Fraction Wizardry: How to Multiply Fractions and Whole Numbers

1. Multiplication of Fractions and Whole Numbers: The Basics

When you multiply a fraction and a whole number, you are basically finding a fraction of a whole number. The process is straightforward: multiply the numerator (top part of the fraction) with the whole number and keep the denominator the same.

Step-by-Step Guide: Multiplying Fractions and Whole Numbers

Step 1: Convert the Whole Number into a Fraction

Every whole number can be written as a fraction. For example, \(3\) can be written as \(\frac{3}{1}\). This step is optional, as you can directly multiply the whole number with the numerator, but it can make understanding the process easier.

Step 2: Multiply the Numerators

Multiply the numerator of the fraction by the whole number (which is the numerator of the new fraction you created). This will give you the numerator of your answer.

Step 3: Carry the Denominator Over

The denominator of your fraction stays the same.

Step 4: Simplify if Necessary

If your fraction can be simplified, do so. This involves dividing both the numerator and denominator by their greatest common factor.

Let’s put these steps into practice:

Suppose you have to multiply \(\frac{2}{3}\) by \(3\).

1. You can write \(3\) as \(\frac{3}{1}\).
2. Next, you multiply the numerators: \(2\times 3 = 6\).
3. The denominator remains the same as the original fraction, so it’s \(3\).
4. Your fraction is now \(\frac{6}{3}\). This can be simplified by dividing both the numerator and denominator by \(3\), giving you \(\frac{2}{1}\), or just \(2\).

So, \(\frac{2}{3}\) of \(3\) is \(2\)!

And that’s it! Multiplying fractions and whole numbers isn’t that scary, right? As with any mathematical concept, practice is key, so try out as many problems as you can to solidify your understanding. Happy learning!