Solve the Ratio Problem: Converting 7:1 to Standard Form

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

The colon symbol represents division in ratio notation. So $ 7:1 $ means $ 7 \div 1 $, just like how $ 8:2 $ means $ 8 \div 2 = 4 $.

Q: Why does dividing by 1 give the same number?

Think of division as sharing equally. When you have 7 items and share them among 1 person, that person gets all 7 items! Mathematically, dividing by 1 never changes the number.

Q: Are ratios and fractions the same thing?

Yes! A ratio like $ 7:1 $ can be written as the fraction $ \frac{7}{1} $. Both represent the same division operation and give the same answer.

Q: What if the ratio was 1:7 instead?

Then you'd calculate $ 1 \div 7 = \frac{1}{7} $. The order matters in ratios - the first number is always divided by the second number.

Q: How can I remember this rule?

Remember: "Anything divided by 1 stays the same!" It's like having a whole pizza and cutting it into 1 piece - you still have the whole pizza.

Division Properties with Unit Denominators

$7:1=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:03 Let's solve a math problem together.

00:06 Remember, any number divided by one is always that same number.

00:11 And that's how we find the answer to our question!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$7:1=$

Step-by-step solution

To solve this problem, we'll follow this straightforward step:

Step 1: Recognize and apply the division rule involving the number 1.

Now, let's work through this step:

Step 1: Consider the expression $7 \div 1$ . According to the division property, any number divided by 1 is the number itself. Therefore:

$7 \div 1 = 7$

Hence, the solution to the problem is that $7 \div 1 = 7$ .

Therefore, the correct choice is 7, which matches choice 3.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Any number divided by 1 equals the original number
Technique: Convert ratio notation to division: $7:1 = 7 \div 1$
Check: Verify using multiplication: $7 \times 1 = 7$ ✓

Common Mistakes

Avoid these frequent errors

Adding the ratio parts instead of dividing
Don't add 7 + 1 = 8! This completely misunderstands ratio notation and gives the wrong result. Always remember that ratio notation a:b means a ÷ b, so perform division instead.

Practice Quiz

Test your knowledge with interactive questions

$1\times1000=$

FAQ

Everything you need to know about this question

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

The colon symbol represents division in ratio notation. So $7:1$ means $7 \div 1$ , just like how $8:2$ means $8 \div 2 = 4$ .

Why does dividing by 1 give the same number?

Think of division as sharing equally. When you have 7 items and share them among 1 person, that person gets all 7 items! Mathematically, dividing by 1 never changes the number.

Are ratios and fractions the same thing?

Yes! A ratio like $7:1$ can be written as the fraction $\frac{7}{1}$ . Both represent the same division operation and give the same answer.

What if the ratio was 1:7 instead?

Then you'd calculate $1 \div 7 = \frac{1}{7}$ . The order matters in ratios - the first number is always divided by the second number.

How can I remember this rule?

Remember: "Anything divided by 1 stays the same!" It's like having a whole pizza and cutting it into 1 piece - you still have the whole pizza.

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