Directions: Using Multiplication Strategies, Find A Whole Number. Remember To Show Your Work.$\frac{5}{8} \times 2 = \square$

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Introduction

Multiplication is a fundamental operation in mathematics that involves finding the product of two or more numbers. In this article, we will explore how to use multiplication strategies to find a whole number, specifically in the context of the given problem 58×2=□\frac{5}{8} \times 2 = \square. We will break down the problem step by step and provide a clear explanation of the solution.

Understanding the Problem

The problem 58×2=□\frac{5}{8} \times 2 = \square involves multiplying a fraction by a whole number. To solve this problem, we need to understand the concept of multiplying fractions and whole numbers.

Multiplying Fractions and Whole Numbers

When multiplying a fraction by a whole number, we can multiply the numerator of the fraction by the whole number and keep the denominator the same. In this case, we have 58×2\frac{5}{8} \times 2. To solve this problem, we can multiply the numerator 5 by 2 and keep the denominator 8 the same.

Step-by-Step Solution

Step 1: Multiply the Numerator by the Whole Number

To solve the problem, we need to multiply the numerator 5 by the whole number 2.

58×2=5×28\frac{5}{8} \times 2 = \frac{5 \times 2}{8}

Step 2: Simplify the Expression

Now, we need to simplify the expression by multiplying the numerator 5 by 2.

5×28=108\frac{5 \times 2}{8} = \frac{10}{8}

Step 3: Reduce the Fraction

The fraction 108\frac{10}{8} can be reduced by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 2.

108=10÷28÷2=54\frac{10}{8} = \frac{10 \div 2}{8 \div 2} = \frac{5}{4}

Conclusion

In conclusion, to solve the problem 58×2=□\frac{5}{8} \times 2 = \square, we need to multiply the numerator 5 by the whole number 2 and keep the denominator 8 the same. We can then simplify the expression by multiplying the numerator and the denominator, and finally reduce the fraction by dividing both the numerator and the denominator by their GCD.

Final Answer

The final answer to the problem 58×2=□\frac{5}{8} \times 2 = \square is 54\frac{5}{4}.

Tips and Tricks

  • When multiplying a fraction by a whole number, we can multiply the numerator of the fraction by the whole number and keep the denominator the same.
  • To simplify the expression, we can multiply the numerator and the denominator.
  • To reduce the fraction, we can divide both the numerator and the denominator by their GCD.

Common Mistakes

  • Not multiplying the numerator by the whole number.
  • Not simplifying the expression.
  • Not reducing the fraction.

Real-World Applications

Multiplication of fractions and whole numbers has many real-world applications, such as:

  • Calculating the area of a rectangle with a fractional side length.
  • Finding the volume of a rectangular prism with a fractional side length.
  • Calculating the cost of a product with a fractional price.

Practice Problems

Here are some practice problems to help you practice multiplying fractions and whole numbers:

  • 34×3=□\frac{3}{4} \times 3 = \square
  • 25×2=□\frac{2}{5} \times 2 = \square
  • 49×3=□\frac{4}{9} \times 3 = \square

Conclusion

In conclusion, multiplying fractions and whole numbers is a fundamental operation in mathematics that involves finding the product of two or more numbers. By following the steps outlined in this article, you can solve problems involving multiplication of fractions and whole numbers. Remember to multiply the numerator by the whole number, simplify the expression, and reduce the fraction to find the final answer.

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Introduction

In our previous article, we explored how to use multiplication strategies to find a whole number, specifically in the context of the given problem 58×2=□\frac{5}{8} \times 2 = \square. In this article, we will provide a Q&A section to help you better understand the concept of multiplying fractions and whole numbers.

Q&A

Q: What is the difference between multiplying a fraction by a whole number and multiplying two fractions?

A: When multiplying a fraction by a whole number, we can multiply the numerator of the fraction by the whole number and keep the denominator the same. When multiplying two fractions, we need to multiply the numerators and denominators separately.

Q: How do I simplify an expression when multiplying a fraction by a whole number?

A: To simplify an expression when multiplying a fraction by a whole number, we can multiply the numerator and the denominator. This will give us a new fraction that is equivalent to the original expression.

Q: What is the greatest common divisor (GCD) and how do I use it to reduce a fraction?

A: The GCD is the largest number that divides both the numerator and the denominator of a fraction. To reduce a fraction, we can divide both the numerator and the denominator by their GCD.

Q: Can I multiply a fraction by a decimal?

A: Yes, you can multiply a fraction by a decimal. To do this, you can convert the decimal to a fraction and then multiply the fractions.

Q: How do I multiply a fraction by a mixed number?

A: To multiply a fraction by a mixed number, you can convert the mixed number to an improper fraction and then multiply the fractions.

Q: What are some real-world applications of multiplying fractions and whole numbers?

A: Multiplying fractions and whole numbers has many real-world applications, such as calculating the area of a rectangle with a fractional side length, finding the volume of a rectangular prism with a fractional side length, and calculating the cost of a product with a fractional price.

Q: Can I use a calculator to multiply fractions and whole numbers?

A: Yes, you can use a calculator to multiply fractions and whole numbers. However, it's always a good idea to check your work by multiplying the fractions and whole numbers manually.

Tips and Tricks

  • When multiplying a fraction by a whole number, make sure to multiply the numerator by the whole number and keep the denominator the same.
  • To simplify an expression, multiply the numerator and the denominator.
  • To reduce a fraction, divide both the numerator and the denominator by their GCD.
  • When multiplying a fraction by a decimal, convert the decimal to a fraction and then multiply the fractions.
  • When multiplying a fraction by a mixed number, convert the mixed number to an improper fraction and then multiply the fractions.

Common Mistakes

  • Not multiplying the numerator by the whole number.
  • Not simplifying the expression.
  • Not reducing the fraction.
  • Not converting a decimal to a fraction when multiplying a fraction by a decimal.
  • Not converting a mixed number to an improper fraction when multiplying a fraction by a mixed number.

Practice Problems

Here are some practice problems to help you practice multiplying fractions and whole numbers:

  • 34×3=□\frac{3}{4} \times 3 = \square
  • 25×2=□\frac{2}{5} \times 2 = \square
  • 49×3=□\frac{4}{9} \times 3 = \square
  • 12×4=□\frac{1}{2} \times 4 = \square
  • 38×2=□\frac{3}{8} \times 2 = \square

Conclusion

In conclusion, multiplying fractions and whole numbers is a fundamental operation in mathematics that involves finding the product of two or more numbers. By following the steps outlined in this article and practicing the Q&A section, you can become more confident in your ability to multiply fractions and whole numbers. Remember to multiply the numerator by the whole number, simplify the expression, and reduce the fraction to find the final answer.