Solve the Ratio Equation: 4a:a+6 Using Proportion Method

Q: What does the colon symbol mean in math?

The colon : means division or "divided by." So 4a:a is the same as $ \frac{4a}{a} $ or 4a ÷ a.

Q: What if 'a' equals zero?

Good question! If a = 0, then we'd have $ \frac{0}{0} $ which is undefined. In ratio problems, we assume variables don't equal zero unless stated otherwise.

Q: Is this the same as solving an equation?

Not exactly! Here we're simplifying an expression, not solving for a specific value of 'a'. We're finding what the ratio equals for any non-zero value of a.

Ratio Simplification with Variable Terms

$4a:a+6=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Always solve multiplication and division before addition and subtraction

00:06 Write division as a fraction, and reduce what's possible

00:11 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

$4a:a+6=$

Step-by-step solution

We rewrite the division exercise as a fraction:

$\frac{4a}{a}+6=$

We simplify a in both the numerator and denominator, and we obtain:

$4+6=10$

Final Answer

$10$

Key Points to Remember

Essential concepts to master this topic

Rule: Rewrite ratios as fractions to simplify more easily
Technique: Cancel common variables: $\frac{4a}{a}$ becomes 4
Check: Verify final answer makes sense in context ✓

Common Mistakes

Avoid these frequent errors

Treating the colon as addition instead of division
Don't read 4a:a+6 as 4a + a + 6 = 5a + 6! The colon means division, not addition. Always convert ratios to fractions first: $\frac{4a}{a} + 6$ .

Practice Quiz

Test your knowledge with interactive questions

$$ 94+12+6= $$

FAQ

Everything you need to know about this question

What does the colon symbol mean in math?

The colon : means division or "divided by." So 4a:a is the same as $\frac{4a}{a}$ or 4a ÷ a.

Why can I cancel the 'a' from top and bottom?

When the same variable appears in both numerator and denominator, you can cancel them out because $\frac{a}{a} = 1$ . This leaves you with just the numbers!

What if 'a' equals zero?

Good question! If a = 0, then we'd have $\frac{0}{0}$ which is undefined. In ratio problems, we assume variables don't equal zero unless stated otherwise.

Is this the same as solving an equation?

Not exactly! Here we're simplifying an expression, not solving for a specific value of 'a'. We're finding what the ratio equals for any non-zero value of a.

Can I do this problem without fractions?

You could think of it as: "4a divided by a equals 4, then add 6." But converting to fractions $\frac{4a}{a} + 6$ makes the cancellation step much clearer!

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