Solve the Equation: 3x Divided by 2t and 4z

Fraction Simplification with Multiple Variables

Solve the following equation:

3x/(2t4z)=? 3x/(2t\cdot4z)=\text{?}

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Step-by-step video solution

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00:00 Solve
00:03 Let's write division as a fraction
00:09 Let's calculate 2 times 4
00:19 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

Solve the following equation:

3x/(2t4z)=? 3x/(2t\cdot4z)=\text{?}

2

Step-by-step solution

First let's rewrite the expression as a fraction:

3x2t×4z= \frac{3x}{2t\times4z}=

We should note that since there is only a multiplication operation in the numerator of the fraction, we will multiply the coefficients together:

3x2×4×t×z=3x8tz \frac{3x}{2\times4\times t\times z}=\frac{3x}{8tz}

3

Final Answer

3x8tz \frac{3x}{8tz}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Multiply coefficients in the denominator before simplifying fractions
  • Technique: Calculate 2×4=8, so 3x2t4z=3x8tz \frac{3x}{2t \cdot 4z} = \frac{3x}{8tz}
  • Check: Verify denominator has all original variables t and z ✓

Common Mistakes

Avoid these frequent errors
  • Adding instead of multiplying coefficients in denominator
    Don't write 2t·4z as (2+4)tz = 6tz! This gives the wrong fraction 3x/6tz instead of 3x/8tz. Multiplication gives different results than addition. Always multiply coefficients: 2×4 = 8, so the denominator becomes 8tz.

Practice Quiz

Test your knowledge with interactive questions

\( 100-(5+55)= \)

FAQ

Everything you need to know about this question

Why do I multiply 2×4 in the denominator?

+

When you have multiplication in the denominator like 2t·4z, you must multiply the numbers together: 2×4=8. The variables t and z stay as they are, giving you 8tz 8tz .

What's the difference between 2t·4z and 2t+4z?

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The · symbol means multiplication, so 2t·4z = 8tz. The + symbol means addition, so 2t+4z cannot be simplified further. Always pay attention to the operation!

Can I cancel any terms in this fraction?

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In 3x8tz \frac{3x}{8tz} , you can only cancel if the same variable or number appears in both numerator and denominator. Here, x is only on top, while t and z are only on bottom, so no canceling is possible.

How do I know when a fraction is fully simplified?

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A fraction is simplified when:

  • No common factors exist between numerator and denominator
  • All multiplication is completed (like 2×4=8)
  • No like terms can be combined

What if there were more variables in the denominator?

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The same rule applies! Multiply all the coefficients (numbers) together, then keep all the variables. For example: 2a3b4c=24abc 2a \cdot 3b \cdot 4c = 24abc .

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