Multiply Mixed Numbers: 1 4/5 × 2 1/2 Step-by-Step Solution

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

Mixed numbers represent single values, not separate parts! $ 1\frac{4}{5} $ means "one and four-fifths as one number." Multiplying parts separately gives wrong results because you're not accounting for the interaction between whole and fractional parts.

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

Use this formula: Multiply the whole number by the denominator, then add the numerator. For $ 1\frac{4}{5} $: (1 × 5) + 4 = 9, so it becomes $ \frac{9}{5} $.

Q: What if my final fraction doesn't simplify to a mixed number evenly?

That's totally normal! For example, $ \frac{7}{3} = 2\frac{1}{3} $. Just divide: 7 ÷ 3 = 2 remainder 1, so you get 2 whole parts and 1/3 left over.

Q: Can I cross out numbers when multiplying fractions?

Yes! You can cancel common factors before multiplying. In $ \frac{9}{5} \times \frac{5}{2} $, the 5s cancel out, giving you $ \frac{9}{2} $ directly!

Mixed Number Multiplication with Improper Conversion

$1\frac{4}{5}\times2\frac{1}{2}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's start by solving this problem.

00:08 First, change each mixed fraction into a simple fraction.

00:24 Now, add up the numerators, which are the top numbers.

00:34 Remember, multiply the top numbers together, and the bottom numbers together.

00:41 Next, find the answer by multiplying those numbers.

00:47 Then, change the answer back to a mixed fraction.

00:52 You can break down forty-five as forty plus five.

00:57 Break the fraction into a whole number and the leftover part.

01:04 Turn the fraction into a whole number, and mix it with any parts left.

01:11 Make sure to simplify as much as you can.

01:18 And there you go! That's your solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$1\frac{4}{5}\times2\frac{1}{2}=$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Convert each mixed number to an improper fraction.
Step 2: Multiply the improper fractions.
Step 3: Simplify the resulting fraction, if needed, and convert it back to a mixed number.

Now, let's work through each step:
Step 1: Convert the mixed numbers to improper fractions.
For $1\frac{4}{5}$ :
$1\frac{4}{5} = \frac{1 \times 5 + 4}{5} = \frac{9}{5}$ .
For $2\frac{1}{2}$ :
$2\frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{5}{2}$ .

Step 2: Multiply the improper fractions:
$\frac{9}{5} \times \frac{5}{2} = \frac{9 \times 5}{5 \times 2} = \frac{45}{10}$ .

Step 3: Simplify the fraction and convert it back to a mixed number:
$\frac{45}{10} = \frac{9}{2} = 4\frac{1}{2}$ .

Therefore, the product of $1\frac{4}{5} \times 2\frac{1}{2}$ is $4\frac{1}{2}$ , which corresponds to choice 2.

Final Answer

$4\frac{1}{2}$

Key Points to Remember

Essential concepts to master this topic

Convert: Transform mixed numbers to improper fractions first
Multiply: $\frac{9}{5} \times \frac{5}{2} = \frac{45}{10}$ by multiplying across
Check: Convert back to mixed form: $\frac{45}{10} = 4\frac{1}{2}$ ✓

Common Mistakes

Avoid these frequent errors

Multiplying whole numbers and fractions separately
Don't multiply 1 × 2 = 2 and 4/5 × 1/2 = 4/10 then add them = wrong answer 2 4/10! This ignores how mixed numbers work as single values. Always convert to improper fractions first, then multiply as one operation.

Practice Quiz

Test your knowledge with interactive questions

$1\frac{4}{5}\times1\frac{1}{3}=$

FAQ

Everything you need to know about this question

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

Mixed numbers represent single values, not separate parts! $1\frac{4}{5}$ means "one and four-fifths as one number." Multiplying parts separately gives wrong results because you're not accounting for the interaction between whole and fractional parts.

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

Use this formula: Multiply the whole number by the denominator, then add the numerator. For $1\frac{4}{5}$ : (1 × 5) + 4 = 9, so it becomes $\frac{9}{5}$ .

Do I always need to convert mixed numbers back at the end?

It depends on what form the answer choices are in! If they're mixed numbers (like in this problem), convert back. If they're improper fractions or decimals, you can leave your answer in that form.

What if my final fraction doesn't simplify to a mixed number evenly?

That's totally normal! For example, $\frac{7}{3} = 2\frac{1}{3}$ . Just divide: 7 ÷ 3 = 2 remainder 1, so you get 2 whole parts and 1/3 left over.

Can I cross out numbers when multiplying fractions?

Yes! You can cancel common factors before multiplying. In $\frac{9}{5} \times \frac{5}{2}$ , the 5s cancel out, giving you $\frac{9}{2}$ directly!

What's the easiest way to check my answer?

Convert your final answer back to a decimal and see if it makes sense! $4\frac{1}{2} = 4.5$ , and since $1.8 \times 2.5 = 4.5$ , our answer checks out! ✓

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