Multiply 4 by 1⅕: Step-by-Step Mixed Number Calculation

Mixed Number Multiplication with Improper Fractions

4×115= 4\times1\frac{1}{5}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:04 First convert mixed number to fraction
00:15 Raise the product to the numerator
00:23 Calculate the product
00:27 Now convert to mixed number
00:33 Break down 24 into 20 plus 4
00:41 Break down the fraction into whole number and remainder
00:48 Convert whole number fraction to integer, and combine with mixed number
00:56 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

4×115= 4\times1\frac{1}{5}=

2

Step-by-step solution

To solve the problem, we will follow these steps:

  • Step 1: Convert the mixed number 115 1\frac{1}{5} to an improper fraction.
  • Step 2: Multiply this improper fraction by the whole number 4.
  • Step 3: Convert the resulting improper fraction back to a mixed number.

Now, let's work through each step:

Step 1: Convert 115 1\frac{1}{5} to an improper fraction.

The mixed number 115 1\frac{1}{5} can be converted as follows:
Multiply the whole number 1 by the denominator 5, and add the numerator 1:
1×5+1=6 1 \times 5 + 1 = 6 .
So, 115 1\frac{1}{5} is equivalent to 65 \frac{6}{5} .

Step 2: Multiply 4 4 by 65 \frac{6}{5} .

We perform the multiplication: 4×65=4×65=245 4 \times \frac{6}{5} = \frac{4 \times 6}{5} = \frac{24}{5} .

Step 3: Convert 245 \frac{24}{5} back to a mixed number.

Divide 24 by 5 to find how many whole parts there are:
24÷5=4 24 \div 5 = 4 with a remainder of 4.
Thus, 245 \frac{24}{5} can be expressed as 445 4\frac{4}{5} .

Therefore, the solution to the problem is 445 4\frac{4}{5} .

3

Final Answer

445 4\frac{4}{5}

Key Points to Remember

Essential concepts to master this topic
  • Conversion: Transform mixed numbers to improper fractions before multiplying
  • Technique: Convert 115 1\frac{1}{5} to 65 \frac{6}{5} by calculating 1×5+1
  • Check: Verify 445 4\frac{4}{5} equals 245 \frac{24}{5} using 4×5+4=24 ✓

Common Mistakes

Avoid these frequent errors
  • Multiplying whole number and fraction parts separately
    Don't multiply 4×1=4 and 4×1/5=4/5 to get 4 + 4/5! This ignores the relationship between parts and gives the wrong structure. Always convert the mixed number to an improper fraction first, then multiply.

Practice Quiz

Test your knowledge with interactive questions

\( 4:\frac{6}{8}= \)

FAQ

Everything you need to know about this question

Why can't I just multiply the whole numbers and fractions separately?

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Because the mixed number 115 1\frac{1}{5} represents one complete unit plus one-fifth. Separating the parts breaks this relationship and leads to incorrect calculations.

How do I convert a mixed number to an improper fraction?

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Use this formula: Multiply the whole number by the denominator, then add the numerator. For 115 1\frac{1}{5} : (1×5)+1 = 6, so it becomes 65 \frac{6}{5} .

When do I need to convert back to a mixed number?

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Convert back when your answer is an improper fraction (numerator larger than denominator). Divide 24÷5 = 4 remainder 4, giving 445 4\frac{4}{5} .

Can I multiply a whole number by a mixed number directly?

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Not recommended! While some shortcuts exist, converting to improper fractions first is the most reliable method that always works and prevents errors.

What if my improper fraction doesn't convert evenly?

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That's normal! Use long division. The quotient becomes the whole number, and the remainder becomes the new numerator over the original denominator.

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