Solve the Expression: 39÷(3x)+y/x÷y/4 Step-by-Step

Q: Why do I change division to multiplication?

Division by a fraction is the same as multiplication by its reciprocal! For example, $ \frac{y}{x} ÷ \frac{y}{4} = \frac{y}{x} \times \frac{4}{y} $. This makes the calculation much clearer.

Q: How do I find the common denominator for these fractions?

Look at the denominators: 3x and x. The least common denominator is 3x because x divides into 3x. Convert $ \frac{4}{x} $ to $ \frac{12}{3x} $ by multiplying top and bottom by 3.

Q: What does the colon (:) mean in math?

The colon (:) is another way to write division! So $ 39:(3x) $ means $ 39 ÷ (3x) $ or $ \frac{39}{3x} $. It's commonly used in some countries instead of the ÷ symbol.

Q: Can I simplify 39/3x differently?

Yes! You can simplify $ \frac{39}{3x} $ to $ \frac{13}{x} $ first (since 39 ÷ 3 = 13). Then add $ \frac{4}{x} $ to get $ \frac{17}{x} $. Both methods work!

Q: What if x equals zero?

Great question! If x = 0, the expression is undefined because we can't divide by zero. In real problems, we assume x ≠ 0 so the expression makes mathematical sense.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:12 Let's solve this!

00:15 First, we write division as a fraction.

00:21 Remember, division is like multiplying by the reciprocal.

00:27 Now, let's factor 39 into 13 times 3.

00:35 Next, we simplify, reducing what we can.

00:50 And that's the solution! Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$39:(x\cdot3)+\frac{y}{x}:\frac{y}{4}=\text{?}$

2

Step-by-step solution

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

Step 1: Simplify each division separately.
Step 2: Combine the results.

Now, let's work through each step:

Step 1: Simplify $39 : (x \cdot 3)$ .

This is equivalent to $\frac{39}{x \cdot 3} = \frac{39}{3x}$ .

Step 2: Simplify $\frac{y}{x} : \frac{y}{4}$ .

This is equivalent to $\frac{y}{x} \times \frac{4}{y} = \frac{4y}{xy} = \frac{4}{x}$ .

Step 3: Add the results from Steps 1 and 2.

We have:

$\frac{39}{3x} + \frac{4}{x}$

Simplifying further, find a common denominator for the fractions, which is $3x$ :

$\frac{39}{3x} + \frac{4 \cdot 3}{3x} = \frac{39 + 12}{3x} = \frac{51}{3x} = \frac{17}{x}$ .

Therefore, the solution to the problem is $\frac{17}{x}$ .

3

Final Answer

$\frac{17}{x}$

Key Points to Remember

Essential concepts to master this topic

Order: Solve divisions separately before combining the results
Division Rule: Change $a ÷ b$ to $a \times \frac{1}{b}$ for clarity
Check: Substitute final answer back: $\frac{39}{3x} + \frac{4}{x} = \frac{17}{x}$ ✓

Common Mistakes

Avoid these frequent errors

Adding fractions without common denominators
Don't add $\frac{39}{3x} + \frac{4}{x}$ directly = wrong answer! The denominators 3x and x are different, so you can't combine them yet. Always find a common denominator first: convert $\frac{4}{x}$ to $\frac{12}{3x}$ , then add.

Practice Quiz

Test your knowledge with interactive questions

$70:(14\times5)=$

FAQ

Everything you need to know about this question

Why do I change division to multiplication?

+

Division by a fraction is the same as multiplication by its reciprocal! For example, $\frac{y}{x} ÷ \frac{y}{4} = \frac{y}{x} \times \frac{4}{y}$ . This makes the calculation much clearer.

How do I find the common denominator for these fractions?

+

Look at the denominators: 3x and x. The least common denominator is 3x because x divides into 3x. Convert $\frac{4}{x}$ to $\frac{12}{3x}$ by multiplying top and bottom by 3.

What does the colon (:) mean in math?

+

The colon (:) is another way to write division! So $39:(3x)$ means $39 ÷ (3x)$ or $\frac{39}{3x}$ . It's commonly used in some countries instead of the ÷ symbol.

Can I simplify 39/3x differently?

+

Yes! You can simplify $\frac{39}{3x}$ to $\frac{13}{x}$ first (since 39 ÷ 3 = 13). Then add $\frac{4}{x}$ to get $\frac{17}{x}$ . Both methods work!

What if x equals zero?

+

Great question! If x = 0, the expression is undefined because we can't divide by zero. In real problems, we assume x ≠ 0 so the expression makes mathematical sense.

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Solve the Expression: 39÷(3x)+y/x÷y/4 Step-by-Step

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