Solve: (3/5 × 1/2) + 3/10 Fraction Operations

Q: Why do I multiply the fractions first instead of adding them all together?

Because of the order of operations (PEMDAS)! Multiplication and division always come before addition and subtraction. So you must calculate $ \frac{3}{5} \times \frac{1}{2} $ first, then add the result to $ \frac{3}{10} $.

Q: How do I multiply fractions?

Simply multiply the numerators together and the denominators together: $ \frac{3}{5} \times \frac{1}{2} = \frac{3 \times 1}{5 \times 2} = \frac{3}{10} $. No need to find common denominators when multiplying!

Q: What if the denominators are different when I need to add?

Find a common denominator first. In this problem, both $ \frac{3}{10} $ terms already have the same denominator (10), so you can add the numerators directly: $ 3 + 3 = 6 $.

Q: Do I always need to simplify my final answer?

Yes, always simplify! $ \frac{6}{10} $ can be reduced by dividing both numerator and denominator by their greatest common factor (2) to get $ \frac{3}{5} $.

Mixed Operations with Common Denominators

Solve the following:

$\frac{3}{5}\times\frac{1}{2}+\frac{3}{10}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Make sure to multiply numerator by numerator and denominator by denominator

00:10 Calculate the multiplications

00:18 Add with the common denominator

00:23 Calculate the numerator

00:26 Reduce the fraction as much as possible

00:30 Make sure to divide both numerator and denominator

00:33 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 following:

$\frac{3}{5}\times\frac{1}{2}+\frac{3}{10}=$

Step-by-step solution

To solve the given expression, follow these steps:

First, multiply the fractions $\frac{3}{5}$ and $\frac{1}{2}$ :

$\frac{3}{5} \times \frac{1}{2} = \frac{3 \times 1}{5 \times 2} = \frac{3}{10}$

Now, add $\frac{3}{10}$ to the result of the multiplication:

Since the fractions $\frac{3}{10}$ and $\frac{3}{10}$ have the same denominator, we can simply add their numerators:

$\frac{3}{10} + \frac{3}{10} = \frac{3 + 3}{10} = \frac{6}{10}$

Simplify $\frac{6}{10}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 2:

$\frac{6}{10} = \frac{6 \div 2}{10 \div 2} = \frac{3}{5}$

Therefore, the solution to the problem is $\frac{3}{5}$ .

Final Answer

$\frac{3}{5}$

Key Points to Remember

Essential concepts to master this topic

Order: Always multiply fractions before adding or subtracting
Technique: Convert $\frac{3}{5} \times \frac{1}{2} = \frac{3}{10}$ first
Check: Verify $\frac{3}{10} + \frac{3}{10} = \frac{6}{10} = \frac{3}{5}$ ✓

Common Mistakes

Avoid these frequent errors

Adding all fractions together without multiplying first
Don't add $\frac{3}{5} + \frac{1}{2} + \frac{3}{10}$ directly = wrong answer! This ignores order of operations and gives incorrect results. Always perform multiplication operations before addition or subtraction.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why do I multiply the fractions first instead of adding them all together?

Because of the order of operations (PEMDAS)! Multiplication and division always come before addition and subtraction. So you must calculate $\frac{3}{5} \times \frac{1}{2}$ first, then add the result to $\frac{3}{10}$ .

How do I multiply fractions?

Simply multiply the numerators together and the denominators together: $\frac{3}{5} \times \frac{1}{2} = \frac{3 \times 1}{5 \times 2} = \frac{3}{10}$ . No need to find common denominators when multiplying!

What if the denominators are different when I need to add?

Find a common denominator first. In this problem, both $\frac{3}{10}$ terms already have the same denominator (10), so you can add the numerators directly: $3 + 3 = 6$ .

Do I always need to simplify my final answer?

Yes, always simplify! $\frac{6}{10}$ can be reduced by dividing both numerator and denominator by their greatest common factor (2) to get $\frac{3}{5}$ .

How can I check if my answer is correct?

Work through the problem step by step again, or substitute your answer back into a calculator. For this problem: $\frac{3}{5} \times \frac{1}{2} + \frac{3}{10} = 0.6 \times 0.5 + 0.3 = 0.3 + 0.3 = 0.6 = \frac{3}{5}$ ✓

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