Verify the Equation: Is (8+3×4)/(6×2+8) = 1?

Q: Why do I multiply 3×4 before adding 8?

The order of operations (PEMDAS) says multiplication comes before addition. So in 8+3×4, you must calculate 3×4=12 first, then 8+12=20.

Q: Can I simplify the fraction before calculating the top and bottom?

No! You must fully evaluate the numerator and denominator separately first. Only after getting $ \frac{20}{20} $ can you simplify to 1.

Q: Why does the order of addition not matter but multiplication order does?

Addition is commutative (8+12 = 12+8), but order of operations still matters! You must do all multiplications before any additions, regardless of position.

Order of Operations with Fraction Verification

Determine if the simplification below is correct:

$\frac{8+3\cdot4}{6\cdot2+8}=1$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Determine if the reduction is correct

00:08 Let's calculate the multiplications

00:23 Use the commutative law and arrange the denominator to match the numerator

00:36 Reduce what's possible, when we reduce the entire fraction we always get 1

00:41 Compare between the expressions

00:45 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

Determine if the simplification below is correct:

$\frac{8+3\cdot4}{6\cdot2+8}=1$

Step-by-step solution

Let's examine the given problem:

$\frac{8+3\cdot4}{6\cdot2+8}\stackrel{?}{= }1$ Note that in the numerator there is a product between the number 8 and the number $3\cdot4$ and in the denominator there is a product between the number 8 and the number $6\cdot2$ , since these two multiplications give the same result:

$3\cdot4=6\cdot2=12$ Both in the numerator and denominator it's the same number:

$8+3\cdot4=6\cdot2+8$ Now we'll remember that dividing a number by itself always yields 1, therefore indeed:

$\frac{8+3\cdot4}{6\cdot2+8}= \frac{8+12}{12+8}\stackrel{!}{= }1$ and thus answer A is the correct answer

Final Answer

Correct

Key Points to Remember

Essential concepts to master this topic

Rule: Follow PEMDAS to evaluate numerator and denominator separately
Technique: Calculate $3\cdot4 = 12$ and $6\cdot2 = 12$ first
Check: Verify both expressions equal 20, so $\frac{20}{20} = 1$ ✓

Common Mistakes

Avoid these frequent errors

Adding before multiplying in expressions
Don't calculate 8+3=11, then 11×4=44! This ignores order of operations and gives $\frac{44}{32} \neq 1$ . Always multiply first: 3×4=12, then add: 8+12=20.

Practice Quiz

Test your knowledge with interactive questions

Determine if the simplification shown below is correct:

$\frac{7}{7\cdot8}=8$

FAQ

Everything you need to know about this question

Why do I multiply 3×4 before adding 8?

The order of operations (PEMDAS) says multiplication comes before addition. So in 8+3×4, you must calculate 3×4=12 first, then 8+12=20.

Can I simplify the fraction before calculating the top and bottom?

No! You must fully evaluate the numerator and denominator separately first. Only after getting $\frac{20}{20}$ can you simplify to 1.

What if the numerator and denominator were different?

Then the fraction wouldn't equal 1! For example, if the numerator was 24 and denominator was 20, you'd get $\frac{24}{20} = \frac{6}{5} = 1.2$ .

How do I check my work on problems like this?

Calculate each part step-by-step: numerator = 8+12=20, denominator = 12+8=20. Since 20÷20=1, the equation is correct!

Why does the order of addition not matter but multiplication order does?

Addition is commutative (8+12 = 12+8), but order of operations still matters! You must do all multiplications before any additions, regardless of position.

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