Mixed Number Division: Splitting $2½ Equally Between Two Children

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

Use the formula: multiply whole number × denominator + numerator. For $ 2\frac{1}{2} $: $ 2 \times 2 + 1 = 5 $, so it becomes $ \frac{5}{2} $.

Q: Why do I multiply by the reciprocal when dividing fractions?

Dividing by a number is the same as multiplying by its reciprocal. So $ \frac{5}{2} \div 2 $ becomes $ \frac{5}{2} \times \frac{1}{2} = \frac{5}{4} $!

Q: How do I convert the answer back to a mixed number?

Divide the numerator by the denominator: $ \frac{5}{4} = 5 \div 4 = 1 $ remainder $ 1 $, so it's $ 1\frac{1}{4} $.

Q: Does my answer make sense in real life?

Yes! $ 1\frac{1}{4} $ dollars is $1.25, and $1.25 × 2 = $2.50, which matches our original $ 2\frac{1}{2} $ dollars perfectly!

Mixed Number Division with Equal Distribution

A mother has $\( 2\frac{1}{2}$ and wants to distribute it equally among her 2 children.

How much in dollars will each child receive?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 How much money will each child receive?

00:04 Divide the amount of money by the number of children

00:07 First, let's convert the mixed number to a fraction

00:23 Convert division to multiplication by reciprocal

00:35 Make sure to multiply numerator by numerator and denominator by denominator

00:42 Calculate the multiplications

00:50 Now let's convert to a mixed number

00:54 Break down 5 into 4 plus 1

00:59 Break down the fraction into whole number and remainder

01:06 Convert the whole fraction to a whole number, and combine with mixed number

01:13 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

A mother has $\( 2\frac{1}{2}$ and wants to distribute it equally among her 2 children.

How much in dollars will each child receive?

Step-by-step solution

To solve this problem, we will follow these steps:

Step 1: Convert the mixed number $2\frac{1}{2}$ to an improper fraction.
Step 2: Divide the improper fraction by 2.
Step 3: Simplify the resulting fraction if necessary.

Now, let's work through each step:
Step 1: Convert the mixed number $2\frac{1}{2}$ to an improper fraction. This is done by multiplying the whole number 2 by the denominator 2 and adding the numerator 1. Hence, $2\frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{5}{2}$ .
Step 2: Divide $\frac{5}{2}$ by 2. Dividing by 2 is equivalent to multiplying by $\frac{1}{2}$ . Therefore, $\frac{5}{2} \div 2 = \frac{5}{2} \times \frac{1}{2} = \frac{5}{4}$ .
Step 3: The fraction $\frac{5}{4}$ is already in its simplest form, but it can also be expressed as a mixed number: $1\frac{1}{4}$ .

Therefore, each child will receive $1\frac{1}{4}$ dollars.

Final Answer

$1\frac{1}{4}$

Key Points to Remember

Essential concepts to master this topic

Rule: Convert mixed numbers to improper fractions before dividing
Technique: $2\frac{1}{2} = \frac{5}{2}$ , then $\frac{5}{2} \div 2 = \frac{5}{4}$
Check: Each child gets $1\frac{1}{4}$ , so $1\frac{1}{4} + 1\frac{1}{4} = 2\frac{1}{2}$ ✓

Common Mistakes

Avoid these frequent errors

Dividing only the whole number part
Don't divide just the 2 and ignore the $\frac{1}{2}$ = each child gets $1 plus leftover money! This doesn't split everything equally. Always convert to improper fraction first, then divide the entire amount.

Practice Quiz

Test your knowledge with interactive questions

$2\times\frac{5}{7}=$

FAQ

Everything you need to know about this question

Why can't I just give each child $1 and split the 50 cents?

While that works for this problem, converting to improper fractions is the standard method that works for all division problems. It ensures you handle the whole amount as one unit!

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

Use the formula: multiply whole number × denominator + numerator. For $2\frac{1}{2}$ : $2 \times 2 + 1 = 5$ , so it becomes $\frac{5}{2}$ .

Why do I multiply by the reciprocal when dividing fractions?

Dividing by a number is the same as multiplying by its reciprocal. So $\frac{5}{2} \div 2$ becomes $\frac{5}{2} \times \frac{1}{2} = \frac{5}{4}$ !

How do I convert the answer back to a mixed number?

Divide the numerator by the denominator: $\frac{5}{4} = 5 \div 4 = 1$ remainder $1$ , so it's $1\frac{1}{4}$ .

Does my answer make sense in real life?

Yes! $1\frac{1}{4}$ dollars is $1.25, and <strong>$ 1.25 × 2 = 2.50, which matches our original $\( 2\frac{1}{2}$ dollars perfectly!

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