What is 3/2 Divided by 3?

What is 3/2 Divided by 3?

To divide 3/2 by 3, you can convert the whole number 3 into a fraction with a denominator of 1, making it 3/1. Then, you can perform the division as follows:

(3/2) ÷ (3/1) = (3/2) * (1/3) = (3 * 1) / (2 * 3) = 3/6.

Now, simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 3:

(3/3) / (6/3) = 1/2.

So, 3/2 divided by 3 is equal to 1/2.

Dividing Fractions by Whole Numbers

Dividing a fraction by a whole number is a foundational math skill. It involves taking a fraction and determining how many times a whole number can divide into it. This relies on understanding the meaning of division as splitting into equal parts.

For example, if we divide the fraction 3/2 by the whole number 3, this means we want to split 3/2 into 3 equal parts. Let’s walk through the steps to solve this problem:

1. Rewrite the whole number as a fraction with the same denominator as the dividend. Here, 3 can be rewritten as 3/2.
2. Divide the numerator of the dividend fraction by the numerator of the re-written divisor fraction. 3 (numerator of 3/2) divided by 3 (numerator of 3/2) equals 1.
3. The denominator of the quotient fraction remains the same as the dividend and divisor. So our quotient so far is 1/2.
4. Simplify the quotient fraction if possible. 1/2 cannot be simplified further.

Therefore, the complete solution is: 3/2 ÷ 3 = 1/2

Understanding the Process

Dividing a fraction by a whole number splits the numerator into the specified number of parts based on the whole number divisor.

For example, dividing 3/2 by 3 splits the numerator of 3 into 3 equal parts. Each part has a size of 3/3 = 1.

Keeping the same denominator of 2 gives us the quotient of 1/2. This makes sense because 1/2 goes into 3/2 a total of 3 times.

Checking Our Work

We can easily verify the solution by multiplying the quotient by the divisor to see if it equals the original dividend:

1/2 x 3 = 3/2

Since the product equals the dividend, this confirms that dividing 3/2 by 3 gives us 1/2.

Being comfortable dividing fractions by whole numbers provides a solid foundation for more advanced fraction arithmetic. It connects to the visual meaning of division as splitting into equal parts.

In summary, dividing a fraction by a whole involves rewriting the whole as a fraction with the same denominator, dividing the numerators, and keeping the same denominator for the final quotient.