Multiplying the Simplified Fraction by 3

Oct 13, 2025 by talynt.org 130 views

Understanding the Problem

To find the simplest form of the expression $\frac{2}{6} \cdot 3$ , we need to follow the order of operations (PEMDAS) and simplify the fraction before multiplying it by 3. The expression involves a fraction and a whole number, so we will first simplify the fraction and then multiply it by 3.

Simplifying the Fraction

The fraction $\frac{2}{6}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 2 and 6 is 2. So, we can simplify the fraction as follows:

$\frac{2}{6} = \frac{2 ÷ 2}{6 ÷ 2} = \frac{1}{3}$

Multiplying the Simplified Fraction by 3

Now that we have simplified the fraction to $\frac{1}{3}$ , we can multiply it by 3:

$\frac{1}{3} \cdot 3 = 1$

Conclusion

Therefore, the simplest form of the expression $\frac{2}{6} \cdot 3$ is 1.

Why is the Answer 1?

The answer is 1 because when we simplify the fraction $\frac{2}{6}$ to $\frac{1}{3}$ , we are essentially canceling out the 3 in the denominator. When we multiply $\frac{1}{3}$ by 3, the 3 in the denominator cancels out the 3 in the numerator, leaving us with 1.

What is the Greatest Common Divisor (GCD)?

The GCD of two numbers is the largest number that divides both numbers without leaving a remainder. In the case of 2 and 6, the GCD is 2 because 2 is the largest number that divides both 2 and 6 without leaving a remainder.

How to Simplify a Fraction

To simplify a fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator and divide both numbers by the GCD. This will give us a simplified fraction with the same value as the original fraction.

Why is Simplifying Fractions Important?

Simplifying fractions is important because it helps us to work with fractions more easily and accurately. When we simplify a fraction, we are essentially canceling out any common factors between the numerator and the denominator, which makes it easier to perform operations with fractions.

What is the Order of Operations (PEMDAS)?

The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The acronym PEMDAS stands for:

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

How to Apply the Order of Operations

To apply the order of operations, we need to follow the rules in the correct order. For example, if we have the expression $3 \cdot 2 + 12 \div 4$ , we would follow the order of operations as follows:

Evaluate the expression inside the parentheses (none in this case).
Evaluate any exponential expressions (none in this case).
Evaluate any multiplication and division operations from left to right:
- $3 \cdot 2 = 6$
- $12 \div 4 = 3$
Finally, evaluate any addition and subtraction operations from left to right:
- $6 + 3 = 9$

Conclusion

In conclusion, the simplest form of the expression $\frac{2}{6} \cdot 3$ is 1. We simplified the fraction $\frac{2}{6}$ to $\frac{1}{3}$ and then multiplied it by 3 to get 1. This problem required us to apply the order of operations and simplify a fraction, which are important skills in mathematics.

Final Answer

The final answer is B. 1.

Understanding the Problem

Q&A Section

Q: What is the greatest common divisor (GCD) of 2 and 6?

A: The GCD of 2 and 6 is 2.

Q: How do we simplify a fraction?

A: To simplify a fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator and divide both numbers by the GCD.

Q: Why is simplifying fractions important?

A: Simplifying fractions is important because it helps us to work with fractions more easily and accurately. When we simplify a fraction, we are essentially canceling out any common factors between the numerator and the denominator, which makes it easier to perform operations with fractions.

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The acronym PEMDAS stands for:

Parentheses: Evaluate expressions inside parentheses first.
Exponents: Evaluate any exponential expressions next.
Multiplication and Division: Evaluate any 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 we apply the order of operations?

A: To apply the order of operations, we need to follow the rules in the correct order. For example, if we have the expression $3 \cdot 2 + 12 \div 4$ , we would follow the order of operations as follows:

Evaluate the expression inside the parentheses (none in this case).
Evaluate any exponential expressions (none in this case).
Evaluate any multiplication and division operations from left to right:
- $3 \cdot 2 = 6$
- $12 \div 4 = 3$
Finally, evaluate any addition and subtraction operations from left to right:
- $6 + 3 = 9$

Q: Why is the answer 1?

A: The answer is 1 because when we simplify the fraction $\frac{2}{6}$ to $\frac{1}{3}$ , we are essentially canceling out the 3 in the denominator. When we multiply $\frac{1}{3}$ by 3, the 3 in the denominator cancels out the 3 in the numerator, leaving us with 1.