Multiplying Fractions with Whole Numbers

Multiplying fractions by whole numbers is a simple process. Here’s a step-by- step guide to help you understand and perform this operation easily.

Step 1: Understand the Problem

When you multiply a fraction by a whole number, you are essentially adding the fraction to itself multiple times. For example:

• 34×2\frac{3}{4}\times 243​×2 means 34+34\frac{3}{4}+\frac{3}{4}43​+43​.

Step 2: Convert the Whole Number to a Fraction

Write the whole number as a fraction by placing it over 1:

• 2=212=\frac{2}{1}2=12​

Step 3: Multiply the Numerators and Denominators

Multiply the numerators (top numbers) together and the denominators (bottom numbers) together:

34×21=3×24×1=64\frac{3}{4}\times \frac{2}{1}=\frac{3\times 2}{4\times 1}=\frac{6}{4}43​×12​=4×13×2​=46​

Step 4: Simplify the Fraction (if possible)

Simplify 64\frac{6}{4}46​ by dividing numerator and denominator by their greatest common divisor (GCD), which is 2:

6÷24÷2=32\frac{6\div 2}{4\div 2}=\frac{3}{2}4÷26÷2​=23​

Step 5: Convert to Mixed Number (optional)

Since 32\frac{3}{2}23​ is an improper fraction (numerator > denominator), you can write it as a mixed number:

32=112\frac{3}{2}=1\frac{1}{2}23​=121​

Summary

Step| Action| Example
---|---|---
1| Convert whole number to fraction| 2=212=\frac{2}{1}2=12​
2| Multiply numerators| 3×2=63\times 2=63×2=6
3| Multiply denominators| 4×1=44\times 1=44×1=4
4| Simplify the fraction| 64=32\frac{6}{4}=\frac{3}{2}46​=23​
5| Convert to mixed number (optional)| 32=112\frac{3}{2}=1\frac{1}{2}23​=121​

If you want, I can provide more examples or practice problems!