Solve Fraction Multiplication: 2/4 × 4/5 Step-by-Step

Q: Can I simplify before multiplying to make it easier?

Absolutely! You can cancel common factors first: $ \frac{2}{4} \times \frac{4}{5} $ - notice the 4s cancel, leaving $ \frac{2}{5} $ directly!

Q: What if one of my fractions is a whole number?

Write the whole number as a fraction over 1. For example, $ 3 = \frac{3}{1} $, then multiply normally: $ \frac{3}{1} \times \frac{2}{5} = \frac{6}{5} $.

Fraction Multiplication with Simplification

$\frac{2}{4}\times\frac{4}{5}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's solve this problem together.

00:07 First, multiply the numerator by the numerator, and the denominator by the denominator.

00:12 Now, let's calculate the multiplications carefully.

00:17 After that, reduce the fraction as much as possible.

00:21 Remember to divide both the numerator and denominator by the same number.

00:28 And there you have it, this is the solution to our question!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\frac{2}{4}\times\frac{4}{5}=$

Step-by-step solution

To solve the problem of multiplying the fractions $\frac{2}{4}$ and $\frac{4}{5}$ , follow these steps:

Step 1: Multiply the numerators. We have the numerators $2$ and $4$ , so we calculate $2 \times 4 = 8$ .
Step 2: Multiply the denominators. We have the denominators $4$ and $5$ , so we calculate $4 \times 5 = 20$ .
Step 3: Form the new fraction using the results from Steps 1 and 2. This gives us $\frac{8}{20}$ .
Step 4: Simplify the fraction $\frac{8}{20}$ . The greatest common divisor (GCD) of $8$ and $20$ is $4$ .
Step 5: Divide both the numerator and the denominator by their GCD, $4$ : $\frac{8 \div 4}{20 \div 4} = \frac{2}{5}$ .

Therefore, the simplified product of $\frac{2}{4}$ and $\frac{4}{5}$ is $\frac{2}{5}$ .

Final Answer

$\frac{2}{5}$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply numerators together and denominators together
Technique: $2 \times 4 = 8$ and $4 \times 5 = 20$ gives $\frac{8}{20}$
Check: Simplify by dividing both parts by GCD: $\frac{8÷4}{20÷4} = \frac{2}{5}$ ✓

Common Mistakes

Avoid these frequent errors

Adding numerators and denominators instead of multiplying
Don't add $2+4 = 6$ and $4+5 = 9$ to get $\frac{6}{9}$ ! This confuses fraction multiplication with addition rules. Always multiply straight across: numerator times numerator, denominator times denominator.

Practice Quiz

Test your knowledge with interactive questions

$\frac{2}{3}\times\frac{5}{7}=$

FAQ

Everything you need to know about this question

Why do I multiply straight across instead of finding a common denominator?

Common denominators are only needed for addition and subtraction! When multiplying fractions, you simply multiply numerator × numerator and denominator × denominator.

Do I always need to simplify my answer?

Yes! Always check if your answer can be simplified. Find the greatest common divisor (GCD) of the numerator and denominator, then divide both by that number.

How do I find the GCD of 8 and 20?

List the factors: 8 has factors 1, 2, 4, 8 and 20 has factors 1, 2, 4, 5, 10, 20. The greatest common factor they share is 4.

Can I simplify before multiplying to make it easier?

Absolutely! You can cancel common factors first: $\frac{2}{4} \times \frac{4}{5}$ - notice the 4s cancel, leaving $\frac{2}{5}$ directly!

What if one of my fractions is a whole number?

Write the whole number as a fraction over 1. For example, $3 = \frac{3}{1}$ , then multiply normally: $\frac{3}{1} \times \frac{2}{5} = \frac{6}{5}$ .

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