an improper fraction by a decimal?

A: To multiply an improper fraction by a decimal, you can multiply the numerator by the decimal and then divide by the denominator. For example, to multiply $\frac{9}{2}$ by 2.25, you would multiply 9 by 2.25, which gives you 20.25. So, $\frac{9}{2} \times 2.25 = \frac{20.25}{2}$ .

Q: What is the correct symbol to use in the box for question 7?

A: The correct symbol to use in the box for question 7 is $\langle$ . This is because the result of multiplying $3 \frac{1}{4}$ by 2.5 is not equal to $3 \frac{1}{4}$ .

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

A: To convert a mixed number to an improper fraction, you need to multiply the whole number by the denominator and then add the numerator. For example, to convert $3 \frac{1}{4}$ to an improper fraction, you would multiply 3 by 4 and add 1, which gives you 13. So, $3 \frac{1}{4}$ is equal to $\frac{13}{4}$ .

Q: What is the correct symbol to use in the box for question 8?

A: The correct symbol to use in the box for question 8 is $\langle$ . This is because the result of multiplying $2 \frac{1}{2}$ by 3.5 is not equal to $2 \frac{1}{2}$ .

Conclusion

In conclusion, the correct symbol to use in the box for questions 3-8 is $\langle$ . This is because the result of multiplying the mixed numbers by the decimals is not equal to the original mixed numbers.