Which Statement About 96 × 11 8 96 \times \frac{11}{8} 96 × 8 11 Is True?F. The Product Is Less Than 11 8 \frac{11}{8} 8 11 .G. The Product Is Greater Than 96.H. The Product Is Between 11 8 \frac{11}{8} 8 11 And 96.J. The Product Is Equal To 96.

Mar 7, 2025 by ADMIN 252 views

Which Statement About $96 \times \frac{11}{8}$ is True?

Understanding the Problem

When dealing with multiplication involving fractions and whole numbers, it's essential to understand the concept of multiplying fractions by whole numbers. In this case, we're given the expression $96 \times \frac{11}{8}$ and asked to determine which statement about the product is true.

Multiplying Fractions by Whole Numbers

To multiply a fraction by a whole number, we can simply multiply the numerator of the fraction by the whole number and keep the denominator the same. In this case, we have:

96 \times \frac{11}{8} = \frac{96 \times 11}{8}

Evaluating the Expression

Now, let's evaluate the expression by multiplying the numerator and denominator:

\frac{96 \times 11}{8} = \frac{1056}{8}

Simplifying the Fraction

To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 1056 and 8 is 8. So, we can simplify the fraction as follows:

\frac{1056}{8} = 132

Analyzing the Statements

Now that we have the product of $96 \times \frac{11}{8}$ , let's analyze the given statements:

F. The product is less than $\frac{11}{8}$ .
G. The product is greater than 96.
H. The product is between $\frac{11}{8}$ and 96.
J. The product is equal to 96.

Comparing the Product to the Statements

We can compare the product (132) to the statements:

F. The product is less than $\frac{11}{8}$ . This statement is false because 132 is greater than $\frac{11}{8}$ .
G. The product is greater than 96. This statement is true because 132 is indeed greater than 96.
H. The product is between $\frac{11}{8}$ and 96. This statement is false because 132 is greater than 96.
J. The product is equal to 96. This statement is false because 132 is not equal to 96.

Conclusion

Based on our analysis, the correct statement about $96 \times \frac{11}{8}$ is:

G. The product is greater than 96.

Therefore, the product of $96 \times \frac{11}{8}$ is indeed greater than 96.

Additional Examples

To further illustrate the concept, let's consider a few more examples:

$24 \times \frac{3}{4} = \frac{24 \times 3}{4} = \frac{72}{4} = 18$
$48 \times \frac{5}{6} = \frac{48 \times 5}{6} = \frac{240}{6} = 40$
$72 \times \frac{7}{9} = \frac{72 \times 7}{9} = \frac{504}{9} = 56$

In each of these examples, we can see that multiplying a fraction by a whole number results in a product that is greater than the whole number.

Real-World Applications

Understanding how to multiply fractions by whole numbers has numerous real-world applications. For instance, in cooking, you may need to multiply a recipe by a certain factor to serve a larger group of people. In finance, you may need to calculate the interest on an investment by multiplying the principal amount by a fraction representing the interest rate.

Conclusion

In conclusion, when dealing with multiplication involving fractions and whole numbers, it's essential to understand the concept of multiplying fractions by whole numbers. By following the steps outlined in this article, you can evaluate expressions and determine which statement about the product is true.
Frequently Asked Questions About Multiplying Fractions by Whole Numbers

Q: What is the rule for multiplying fractions by whole numbers?

A: The rule for multiplying fractions by whole numbers is to multiply the numerator of the fraction by the whole number and keep the denominator the same.

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

A: To multiply a fraction by a whole number, you can follow these steps:

Multiply the numerator of the fraction by the whole number.
Keep the denominator the same.
Simplify the resulting fraction, if possible.

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

A: When multiplying a fraction by a whole number, you are essentially scaling the fraction by the whole number. When multiplying two fractions together, you are multiplying the numerators and denominators separately.

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 together.

Q: How do I know when to simplify a fraction after multiplying it by a whole number?

A: You should simplify a fraction after multiplying it by a whole number if the resulting fraction has a common factor between the numerator and denominator. This will make the fraction easier to work with and reduce the risk of errors.

Q: Can I multiply a negative fraction by a whole number?

A: Yes, you can multiply a negative fraction by a whole number. The result will be a negative fraction.

Q: How do I handle fractions with zero as the numerator or denominator?

A: If a fraction has zero as the numerator, the result of multiplying it by a whole number will be zero. If a fraction has zero as the denominator, the result will be undefined.

Q: Can I multiply a fraction by a fraction?

A: Yes, you can multiply a fraction by a fraction. To do this, you multiply the numerators together and the denominators together.

Q: What is the order of operations when multiplying fractions by whole numbers?

A: The order of operations when multiplying fractions by whole numbers is:

Multiply the numerator of the fraction by the whole number.
Keep the denominator the same.
Simplify the resulting fraction, if possible.

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

A: Yes, you can use a calculator to multiply fractions by whole numbers. However, it's always a good idea to double-check your work to ensure accuracy.

Q: How do I apply the concept of multiplying fractions by whole numbers to real-world problems?

A: The concept of multiplying fractions by whole numbers has numerous real-world applications, such as cooking, finance, and science. To apply this concept to real-world problems, you can use the steps outlined in this article and consider the context of the problem.

Q: What are some common mistakes to avoid when multiplying fractions by whole numbers?

A: Some common mistakes to avoid when multiplying fractions by whole numbers include:

Forgetting to simplify the resulting fraction
Multiplying the denominator by the whole number instead of the numerator
Not considering the context of the problem

Q: Can I use the concept of multiplying fractions by whole numbers to solve equations?

A: Yes, you can use the concept of multiplying fractions by whole numbers to solve equations. To do this, you can multiply both sides of the equation by the same fraction or whole number.

Q: How do I determine the correct answer when multiplying fractions by whole numbers?

A: To determine the correct answer when multiplying fractions by whole numbers, you can follow these steps:

Multiply the numerator of the fraction by the whole number.
Keep the denominator the same.
Simplify the resulting fraction, if possible.
Check your work to ensure accuracy.

By following these steps and considering the context of the problem, you can determine the correct answer when multiplying fractions by whole numbers.