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

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

When you need to perform calculations involving fractions, one of the fundamental operations is multiplying fractions by whole numbers. This process might seem daunting at first, but with a clear understanding of the steps and the rules involved, you'll find it's quite straightforward.

Step 1: Simplify the fraction

Before you can multiply a fraction by a whole number, make sure the fraction is in its simplest form. This means finding the highest common factor (HCF) for both the numerator and denominator, then dividing both by the HCF.

For example, ( \frac{12}{18} ) can be simplified to ( \frac{2}{3} ) by dividing both the numerator and denominator by their HCF, which is 6 in this case.

Step 2: Multiply the numerator by the whole number

Take the simplified numerator and multiply it by the whole number.

For instance, multiplying ( \frac{2}{3} ) by 5 gives you ( (2 \times 5) = 10 ).

Step 3: Multiply the denominator by the whole number

Next, multiply the simplified denominator by the whole number.

Continuing the example, multiplying ( 3 \times 5 ) gives ( 15 ).

Step 4: Simplify the result

Now, find the highest common factor for the result of the product in the numerator and the product in the denominator, then divide both by this HCF.

Applying this to our example, the result is ( \frac{10}{15} ), and the HCF of 10 and 15 is 5. We can simplify this fraction to ( \frac{2}{3} ), which is the original simplified fraction, confirming our result.

Common pitfalls

One of the most common mistakes when multiplying fractions by whole numbers is forgetting to simplify the fraction before performing the multiplication. This can result in a more complex fraction that's actually equivalent to the original simplified fraction.

Another common mistake is forgetting to multiply both the numerator and the denominator. If you multiply only the numerator, you'll end up with a fraction that's not equivalent to the original fraction and might not reflect the intended result.

Applications

Understanding how to multiply fractions by whole numbers is important in a wide variety of applications, including cooking, carpentry, and science. For instance, in cooking, you might need to convert a recipe that calls for a fraction of an ingredient to a standard unit of measurement. In carpentry, you might need to calculate a fraction of a board's length when building a project. In science, you might need to convert a fraction of a unit of time or distance to a standard unit when conducting an experiment.

Summary

Mastering the art of multiplying fractions by whole numbers is essential when working with fractions. By following the steps and avoiding common pitfalls, you'll be able to perform these calculations with ease.

Practice problems

1. Multiply ( \frac{3}{5} ) by 8.
2. Multiply ( \frac{1}{4} ) by 12.
3. Multiply ( \frac{4}{7} ) by 9.

Confidence: 95%