Multiply Fractions Khan Academy? Step-by-Step Guide

If you searched “multiply fractions Khan Academy,” you’re likely looking for a clear, step-by-step method to multiply fractions, similar to the lessons on Khan Academy. This guide explains the exact process, shows worked examples, and covers common mistakes, so you can multiply any fractions confidently.

Formula

To multiply two fractions, multiply the numerators (top numbers) together and multiply the denominators (bottom numbers) together. The formula is:

(a/b) × (c/d) = (a × c) / (b × d)

• a = numerator of the first fraction
• b = denominator of the first fraction (cannot be zero)
• c = numerator of the second fraction
• d = denominator of the second fraction (cannot be zero)

The result is a new fraction. You can simplify it if the numerator and denominator share a common factor.

Worked Example

Using the calculator defaults: multiply 2/3 by 4/5.

1. Multiply the numerators: 2 × 4 = 8
2. Multiply the denominators: 3 × 5 = 15
3. Write the product: 8/15
4. Check if it simplifies: 8 and 15 have no common factors (other than 1), so 8/15 is already in simplest form.

The calculator gives 8/15 as the fraction and 0.5333 as the decimal.

Why Multiplying Fractions Is Easier Than Adding

Unlike addition or subtraction, multiplication does not require a common denominator. You simply multiply straight across. This is because a fraction represents a part of a whole, and multiplying two fractions means finding a part of a part. For example, 1/2 × 1/4 means “half of a quarter,” which is 1/8.

How to Multiply Mixed Numbers and Whole Numbers

Khan Academy lessons often include mixed numbers and whole numbers. Here’s how to handle them:

• Whole numbers: Write the whole number as a fraction with denominator 1. For example, 3 × 2/5 = 3/1 × 2/5 = 6/5.
• Mixed numbers: Convert to improper fractions first. For example, 1 1/2 = 3/2, then multiply as usual.

Simplifying Before or After Multiplying

You can simplify the fractions before multiplying (cross-cancel) or simplify the final answer. Both methods give the same result. Cross-canceling can make numbers smaller and easier to multiply. For example, 2/3 × 3/4: cancel the 3s and the 2 with 4, leaving 1/1 × 1/2 = 1/2. If you multiply first, you get 6/12, which simplifies to 1/2.

Common Mistakes and How to Avoid Them

• Adding denominators: Remember, you multiply denominators, not add them.
• Forgetting to simplify: Always check if the product can be reduced.
• Mixed number errors: Do not multiply the whole number and fraction separately; convert to an improper fraction first.
• Zero denominator: A fraction with zero denominator is undefined. Ensure no denominator is zero.

Why This Method Works

Multiplying fractions is based on the idea of scaling. When you multiply by a fraction less than 1, the result is smaller than the original. For example, 1/2 × 1/2 = 1/4. This is because you are taking a part of a part. The denominator tells you into how many equal parts the whole is divided, and the numerator tells you how many of those parts you have. Multiplying numerators counts the total parts you have, and multiplying denominators counts the total number of equal parts in the new whole.

Frequently Asked Questions

Do I need a common denominator to multiply fractions?

No. A common denominator is only needed for adding or subtracting fractions. For multiplication, simply multiply the numerators and denominators directly.

How do I multiply three fractions?

Multiply all three numerators together and all three denominators together. For example, 1/2 × 2/3 × 3/4 = (1×2×3) / (2×3×4) = 6/24, which simplifies to 1/4.

What if the fractions have different denominators?

It doesn’t matter. Different denominators are fine for multiplication. Just multiply across.

How do I multiply a fraction by a whole number?

Write the whole number as a fraction with denominator 1. For example, 5 × 3/4 = 5/1 × 3/4 = 15/4, which is 3 3/4.

Can I cross-cancel before multiplying?

Yes. Cross-canceling (dividing a numerator and a denominator by a common factor) before multiplying makes the numbers smaller and the math easier. It does not change the final answer.

What is the difference between multiplying fractions and multiplying decimals?

Multiplying decimals is another way to represent the same operation, but fractions give exact values. For example, 1/3 × 1/3 = 1/9 exactly, while 0.333 × 0.333 = 0.110889 (a rounded decimal).

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in a | First numerator | - | 2 | 0
in b | First denominator | - | 3 | 0
in c | Second numerator | - | 4 | 0
in d | Second denominator | - | 5 | 0
out frac | Product (as fraction) | - | (a*c) / (b*d) | 0
out dec | Product (decimal) | - | (a*c) / (b*d) | 4