Solve the Ratio Problem: Finding the Value of (+5:+30)

Q: What's the difference between +5:+30 and 5:30?

The plus signs don't change the calculation at all! $ +5:+30 $ is exactly the same as $ 5:30 $. Positive signs are often written to emphasize that the numbers are positive.

Q: Why do we write ratios as fractions?

Converting ratios to fractions makes them much easier to simplify! You can use all the same rules for reducing fractions, like finding common factors and canceling them out.

Q: Can I get a decimal answer instead?

Yes! $ \frac{1}{6} $ equals approximately 0.167, but fractions are usually preferred for exact answers. Keep your answer as $ \frac{1}{6} $ unless specifically asked for decimal form.

Q: What if the ratio can't be simplified?

Some ratios are already in simplest form! If the two numbers share no common factors other than 1, then your fraction is already fully reduced. For example, $ 3:7 = \frac{3}{7} $ cannot be simplified further.

Ratio Simplification with Common Factor Cancellation

$+5:+30=$ ?

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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 write division as a fraction

00:08 Positive divided by positive is always positive

00:18 Let's break down 30 into factors 5 and 6

00:23 Let's reduce what we can

00:28 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

$+5:+30=$ ?

Step-by-step solution

First let's write the exercise in the form of a simple fraction:

$\frac{5}{30}$

Next, we'll break down the 30 into a multiplication operation:

$\frac{5}{5\times6}=$

Finally, cancel out the 5 in both the numerator and denominator of the fraction, leaving us with:

$\frac{1}{6}$

Final Answer

$\frac{1}{6}$

Key Points to Remember

Essential concepts to master this topic

Ratio Rule: Express ratios as fractions to simplify them easily
Technique: Find common factors: $\frac{5}{30} = \frac{5}{5 \times 6}$
Check: Verify by multiplying: $\frac{1}{6} \times 6 = 1$ and $1 \times 5 = 5$ ✓

Common Mistakes

Avoid these frequent errors

Dividing the wrong way or not simplifying the fraction
Don't calculate $\frac{30}{5} = 6$ instead of $\frac{5}{30}$ ! This reverses the ratio and gives completely wrong results. Always write the first number as numerator, second as denominator, then simplify by canceling common factors.

Practice Quiz

Test your knowledge with interactive questions

What will be the sign of the result of the next exercise?

$(-2)\cdot(-4)=$

FAQ

Everything you need to know about this question

What's the difference between +5:+30 and 5:30?

The plus signs don't change the calculation at all! $+5:+30$ is exactly the same as $5:30$ . Positive signs are often written to emphasize that the numbers are positive.

Why do we write ratios as fractions?

Converting ratios to fractions makes them much easier to simplify! You can use all the same rules for reducing fractions, like finding common factors and canceling them out.

How do I find the common factor quickly?

Look for numbers that divide evenly into both parts of the ratio. For $5:30$ , notice that 5 divides into both: $5 ÷ 5 = 1$ and $30 ÷ 5 = 6$ .

Can I get a decimal answer instead?

Yes! $\frac{1}{6}$ equals approximately 0.167, but fractions are usually preferred for exact answers. Keep your answer as $\frac{1}{6}$ unless specifically asked for decimal form.

What if the ratio can't be simplified?

Some ratios are already in simplest form! If the two numbers share no common factors other than 1, then your fraction is already fully reduced. For example, $3:7 = \frac{3}{7}$ cannot be simplified further.

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