The Model Represents $3 \div \frac{1}{5}$. Which Multiplication Can You Use To Check The Answer?A. $3 \times \frac{1}{5} = \frac{3}{5}$B. \$15 \times \frac{1}{5} = 3$[/tex\]C. $15 \times \frac{3}{5} = 9$D.

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Introduction

In mathematics, division is a fundamental operation that involves sharing a certain quantity into equal parts or groups. However, when dealing with fractions, division can become a bit more complex. In this article, we will explore how to check the answer to a division problem involving fractions by using multiplication.

Understanding the Problem

The given problem is $3 \div \frac{1}{5}$. To check the answer, we need to find a multiplication that is equivalent to this division problem. Let's break down the problem and understand what it means.

Division as Multiplication

When we divide a number by a fraction, we are essentially asking how many times the fraction fits into the number. In this case, we are dividing 3 by $\frac{1}{5}$. To check the answer, we need to find a multiplication that is equivalent to this division problem.

Option A: $3 \times \frac{1}{5} = \frac{3}{5}$

Option A suggests that we multiply 3 by $\frac{1}{5}$. However, this is not the correct multiplication to check the answer. When we multiply 3 by $\frac{1}{5}$, we get $\frac{3}{5}$, which is not the same as dividing 3 by $\frac{1}{5}$.

Option B: $15 \times \frac{1}{5} = 3$

Option B suggests that we multiply 15 by $\frac{1}{5}$. This is a correct multiplication to check the answer. When we multiply 15 by $\frac{1}{5}$, we get 3, which is the same as dividing 3 by $\frac{1}{5}$.

Why Option B Works

Option B works because multiplying 15 by $\frac{1}{5}$ is equivalent to dividing 15 by 5 and then multiplying the result by 3. This is because $\frac{1}{5}$ is the same as dividing 1 by 5, and multiplying 15 by $\frac{1}{5}$ is the same as multiplying 15 by 1 and then dividing the result by 5.

Conclusion

In conclusion, to check the answer to a division problem involving fractions, we need to find a multiplication that is equivalent to the division problem. In this case, option B, $15 \times \frac{1}{5} = 3$, is the correct multiplication to check the answer.

Tips and Tricks

  • When dealing with division problems involving fractions, it's essential to find a multiplication that is equivalent to the division problem.
  • To check the answer, multiply the dividend by the reciprocal of the divisor.
  • The reciprocal of a fraction is obtained by swapping the numerator and the denominator.

Common Mistakes

  • Not finding a multiplication that is equivalent to the division problem.
  • Not using the correct multiplication to check the answer.
  • Not understanding the concept of division as multiplication.

Real-World Applications

  • In finance, division is used to calculate interest rates and investment returns.
  • In science, division is used to calculate concentrations and dilutions.
  • In everyday life, division is used to calculate quantities and proportions.

Practice Problems

  • 4÷234 \div \frac{2}{3}

  • 6÷346 \div \frac{3}{4}

  • 9÷129 \div \frac{1}{2}

Solutions

  • 4÷23=4×32=64 \div \frac{2}{3} = 4 \times \frac{3}{2} = 6

  • 6÷34=6×43=86 \div \frac{3}{4} = 6 \times \frac{4}{3} = 8

  • 9÷12=9×2=189 \div \frac{1}{2} = 9 \times 2 = 18

Conclusion

Introduction

In our previous article, we explored how to check the answer to a division problem involving fractions by using multiplication. In this article, we will answer some frequently asked questions related to this topic.

Q: What is the concept of division as multiplication?

A: Division as multiplication is a concept that involves finding a multiplication that is equivalent to a division problem. When we divide a number by a fraction, we are essentially asking how many times the fraction fits into the number. To check the answer, we need to find a multiplication that is equivalent to this division problem.

Q: How do I find a multiplication that is equivalent to a division problem?

A: To find a multiplication that is equivalent to a division problem, you need to multiply the dividend by the reciprocal of the divisor. The reciprocal of a fraction is obtained by swapping the numerator and the denominator.

Q: What is the reciprocal of a fraction?

A: The reciprocal of a fraction is obtained by swapping the numerator and the denominator. For example, the reciprocal of $\frac{1}{2}$ is $\frac{2}{1}$, and the reciprocal of $\frac{3}{4}$ is $\frac{4}{3}$.

Q: How do I check the answer to a division problem involving fractions?

A: To check the answer to a division problem involving fractions, you need to find a multiplication that is equivalent to the division problem. Then, you multiply the dividend by the reciprocal of the divisor to get the answer.

Q: What are some common mistakes to avoid when dealing with division problems involving fractions?

A: Some common mistakes to avoid when dealing with division problems involving fractions include:

  • Not finding a multiplication that is equivalent to the division problem.
  • Not using the correct multiplication to check the answer.
  • Not understanding the concept of division as multiplication.

Q: How do I apply division as multiplication in real-world situations?

A: Division as multiplication can be applied in various real-world situations, such as:

  • In finance, division is used to calculate interest rates and investment returns.
  • In science, division is used to calculate concentrations and dilutions.
  • In everyday life, division is used to calculate quantities and proportions.

Q: What are some practice problems to help me understand division as multiplication?

A: Here are some practice problems to help you understand division as multiplication:

  • 4÷234 \div \frac{2}{3}

  • 6÷346 \div \frac{3}{4}

  • 9÷129 \div \frac{1}{2}

Solutions

  • 4÷23=4×32=64 \div \frac{2}{3} = 4 \times \frac{3}{2} = 6

  • 6÷34=6×43=86 \div \frac{3}{4} = 6 \times \frac{4}{3} = 8

  • 9÷12=9×2=189 \div \frac{1}{2} = 9 \times 2 = 18

Conclusion

In conclusion, division as multiplication is a powerful concept that can help you check the answer to division problems involving fractions. By finding a multiplication that is equivalent to the division problem, you can ensure that you have the correct result. Remember to avoid common mistakes and apply division as multiplication in real-world situations.

Tips and Tricks

  • When dealing with division problems involving fractions, always find a multiplication that is equivalent to the division problem.
  • Use the correct multiplication to check the answer.
  • Understand the concept of division as multiplication.

Common Mistakes

  • Not finding a multiplication that is equivalent to the division problem.
  • Not using the correct multiplication to check the answer.
  • Not understanding the concept of division as multiplication.

Real-World Applications

  • In finance, division is used to calculate interest rates and investment returns.
  • In science, division is used to calculate concentrations and dilutions.
  • In everyday life, division is used to calculate quantities and proportions.

Practice Problems

  • 8÷458 \div \frac{4}{5}

  • 12÷3212 \div \frac{3}{2}

  • 15÷1315 \div \frac{1}{3}

Solutions

  • 8÷45=8×54=108 \div \frac{4}{5} = 8 \times \frac{5}{4} = 10

  • 12÷32=12×23=812 \div \frac{3}{2} = 12 \times \frac{2}{3} = 8

  • 15÷13=15×3=4515 \div \frac{1}{3} = 15 \times 3 = 45