Multiplying the Whole Numbers

Oct 13, 2025 by miodeya.com 57 views

Understanding the Problem

Multiplication of mixed numbers and fractions can be a challenging task, especially when dealing with multiple numbers. In this article, we will explore the steps to multiply the given expression: $4 \times \frac{3}{8} \times 1 \frac{1}{15}$ . We will break down the problem into smaller parts and use the correct order of operations to simplify the expression.

Breaking Down the Problem

To multiply the given expression, we need to follow the order of operations (PEMDAS):

Multiply the whole numbers
Multiply the fractions
Multiply the mixed numbers

Let's start by breaking down the given expression:

$4 \times \frac{3}{8} \times 1 \frac{1}{15}$

We can rewrite the mixed number $1 \frac{1}{15}$ as an improper fraction:

$1 \frac{1}{15} = \frac{16}{15}$

Now, we can rewrite the expression as:

$4 \times \frac{3}{8} \times \frac{16}{15}$

Multiplying the Whole Numbers

The first step is to multiply the whole numbers:

$4 \times 1 = 4$

Multiplying the Fractions

Next, we need to multiply the fractions:

$\frac{3}{8} \times \frac{16}{15}$

To multiply fractions, we need to multiply the numerators and denominators separately:

$\frac{3 \times 16}{8 \times 15} = \frac{48}{120}$

We can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 24:

$\frac{48}{120} = \frac{2}{5}$

Multiplying the Mixed Numbers

Now, we need to multiply the mixed number $\frac{16}{15}$ by the result of the previous step:

$4 \times \frac{2}{5} \times \frac{16}{15}$

We can rewrite the expression as:

$\frac{4 \times 2 \times 16}{5 \times 15}$

To multiply the numerators and denominators, we need to follow the order of operations:

$\frac{(4 \times 2) \times 16}{5 \times 15}$

First, we multiply the whole numbers:

$4 \times 2 = 8$

Then, we multiply the result by 16:

$8 \times 16 = 128$

Next, we multiply the denominators:

$5 \times 15 = 75$

Now, we can rewrite the expression as:

$\frac{128}{75}$

Simplifying the Result

The final step is to simplify the result, if possible. In this case, the fraction $\frac{128}{75}$ cannot be simplified further.

Conclusion

Multiplying mixed numbers and fractions can be a challenging task, but by following the order of operations and breaking down the problem into smaller parts, we can simplify the expression. In this article, we explored the steps to multiply the given expression: $4 \times \frac{3}{8} \times 1 \frac{1}{15}$ . We broke down the problem into smaller parts, multiplied the whole numbers, fractions, and mixed numbers, and simplified the result.

Key Takeaways

To multiply mixed numbers and fractions, follow the order of operations (PEMDAS)
Break down the problem into smaller parts
Multiply the whole numbers, fractions, and mixed numbers separately
Simplify the result, if possible

Common Mistakes

Not following the order of operations (PEMDAS)
Not breaking down the problem into smaller parts
Not multiplying the whole numbers, fractions, and mixed numbers separately

Real-World Applications

Multiplying mixed numbers and fractions has many real-world applications, such as:

Calculating the area of a rectangle with mixed number dimensions
Finding the volume of a rectangular prism with mixed number dimensions
Solving problems involving mixed number and fraction measurements in cooking, construction, and other fields.

Practice Problems

Try these practice problems to reinforce your understanding of multiplying mixed numbers and fractions:

$3 \times \frac{2}{5} \times 1 \frac{3}{4}$
$2 \times \frac{3}{8} \times 1 \frac{1}{2}$
$5 \times \frac{4}{9} \times 1 \frac{2}{3}$

References

[1] Khan Academy. (n.d.). Multiplying fractions. Retrieved from https://www.khanacademy.org/math/fraction-arithmetic/fraction-multiplication/fraction-multiplication/v/multiplying-fractions
[2] Math Open Reference. (n.d.). Multiplying mixed numbers. Retrieved from https://www.mathopenref.com/mixednumbersmultiplication.html

Frequently Asked Questions

In this article, we will answer some of the most frequently asked questions about multiplying mixed numbers and fractions.

Q: What is the order of operations for multiplying mixed numbers and fractions?

A: The order of operations for multiplying mixed numbers and fractions is:

Multiply the whole numbers
Multiply the fractions
Multiply the mixed numbers

Q: How do I multiply fractions?

A: To multiply fractions, you need to multiply the numerators and denominators separately. For example:

$\frac{3}{8} \times \frac{16}{15}$

To multiply the numerators and denominators, you need to follow the order of operations:

$\frac{(3 \times 16)}{(8 \times 15)}$

First, multiply the whole numbers:

$3 \times 16 = 48$

Then, multiply the result by 16:

$48 \times 16 = 768$

Next, multiply the denominators:

$8 \times 15 = 120$

Now, you can rewrite the expression as:

$\frac{768}{120}$

Q: How do I simplify a fraction after multiplying?

A: To simplify a fraction after multiplying, you need to find the greatest common divisor (GCD) of the numerator and denominator. For example:

$\frac{48}{120}$

To find the GCD, you can use the following steps:

List the factors of the numerator and denominator:
- Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
- Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
Find the greatest common factor:
- The greatest common factor of 48 and 120 is 24
Divide both the numerator and denominator by the GCD:
- $\frac{48}{24} = 2$
- $\frac{120}{24} = 5$
Simplify the fraction:
- $\frac{2}{5}$

Q: What is the difference between multiplying mixed numbers and fractions?

A: Multiplying mixed numbers and fractions involves multiplying the whole numbers, fractions, and mixed numbers separately. For example:

$4 \times \frac{3}{8} \times 1 \frac{1}{15}$

To multiply the mixed number and fraction, you need to follow the order of operations:

Multiply the whole numbers:
- $4 \times 1 = 4$
Multiply the fractions:
- $\frac{3}{8} \times \frac{16}{15} = \frac{48}{120}$
Multiply the mixed number and fraction:
- $4 \times \frac{48}{120} = \frac{192}{120}$

Q: How do I handle negative numbers when multiplying mixed numbers and fractions?

A: When multiplying mixed numbers and fractions with negative numbers, you need to follow the same order of operations as before. For example:

$-4 \times \frac{3}{8} \times 1 \frac{1}{15}$

To multiply the mixed number and fraction, you need to follow the order of operations:

Multiply the whole numbers:
- $-4 \times 1 = -4$
Multiply the fractions:
- $\frac{3}{8} \times \frac{16}{15} = \frac{48}{120}$
Multiply the mixed number and fraction:
- $-4 \times \frac{48}{120} = \frac{-192}{120}$

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

A: Yes, you can use a calculator to multiply mixed numbers and fractions. However, it's always a good idea to double-check your work by following the order of operations and simplifying the fraction.

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

A: Some common mistakes to avoid when multiplying mixed numbers and fractions include:

Not following the order of operations (PEMDAS)
Not breaking down the problem into smaller parts
Not multiplying the whole numbers, fractions, and mixed numbers separately
Not simplifying the fraction after multiplying