Solve Fraction Multiplication: 2/3 × 3/4 Step-by-Step

Q: Do I multiply across like this for all fraction problems?

This multiply across method only works for multiplication! For addition or subtraction, you need a common denominator first. Make sure you're doing the right operation.

Q: What if the numbers don't simplify evenly?

Sometimes fractions don't simplify! If the GCD is 1, then your fraction is already in simplest form. For example, $ \frac{3}{8} $ can't be simplified further.

Q: Can I cancel numbers before multiplying?

Yes! You can cross-cancel before multiplying. In $ \frac{2}{3} \times \frac{3}{4} $, the 3's cancel out, giving you $ \frac{2}{1} \times \frac{1}{4} = \frac{2}{4} = \frac{1}{2} $.

Q: What if I get confused about which numbers go where?

Remember the pattern: $ \frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d} $. Top numbers (numerators) multiply together, bottom numbers (denominators) multiply together.

Fraction Multiplication with Simplification Steps

$\frac{2}{3}\times\frac{3}{4}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's solve this together.

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

00:13 Now, let's reduce as much as we can.

00:18 Try to simplify the fraction further if possible.

00:22 Remember to divide both the numerator and the denominator by their greatest common factor.

00:29 And that's how we find the solution to our question!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\frac{2}{3}\times\frac{3}{4}=$

Step-by-step solution

To solve this problem, follow these steps:

Step 1: Multiply the numerators of the fractions. The numerators are $2$ and $3$ .
Step 2: Multiply the denominators of the fractions. The denominators are $3$ and $4$ .
Step 3: Simplify the resulting fraction if necessary.

Now, let us perform the multiplication:

Step 1: Multiply the numerators:

$2 \times 3 = 6$

Step 2: Multiply the denominators:

$3 \times 4 = 12$

So, the product of the fractions is:

$\frac{6}{12}$

Step 3: Simplify the fraction. To simplify, find the greatest common divisor (GCD) of 6 and 12, which is 6. Divide both numerator and denominator by 6:

$\frac{6 \div 6}{12 \div 6} = \frac{1}{2}$

Therefore, the simplified product of the fractions $\frac{2}{3} \times \frac{3}{4}$ is $\frac{1}{2}$ .

This matches choice 4, which is $\frac{1}{2}$ .

Final Answer

$\frac{1}{2}$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply numerators together, then multiply denominators together
Technique: $2 \times 3 = 6$ and $3 \times 4 = 12$ gives $\frac{6}{12}$
Check: Always simplify by dividing by GCD: $\frac{6}{12} = \frac{1}{2}$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to simplify the final answer
Don't leave your answer as $\frac{6}{12}$ = incomplete solution! This isn't in simplest form and may not match answer choices. Always find the GCD and divide both numerator and denominator to get $\frac{1}{2}$ .

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Do I multiply across like this for all fraction problems?

This multiply across method only works for multiplication! For addition or subtraction, you need a common denominator first. Make sure you're doing the right operation.

What if the numbers don't simplify evenly?

Sometimes fractions don't simplify! If the GCD is 1, then your fraction is already in simplest form. For example, $\frac{3}{8}$ can't be simplified further.

How do I find the GCD quickly?

List the factors of both numbers and find the largest one they share. For 6 and 12: factors of 6 are 1,2,3,6 and factors of 12 are 1,2,3,4,6,12. The largest common factor is 6.

Can I cancel numbers before multiplying?

Yes! You can cross-cancel before multiplying. In $\frac{2}{3} \times \frac{3}{4}$ , the 3's cancel out, giving you $\frac{2}{1} \times \frac{1}{4} = \frac{2}{4} = \frac{1}{2}$ .

What if I get confused about which numbers go where?

Remember the pattern: $\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$ . Top numbers (numerators) multiply together, bottom numbers (denominators) multiply together.

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