Solve: 1/3 × 3/4 × 1/3 Using the Substitutive Property

Q: What is the substitutive property in fraction multiplication?

The substitutive property means you can substitute equivalent expressions. Here, you substitute the multiplication of three fractions with one simplified result: $ \frac{1}{3} \times \frac{3}{4} \times \frac{1}{3} = \frac{1}{12} $.

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

Unlike addition and subtraction, multiplication of fractions doesn't need common denominators! You simply multiply numerator × numerator and denominator × denominator. Common denominators are only needed when adding or subtracting fractions.

Q: How do I know what the greatest common divisor (GCD) is?

Find the largest number that divides both the numerator and denominator evenly. For $ \frac{3}{36} $, try dividing both by 3: 3÷3=1 and 36÷3=12, so GCD is 3.

Q: Can I simplify before multiplying instead of after?

Yes! This can make calculations easier. You can cancel common factors between any numerator and any denominator before multiplying. For example, the 3 in $ \frac{3}{4} $ cancels with one 3 in the denominators.

Q: What if I get a different answer than the choices given?

Double-check your work! Make sure you multiplied correctly and simplified fully. The most common errors are adding instead of multiplying denominators, or forgetting to simplify the final fraction.

Fraction Multiplication with Substitutive Property

Solve the exercise using the substitutive property:

$\frac{1}{3}\times\frac{3}{4}\times\frac{1}{3}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve using the substitution method

00:03 We'll use the substitution method and arrange the exercise in a way that's convenient to solve

00:12 Make sure to multiply numerator by numerator and denominator by denominator

00:20 Reduce what we can

00:23 Calculate the multiplications

00:27 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:

$\frac{1}{3}\times\frac{3}{4}\times\frac{1}{3}=$

Step-by-step solution

To solve this problem, follow these steps:

Step 1: Identify the fractions to be multiplied: $\frac{1}{3}$ , $\frac{3}{4}$ , $\frac{1}{3}$ .
Step 2: Multiply the numerators: $1 \times 3 \times 1 = 3$ .
Step 3: Multiply the denominators: $3 \times 4 \times 3 = 36$ .
Step 4: Write the resulting fraction: $\frac{3}{36}$ .
Step 5: Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 3: $\frac{3 \div 3}{36 \div 3} = \frac{1}{12}$ .

The solution to the problem is therefore $\frac{1}{12}$ .

Final Answer

$\frac{1}{12}$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply numerators together and denominators together separately
Technique: $\frac{1}{3} \times \frac{3}{4} \times \frac{1}{3} = \frac{1 \times 3 \times 1}{3 \times 4 \times 3} = \frac{3}{36}$
Check: Simplify by dividing by GCD: $\frac{3}{36} = \frac{1}{12}$ ✓

Common Mistakes

Avoid these frequent errors

Adding denominators instead of multiplying
Don't add denominators like 3 + 4 + 3 = 10 to get $\frac{3}{10}$ ! This completely changes the value and gives wrong answers. Always multiply all numerators together and all denominators together when multiplying fractions.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

What is the substitutive property in fraction multiplication?

The substitutive property means you can substitute equivalent expressions. Here, you substitute the multiplication of three fractions with one simplified result: $\frac{1}{3} \times \frac{3}{4} \times \frac{1}{3} = \frac{1}{12}$ .

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

Unlike addition and subtraction, multiplication of fractions doesn't need common denominators! You simply multiply numerator × numerator and denominator × denominator. Common denominators are only needed when adding or subtracting fractions.

How do I know what the greatest common divisor (GCD) is?

Find the largest number that divides both the numerator and denominator evenly. For $\frac{3}{36}$ , try dividing both by 3: 3÷3=1 and 36÷3=12, so GCD is 3.

Can I simplify before multiplying instead of after?

Yes! This can make calculations easier. You can cancel common factors between any numerator and any denominator before multiplying. For example, the 3 in $\frac{3}{4}$ cancels with one 3 in the denominators.

What if I get a different answer than the choices given?

Double-check your work! Make sure you multiplied correctly and simplified fully. The most common errors are adding instead of multiplying denominators, or forgetting to simplify the final fraction.

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