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

Complete the following exercise:

$\frac{1}{2}:\frac{3}{5}=\text{?}$

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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