Solve Decimal Division: Calculate 4.4:1.1 Using Ratio Notation

Decimal Division with Ratio Notation

4.4:1.1= 4.4:\text{1}.1=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:05 Let's solve this problem together.
00:08 First, we'll change each decimal number into a whole number.
00:28 Now, divide the whole numbers and find the answer.
00:35 And that's how we solve this question!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

4.4:1.1= 4.4:\text{1}.1=

2

Step-by-step solution

To solve the problem 4.4÷1.1 4.4 \div 1.1 , we will proceed with the following steps:

  • Step 1: Convert the decimals to whole numbers. Multiply both the numerator (4.4) and the denominator (1.1) by 10 to eliminate the decimal points, resulting in 44÷11 44 \div 11 .
  • Step 2: Perform the division 44÷11 44 \div 11 . Since 44 44 divided by 11 11 is 4 4 , the quotient is 4.
  • Step 3: Interpret and verify the result. Since multiplying by 10 does not affect the ratio (or quotient), the result is valid for the original problem.

Therefore, the solution to the problem 4.4÷1.1 4.4 \div 1.1 is 4 4 .

3

Final Answer

4 4

Key Points to Remember

Essential concepts to master this topic
  • Rule: Convert ratio to division to find quotient
  • Technique: Multiply both terms by 10: 4.4:1.1 becomes 44:11
  • Check: Verify 4 × 1.1 = 4.4 gives original first term ✓

Common Mistakes

Avoid these frequent errors
  • Trying to simplify ratio without converting to division
    Don't try to cancel decimal digits directly like 4.4:1.1 = 4:1! This ignores place value and gives wrong answers. Always convert to division first: 4.4 ÷ 1.1, then multiply both by 10 to get whole numbers.

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

22.1-12.0

FAQ

Everything you need to know about this question

What's the difference between 4.4:1.1 and 4.4 ÷ 1.1?

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They're the same thing! The colon (:) in ratio notation means division. So 4.4:1.1 4.4:1.1 is asking how many times does 1.1 go into 4.4?

Why multiply both numbers by 10?

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Multiplying by 10 removes the decimal points, making division easier. Since we multiply both the dividend and divisor by the same number, the quotient stays the same!

Can I use a calculator for decimal division?

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Yes, but understanding the multiplication method helps you work without a calculator and avoid decimal errors. Try both ways to check your work!

What if the decimals have different numbers of places?

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Multiply by enough powers of 10 to clear all decimal places. For example, with 4.45:1.1, multiply both by 100 to get 445:110.

How do I know my ratio answer is simplified?

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Check if the result is a whole number. If you get a fraction, make sure it's in lowest terms. In this case, 4 is already simplified!

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