Multiplying the Whole Number by the Numerator

Oct 13, 2025 by recoveryshake.com 142 views

Understanding the Expression

When we encounter an expression like $4 \times \frac{3}{5}$ , we need to understand the order of operations to evaluate it correctly. The expression involves multiplication and division, which are both essential operations in mathematics. In this case, we have a whole number (4) multiplied by a fraction ( $\frac{3}{5}$ ).

The Order of Operations

To solve this expression, we need to follow the order of operations, which is a set of rules that dictate the order in which we perform mathematical operations. The order of operations is often remembered using the acronym PEMDAS, which stands for:

Parentheses: Evaluate expressions inside parentheses first.
Exponents: Evaluate any exponential expressions next.
Multiplication and Division: Evaluate multiplication and division operations from left to right.
Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Evaluating the Expression

In this case, we have a multiplication operation ( $4 \times \frac{3}{5}$ ), so we will follow the order of operations to evaluate it. We can start by multiplying the whole number (4) by the numerator of the fraction (3).

Multiplying the Whole Number by the Numerator

When we multiply 4 by 3, we get:

$4 \times 3 = 12$

Dividing by the Denominator

Now that we have the product of 4 and 3, we need to divide it by the denominator of the fraction (5). To do this, we can simply divide 12 by 5.

Simplifying the Fraction

When we divide 12 by 5, we get:

$\frac{12}{5} = 2.4$

Conclusion

In conclusion, to solve the expression $4 \times \frac{3}{5}$ , we need to follow the order of operations and multiply the whole number (4) by the numerator of the fraction (3), and then divide the result by the denominator (5). The final answer is $\boxed{2.4}$ .

Real-World Applications

This type of expression is commonly encountered in real-world applications, such as:

Finance: When calculating interest rates or investment returns, we often encounter expressions involving multiplication and division.
Science: In scientific calculations, we may need to evaluate expressions involving fractions and decimals.
Engineering: In engineering applications, we may need to solve expressions involving multiplication and division to determine the dimensions of a structure or the amount of material required.

Tips and Tricks

Here are some tips and tricks to help you solve expressions involving multiplication and division:

Use the order of operations: Always follow the order of operations to ensure that you evaluate expressions correctly.
Simplify fractions: When simplifying fractions, make sure to divide the numerator and denominator by their greatest common divisor (GCD).
Use decimal equivalents: When working with fractions, you can often use decimal equivalents to simplify calculations.

Practice Problems

Here are some practice problems to help you reinforce your understanding of expressions involving multiplication and division:

$2 \times \frac{4}{3} = ?$
$5 \times \frac{2}{7} = ?$
$3 \times \frac{5}{9} = ?$

Solutions

Here are the solutions to the practice problems:

$2 \times \frac{4}{3} = \frac{8}{3} = 2.67$
$5 \times \frac{2}{7} = \frac{10}{7} = 1.43$
$3 \times \frac{5}{9} = \frac{15}{9} = 1.67$

Conclusion

In conclusion, solving expressions involving multiplication and division requires a clear understanding of the order of operations and the ability to simplify fractions. By following the tips and tricks outlined in this article, you can become more confident in your ability to solve these types of expressions and apply them to real-world applications.

Q: What is the order of operations?

A: The order of operations is a set of rules that dictate the order in which we perform mathematical operations. The order of operations is often remembered using the acronym PEMDAS, which stands for:

Parentheses: Evaluate expressions inside parentheses first.
Exponents: Evaluate any exponential expressions next.
Multiplication and Division: Evaluate multiplication and division operations from left to right.
Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I evaluate an expression involving multiplication and division?

A: To evaluate an expression involving multiplication and division, follow the order of operations. First, multiply the whole number by the numerator of the fraction, and then divide the result by the denominator.

Q: What is the difference between multiplication and division?

A: Multiplication is the process of adding a number a certain number of times, while division is the process of sharing a certain number of items into equal groups.

Q: How do I simplify a fraction?

A: To simplify a fraction, divide the numerator and denominator by their greatest common divisor (GCD). For example, to simplify the fraction $\frac{12}{16}$ , divide both numbers by 4 to get $\frac{3}{4}$ .

Q: What is the decimal equivalent of a fraction?

A: The decimal equivalent of a fraction is a way of expressing the fraction as a decimal number. For example, the decimal equivalent of the fraction $\frac{1}{2}$ is 0.5.

Q: How do I use the order of operations to evaluate an expression?

A: To use the order of operations to evaluate an expression, follow the steps outlined in the order of operations. First, evaluate any expressions inside parentheses, then evaluate any exponential expressions, and finally evaluate any multiplication and division operations from left to right.

Q: What are some common mistakes to avoid when evaluating expressions involving multiplication and division?

A: Some common mistakes to avoid when evaluating expressions involving multiplication and division include:

Not following the order of operations: Make sure to follow the order of operations to ensure that you evaluate expressions correctly.
Not simplifying fractions: Make sure to simplify fractions by dividing the numerator and denominator by their greatest common divisor (GCD).
Not using decimal equivalents: Make sure to use decimal equivalents to simplify calculations.

Q: How do I apply expressions involving multiplication and division to real-world applications?

A: Expressions involving multiplication and division are commonly encountered in real-world applications, such as finance, science, and engineering. To apply these expressions to real-world applications, make sure to follow the order of operations and simplify fractions as needed.

Q: What are some tips and tricks for solving expressions involving multiplication and division?

A: Some tips and tricks for solving expressions involving multiplication and division include:

Use the order of operations: Always follow the order of operations to ensure that you evaluate expressions correctly.
Simplify fractions: Make sure to simplify fractions by dividing the numerator and denominator by their greatest common divisor (GCD).
Use decimal equivalents: Make sure to use decimal equivalents to simplify calculations.

Q: How do I practice solving expressions involving multiplication and division?

A: To practice solving expressions involving multiplication and division, try the following:

Practice problems: Try solving practice problems involving multiplication and division.
Real-world applications: Apply expressions involving multiplication and division to real-world applications.
Online resources: Use online resources, such as calculators and worksheets, to practice solving expressions involving multiplication and division.

Q: What are some common expressions involving multiplication and division that I should know?

A: Some common expressions involving multiplication and division that you should know include:

$2 \times \frac{4}{3} = ?$
$5 \times \frac{2}{7} = ?$
$3 \times \frac{5}{9} = ?$

Q: How do I solve expressions involving multiplication and division with negative numbers?

A: To solve expressions involving multiplication and division with negative numbers, follow the same steps as you would with positive numbers. However, make sure to follow the rules of multiplication and division with negative numbers, which are:

$(-a) \times (-b) = ab$
$(-a) \times b = -ab$
$a \times (-b) = -ab$
$\frac{-a}{b} = -\frac{a}{b}$

Q: How do I solve expressions involving multiplication and division with decimals?

A: To solve expressions involving multiplication and division with decimals, follow the same steps as you would with fractions. However, make sure to use decimal equivalents to simplify calculations.

Q: What are some common mistakes to avoid when solving expressions involving multiplication and division with decimals?

A: Some common mistakes to avoid when solving expressions involving multiplication and division with decimals include:

Not using decimal equivalents: Make sure to use decimal equivalents to simplify calculations.
Not following the order of operations: Make sure to follow the order of operations to ensure that you evaluate expressions correctly.
Not simplifying fractions: Make sure to simplify fractions by dividing the numerator and denominator by their greatest common divisor (GCD).