Multiply: − 0.5 × − 2 1 2 = -0.5 \times -2 \frac{1}{2} = − 0.5 × − 2 2 1 =

Mar 13, 2025 by ADMIN 77 views

$Multiply: $-0.5 \times -2 \frac{1}{2} =$$

Understanding the Problem

When dealing with multiplication of fractions and decimals, it's essential to follow the correct order of operations and to convert all numbers to a common format. In this problem, we are required to multiply $-0.5$ by $-2 \frac{1}{2}$ . To solve this, we need to convert the mixed number $-2 \frac{1}{2}$ to an improper fraction.

Converting Mixed Numbers to Improper Fractions

A mixed number is a combination of a whole number and a fraction. To convert a mixed number to an improper fraction, we multiply the whole number by the denominator and then add the numerator. The result is then written as the new numerator over the denominator.

In this case, we have $-2 \frac{1}{2}$ . To convert this to an improper fraction, we multiply the whole number $-2$ by the denominator $2$ and then add the numerator $1$ . This gives us:

-2 \times 2 + 1 = -4 + 1 = -3

So, the mixed number $-2 \frac{1}{2}$ is equivalent to the improper fraction $-\frac{3}{2}$ .

Multiplying Fractions and Decimals

Now that we have converted the mixed number to an improper fraction, we can multiply $-0.5$ by $-\frac{3}{2}$ . To multiply fractions and decimals, we can follow these steps:

Convert the decimal to a fraction by writing it as a fraction with a denominator of 1.
Multiply the numerators together and the denominators together.
Simplify the resulting fraction.

Let's follow these steps to multiply $-0.5$ by $-\frac{3}{2}$ .

Converting the Decimal to a Fraction

To convert the decimal $-0.5$ to a fraction, we can write it as a fraction with a denominator of 1:

-0.5 = -\frac{0.5}{1}

Multiplying the Numerators and Denominators

Now that we have converted the decimal to a fraction, we can multiply the numerators together and the denominators together:

-\frac{0.5}{1} \times -\frac{3}{2} = \frac{0.5 \times -3}{1 \times 2}

Simplifying the Resulting Fraction

Now that we have multiplied the numerators and denominators, we can simplify the resulting fraction:

\frac{0.5 \times -3}{1 \times 2} = \frac{-1.5}{2}

Writing the Answer as a Decimal

Finally, we can write the answer as a decimal by dividing the numerator by the denominator:

\frac{-1.5}{2} = -0.75

Conclusion

In this problem, we were required to multiply $-0.5$ by $-2 \frac{1}{2}$ . To solve this, we converted the mixed number to an improper fraction and then multiplied the fractions together. The resulting answer was $-0.75$ .

Real-World Applications

Multiplying fractions and decimals is an essential skill in many real-world applications, such as:

Cooking: When a recipe calls for a certain amount of an ingredient, you may need to multiply the amount by a fraction or decimal to get the correct amount.
Building: When building a structure, you may need to multiply the dimensions of a room or a piece of furniture by a fraction or decimal to get the correct size.
Science: When conducting experiments, you may need to multiply the amount of a substance by a fraction or decimal to get the correct amount.

Tips and Tricks

Here are some tips and tricks for multiplying fractions and decimals:

Always follow the order of operations: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
When multiplying fractions, multiply the numerators together and the denominators together.
When multiplying decimals, multiply the numbers as you would with whole numbers and then divide by the product of the denominators.
To convert a decimal to a fraction, write it as a fraction with a denominator of 1.

Common Mistakes

Here are some common mistakes to avoid when multiplying fractions and decimals:

Not following the order of operations.
Not converting the decimal to a fraction before multiplying.
Not multiplying the numerators and denominators together when multiplying fractions.
Not simplifying the resulting fraction.

Conclusion

Multiplying fractions and decimals is an essential skill in mathematics. By following the correct order of operations and converting decimals to fractions, we can multiply fractions and decimals with ease. Remember to always simplify the resulting fraction and to follow the tips and tricks outlined above to avoid common mistakes.

Frequently Asked Questions

Q: What is the correct order of operations when multiplying fractions and decimals?

A: The correct order of operations when multiplying fractions and decimals is to follow the order of operations: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

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

A: To convert a mixed number to an improper fraction, you multiply the whole number by the denominator and then add the numerator. The result is then written as the new numerator over the denominator.

Q: What is the difference between multiplying fractions and multiplying decimals?

A: When multiplying fractions, you multiply the numerators together and the denominators together. When multiplying decimals, you multiply the numbers as you would with whole numbers and then divide by the product of the denominators.

Q: How do I simplify a fraction after multiplying?

A: To simplify a fraction, you divide the numerator and denominator by their greatest common divisor (GCD).

Q: What is the GCD of two numbers?

A: The GCD of two numbers is the largest number that divides both numbers without leaving a remainder.

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

A: To convert a decimal to a fraction, you write it as a fraction with a denominator of 1.

Q: What is the product of two negative numbers?

A: The product of two negative numbers is a positive number.

Q: What is the product of two positive numbers?

A: The product of two positive numbers is a positive number.

Q: What is the product of a positive number and a negative number?

A: The product of a positive number and a negative number is a negative number.

Q: What is the product of a negative number and a negative number?

A: The product of a negative number and a negative number is a positive number.

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

A: To multiply a fraction by a decimal, you multiply the numerator of the fraction by the decimal and then divide by the denominator of the fraction.

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

A: To multiply a decimal by a fraction, you multiply the decimal by the numerator of the fraction and then divide by the denominator of the fraction.

Q: What is the difference between multiplying fractions and multiplying decimals in real-world applications?

A: In real-world applications, multiplying fractions and decimals is used to calculate quantities, such as the amount of a substance needed for a recipe or the dimensions of a room.

Q: How do I use multiplication of fractions and decimals in real-world applications?

A: To use multiplication of fractions and decimals in real-world applications, you need to understand the concept of equivalent ratios and how to convert between fractions and decimals.

Q: What are some common mistakes to avoid when multiplying fractions and decimals?

A: Some common mistakes to avoid when multiplying fractions and decimals include not following the order of operations, not converting decimals to fractions, and not simplifying the resulting fraction.

Q: How do I avoid common mistakes when multiplying fractions and decimals?

A: To avoid common mistakes when multiplying fractions and decimals, you need to follow the order of operations, convert decimals to fractions, and simplify the resulting fraction.

Conclusion

Multiplying fractions and decimals is an essential skill in mathematics. By understanding the correct order of operations, converting decimals to fractions, and simplifying the resulting fraction, you can multiply fractions and decimals with ease. Remember to avoid common mistakes and to use multiplication of fractions and decimals in real-world applications.