Solve (3/5 × 2/3 × 2/5): Applying the Substitutive Property

Q: Why do I multiply straight across instead of finding common denominators?

When multiplying fractions, you don't need common denominators! Just multiply numerators together (3×2×2=12) and denominators together (5×3×5=75). Common denominators are only for adding or subtracting fractions.

Q: Can I simplify before multiplying instead?

Yes! You can cancel common factors first: $ \frac{3}{5} \times \frac{2}{3} \times \frac{2}{5} $ - the 3s cancel, giving $ \frac{1}{5} \times 2 \times \frac{2}{5} = \frac{4}{25} $. This often makes calculations easier!

Q: Is there a way to check if my simplification is correct?

Yes! Convert both fractions to decimals: $ \frac{12}{75} = 0.16 $ and $ \frac{4}{25} = 0.16 $. If they're equal, your simplification is correct!

Fraction Multiplication with Simplification

Solve the exercise using the substitutive property:

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve using the distribution law

00:03 Let's use the distribution law and arrange the exercise in a convenient way to solve

00:13 Make sure to multiply numerator by numerator and denominator by denominator

00:20 Calculate the multiplications

00:23 Reduce what's possible

00:28 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the exercise using the substitutive property:

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

Step-by-step solution

To solve the exercise $\frac{3}{5} \times \frac{2}{3} \times \frac{2}{5}$ , we will follow a step-by-step approach:

Step 1: Multiply the numerators:
$3 \times 2 \times 2 = 12$

Step 2: Multiply the denominators:
$5 \times 3 \times 5 = 75$

Step 3: Form the fraction by placing the product of numerators over the product of denominators:
$\frac{12}{75}$

Step 4: Simplify the fraction. We find the greatest common divisor of 12 and 75, which is 3:
Divide the numerator and the denominator by 3:
$\frac{12 \div 3}{75 \div 3} = \frac{4}{25}$

Therefore, the simplified product of the given fractions is $\frac{4}{25}$ .

Final Answer

$\frac{4}{25}$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply numerators together, then multiply denominators together
Technique: Simplify by dividing both by GCD: 12÷3 and 75÷3
Check: Verify $\frac{4}{25}$ cannot be simplified further ✓

Common Mistakes

Avoid these frequent errors

Forgetting to simplify the final fraction
Don't leave your answer as $\frac{12}{75}$ = incorrect final answer! This isn't in simplest form and loses points. Always find the GCD and divide both numerator and denominator to get the simplest form.

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 common denominators?

When multiplying fractions, you don't need common denominators! Just multiply numerators together (3×2×2=12) and denominators together (5×3×5=75). Common denominators are only for adding or subtracting fractions.

How do I find the GCD of 12 and 75?

List the factors: 12 has factors 1, 2, 3, 4, 6, 12 and 75 has factors 1, 3, 5, 15, 25, 75. The greatest common factor they share is 3, so divide both by 3.

Can I simplify before multiplying instead?

Yes! You can cancel common factors first: $\frac{3}{5} \times \frac{2}{3} \times \frac{2}{5}$ - the 3s cancel, giving $\frac{1}{5} \times 2 \times \frac{2}{5} = \frac{4}{25}$ . This often makes calculations easier!

What if I get a different denominator in my final answer?

Double-check your multiplication! The denominators should be 5×3×5=75. If you got something else, you might have added instead of multiplied, or made an arithmetic error.

Is there a way to check if my simplification is correct?

Yes! Convert both fractions to decimals: $\frac{12}{75} = 0.16$ and $\frac{4}{25} = 0.16$ . If they're equal, your simplification is correct!

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