Solve Basic Multiplication: Calculate 8 × 1/2 Step-by-Step

Q: Why don't I multiply 8 by both the numerator and denominator?

Great question! You only multiply by the numerator (top number). The denominator tells you how many parts to divide into. So $ 8 \times \frac{1}{2} $ means "8 groups of one-half" = $ \frac{8}{2} = 4 $.

Q: What's the easiest way to think about this problem?

Think of it as "What's half of 8?" Since $ \frac{1}{2} $ means "one half," you're finding half of 8, which is 4. This makes fraction multiplication much more intuitive!

Q: Do I always get a whole number when multiplying by a fraction?

Not always! You get a whole number when the numerator times the whole number is divisible by the denominator. For example, $ 7 \times \frac{1}{2} = \frac{7}{2} = 3\frac{1}{2} $.

Q: How can I check if my answer is correct?

Use the reverse operation! Since $ 8 \times \frac{1}{2} = 4 $, check by multiplying: $ 4 \times 2 = 8 $ ✓. Or think: "Is 4 half of 8?" Yes!

Q: What if the fraction has a bigger numerator, like 3/2?

Same process! $ 8 \times \frac{3}{2} = \frac{8 \times 3}{2} = \frac{24}{2} = 12 $. You're still multiplying by the numerator first, then dividing by the denominator.

Fraction Multiplication with Whole Numbers

$8\times\frac{1}{2}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Let's raise the product to the numerator

00:07 Let's calculate the product, any number multiplied by 1 always equals itself

00:10 Let's calculate the quotient

00:13 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

$8\times\frac{1}{2}=$

Step-by-step solution

To solve this mathematical problem, we need to multiply a whole number, 8, with the fraction, $\frac{1}{2}$ .

Here are the steps:

Step 1: Identify the given values. The integer is 8 and the fraction is $\frac{1}{2}$ .
Step 2: Apply the multiplication formula for an integer and a fraction: $a \times \frac{b}{c} = \frac{a \times b}{c}$ .
Step 3: Multiply the integer by the numerator of the fraction: $8 \times 1 = 8$ .
Step 4: Divide the result by the denominator of the fraction: $\frac{8}{2} = 4$ .
Step 5: Simplify the fraction if necessary. In this case, $\frac{8}{2}$ simplifies directly to 4.

Therefore, the multiplication of 8 by $\frac{1}{2}$ is $4$ .

In the context of the multiple-choice options provided, the correct answer is choice (4): $4$ .

Final Answer

$4$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply whole number by numerator, then divide by denominator
Technique: $8 \times \frac{1}{2} = \frac{8 \times 1}{2} = \frac{8}{2}$
Check: Verify by thinking: half of 8 is 4 ✓

Common Mistakes

Avoid these frequent errors

Adding instead of multiplying the whole number
Don't add 8 + 1/2 = 8½! This gives a completely wrong result because you're combining terms instead of multiplying. Always multiply the whole number by the numerator: 8 × 1 = 8, then divide by the denominator.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why don't I multiply 8 by both the numerator and denominator?

Great question! You only multiply by the numerator (top number). The denominator tells you how many parts to divide into. So $8 \times \frac{1}{2}$ means "8 groups of one-half" = $\frac{8}{2} = 4$ .

What's the easiest way to think about this problem?

Think of it as "What's half of 8?" Since $\frac{1}{2}$ means "one half," you're finding half of 8, which is 4. This makes fraction multiplication much more intuitive!

Do I always get a whole number when multiplying by a fraction?

Not always! You get a whole number when the numerator times the whole number is divisible by the denominator. For example, $7 \times \frac{1}{2} = \frac{7}{2} = 3\frac{1}{2}$ .

How can I check if my answer is correct?

Use the reverse operation! Since $8 \times \frac{1}{2} = 4$ , check by multiplying: $4 \times 2 = 8$ ✓. Or think: "Is 4 half of 8?" Yes!

What if the fraction has a bigger numerator, like 3/2?

Same process! $8 \times \frac{3}{2} = \frac{8 \times 3}{2} = \frac{24}{2} = 12$ . You're still multiplying by the numerator first, then dividing by the denominator.

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Solve Basic Multiplication: Calculate 8 × 1/2 Step-by-Step

Fraction Multiplication with Whole Numbers

❤️ 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 don't I multiply 8 by both the numerator and denominator?

What's the easiest way to think about this problem?

Do I always get a whole number when multiplying by a fraction?

How can I check if my answer is correct?

What if the fraction has a bigger numerator, like 3/2?

🌟 Unlock Your Math Potential

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