Solve x(1/3 + 1/2): Step-by-Step Fraction Multiplication

Fraction Addition with Variable Distribution

Solve the following expression:

x(13+12)= x(\frac{1}{3}+\frac{1}{2})=

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:10 Find a common denominator, multiply each fraction by the other's denominator
00:30 Add the fractions
00:36 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following expression:

x(13+12)= x(\frac{1}{3}+\frac{1}{2})=

2

Step-by-step solution

According to the order of operations rules, we will first address the expression in parentheses.

The common denominator between the fractions is 6, so we will multiply each numerator by the number needed to make its denominator reach 6.

We will multiply the first fraction's numerator by 2 and the second fraction's numerator by 3:

(13+12)=1×2+1×36=2+36=56 (\frac{1}{3}+\frac{1}{2})=\frac{1\times2+1\times3}{6}=\frac{2+3}{6}=\frac{5}{6}

Now we have the expression:

x×56= x\times\frac{5}{6}=

We will use the distributive property and get the result:

56x \frac{5}{6}x

3

Final Answer

56x \frac{5}{6}x

Key Points to Remember

Essential concepts to master this topic
  • Order of Operations: Simplify expressions inside parentheses first
  • Technique: Find LCD of 3 and 2, which is 6: 13+12=2+36=56 \frac{1}{3} + \frac{1}{2} = \frac{2+3}{6} = \frac{5}{6}
  • Check: Verify by distributing: x(13+12)=56x x(\frac{1}{3} + \frac{1}{2}) = \frac{5}{6}x

Common Mistakes

Avoid these frequent errors
  • Distributing x before adding fractions
    Don't multiply x by each fraction separately first = x3+x2 \frac{x}{3} + \frac{x}{2} makes it harder! This creates more complex fractions to add. Always follow order of operations: solve parentheses first, then multiply by x.

Practice Quiz

Test your knowledge with interactive questions

\( \frac{2}{4}+\frac{1}{4}= \)\( \)

FAQ

Everything you need to know about this question

Why can't I just distribute x to both fractions first?

+

While mathematically correct, it makes the problem much harder! You'd get x3+x2 \frac{x}{3} + \frac{x}{2} , which requires finding a common denominator with variables. Following order of operations keeps it simple.

How do I find the LCD of 3 and 2?

+

List the multiples of each: 3: 3, 6, 9, 12... and 2: 2, 4, 6, 8... The smallest number that appears in both lists is 6.

What does it mean to 'distribute' the x?

+

Distribution means multiplying x by the entire result in parentheses. Once you get 56 \frac{5}{6} inside the parentheses, you multiply: x×56=56x x \times \frac{5}{6} = \frac{5}{6}x

Why is the answer not just 5/6?

+

The expression asks for x(13+12) x(\frac{1}{3}+\frac{1}{2}) , not just what's in parentheses. You must keep the x as part of your final answer: 56x \frac{5}{6}x

Can I write the answer as 5x/6 instead?

+

Absolutely! Both 56x \frac{5}{6}x and 5x6 \frac{5x}{6} mean exactly the same thing. Choose whichever format your teacher prefers.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Commutative, Distributive and Associative Properties questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations