Solve: (1/4 × 1/2) + 3/8 - Mixed Fraction Operations

Q: Why do I multiply first instead of going left to right?

Order of operations (PEMDAS) requires multiplication before addition! Even though multiplication comes after addition in the expression, it has higher priority and must be done first.

Q: How do I multiply fractions quickly?

Multiply straight across: numerator × numerator over denominator × denominator. So $ \frac{1}{4} \times \frac{1}{2} = \frac{1 \times 1}{4 \times 2} = \frac{1}{8} $.

Q: What if the fractions don't have the same denominator when adding?

Find a common denominator first! In this problem, $ \frac{1}{8} $ and $ \frac{3}{8} $ already have the same denominator (8), so you can add directly.

Q: Do I need to simplify my final answer?

Always simplify to lowest terms! $ \frac{4}{8} $ simplifies to $ \frac{1}{2} $ by dividing both numerator and denominator by their GCD (4).

Q: Can I use decimals instead of fractions?

You could convert to decimals, but fractions are more accurate for this type of problem. Decimals might introduce rounding errors, especially with repeating decimals.

Fraction Operations with Order Precedence

$\frac{1}{4}\times\frac{1}{2}+\frac{3}{8}=$

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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

00:06 Calculate the multiplications

00:18 Connect with the common denominator

00:21 Calculate the numerator

00:26 Reduce the fraction as much as possible

00:30 Make sure to divide both numerator and denominator

00:34 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\frac{1}{4}\times\frac{1}{2}+\frac{3}{8}=$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Multiply the given fractions.
Step 2: Simplify if necessary.
Step 3: Perform the addition of resulting fractions.

Now, let's work through each step:

Step 1: Multiply the fractions:
$\frac{1}{4} \times \frac{1}{2} = \frac{1 \times 1}{4 \times 2} = \frac{1}{8}$

Step 2: We find that the result is already simplified.

Step 3: Add $\frac{1}{8}$ to $\frac{3}{8}$ :
$\frac{1}{8} + \frac{3}{8} = \frac{1 + 3}{8} = \frac{4}{8} = \frac{1}{2}$

The fractions have the same denominator, allowing for direct addition.

Therefore, the solution to the problem is $\frac{1}{2}$ .

Final Answer

$\frac{1}{2}$

Key Points to Remember

Essential concepts to master this topic

Order Rule: Always multiply fractions before adding or subtracting
Technique: $\frac{1}{4} \times \frac{1}{2} = \frac{1}{8}$ then add to $\frac{3}{8}$
Check: Final answer $\frac{1}{2}$ equals $\frac{4}{8}$ in lowest terms ✓

Common Mistakes

Avoid these frequent errors

Adding all fractions first without following order of operations
Don't add $\frac{1}{4} + \frac{1}{2} + \frac{3}{8}$ first = $\frac{9}{8}$ wrong answer! This ignores multiplication priority and changes the problem completely. Always multiply $\frac{1}{4} \times \frac{1}{2}$ first, then add the result to $\frac{3}{8}$ .

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 first instead of going left to right?

Order of operations (PEMDAS) requires multiplication before addition! Even though multiplication comes after addition in the expression, it has higher priority and must be done first.

How do I multiply fractions quickly?

Multiply straight across: numerator × numerator over denominator × denominator. So $\frac{1}{4} \times \frac{1}{2} = \frac{1 \times 1}{4 \times 2} = \frac{1}{8}$ .

What if the fractions don't have the same denominator when adding?

Find a common denominator first! In this problem, $\frac{1}{8}$ and $\frac{3}{8}$ already have the same denominator (8), so you can add directly.

Do I need to simplify my final answer?

Always simplify to lowest terms! $\frac{4}{8}$ simplifies to $\frac{1}{2}$ by dividing both numerator and denominator by their GCD (4).

Can I use decimals instead of fractions?

You could convert to decimals, but fractions are more accurate for this type of problem. Decimals might introduce rounding errors, especially with repeating decimals.

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Solve: (1/4 × 1/2) + 3/8 - Mixed Fraction Operations

Fraction Operations with Order Precedence

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do I multiply first instead of going left to right?

How do I multiply fractions quickly?

What if the fractions don't have the same denominator when adding?

Do I need to simplify my final answer?

Can I use decimals instead of fractions?

🌟 Unlock Your Math Potential

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