Solve: Subtracting 2⅝ from 4 - Mixed Number Arithmetic

Q: Why can't I just subtract 4 - 2 and then worry about the fraction?

Because $ 2\frac{5}{7} $ means 2 plus $ \frac{5}{7} $, not just 2. You need to subtract the entire value $ 2\frac{5}{7} $ from 4, which requires converting to common denominators first.

Q: How do I convert 4 to sevenths?

Multiply 4 by $ \frac{7}{7} $ (which equals 1): $ 4 \times \frac{7}{7} = \frac{28}{7} $. Now both numbers have the same denominator and you can subtract directly!

Q: What if I get confused about converting improper fractions to mixed numbers?

Use division! For $ \frac{23}{7} $, divide: 23 ÷ 7 = 3 remainder 2. The quotient (3) becomes the whole number, and the remainder (2) goes over the original denominator: $ 3\frac{2}{7} $.

Q: Why is the answer different from what's shown in the explanation?

The explanation shows $ 4 - 2\frac{5}{7} $ but the question asks for $ 4 - 2\frac{5}{7} $. The correct answer should be $ 1\frac{2}{7} $, not $ 3\frac{2}{7} $. Always double-check your problem setup!

Mixed Number Subtraction with Improper Result

$4-2\frac{5}{7}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 First, decompose each mixed fraction into a whole number and fraction

00:10 Subtract

00:18 Calculate the difference of whole numbers

00:25 Multiply the whole number by the denominator to find the common denominator

00:36 Subtract under the common denominator

00:43 Break down 9 into 7 plus 2

00:49 Break down the fraction into a whole fraction and remainder

00:55 Convert from a whole fraction to a whole number

00:59 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

$4-2\frac{5}{7}=$

Step-by-step solution

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

Step 1: Convert 4 to a fraction that shares a common denominator with $\frac{5}{7}$ .
Step 2: Perform the subtraction.
Step 3: Simplify the result into a mixed fraction.

Now, let's work through each step:
Step 1: Convert 4 to the fraction form $\frac{28}{7}$ , because $\frac{28}{7}$ is equivalent to 4.

Step 2: Subtract the fractions:
$\frac{28}{7} - \frac{5}{7} = \frac{28 - 5}{7} = \frac{23}{7}$ .

Step 3: Convert $\frac{23}{7}$ to a mixed fraction.
Divide 23 by 7, which goes 3 times with a remainder of 2. Hence, $\frac{23}{7} = 3\frac{2}{7}$ .

Therefore, the solution to the problem is $3\frac{2}{7}$ .

Final Answer

$1\frac{2}{7}$

Key Points to Remember

Essential concepts to master this topic

Conversion: Convert whole numbers to equivalent fractions with common denominators
Technique: Convert 4 to $\frac{28}{7}$ then subtract: $\frac{28}{7} - \frac{5}{7} = \frac{23}{7}$
Check: Convert final answer back: $3\frac{2}{7} = \frac{23}{7}$ matches our calculation ✓

Common Mistakes

Avoid these frequent errors

Subtracting mixed number parts separately
Don't subtract 4 - 2 = 2 and then deal with $\frac{5}{7}$ separately = wrong approach! This ignores that we're subtracting the entire mixed number. Always convert everything to the same denominator first, then perform one subtraction operation.

Practice Quiz

Test your knowledge with interactive questions

$2\frac{2}{5}+2\frac{2}{5}=$

FAQ

Everything you need to know about this question

Why can't I just subtract 4 - 2 and then worry about the fraction?

Because $2\frac{5}{7}$ means 2 plus $\frac{5}{7}$ , not just 2. You need to subtract the entire value $2\frac{5}{7}$ from 4, which requires converting to common denominators first.

How do I convert 4 to sevenths?

Multiply 4 by $\frac{7}{7}$ (which equals 1): $4 \times \frac{7}{7} = \frac{28}{7}$ . Now both numbers have the same denominator and you can subtract directly!

What if I get confused about converting improper fractions to mixed numbers?

Use division! For $\frac{23}{7}$ , divide: 23 ÷ 7 = 3 remainder 2. The quotient (3) becomes the whole number, and the remainder (2) goes over the original denominator: $3\frac{2}{7}$ .

Why is the answer different from what's shown in the explanation?

The explanation shows $4 - 2\frac{5}{7}$ but the question asks for $4 - 2\frac{5}{7}$ . The correct answer should be $1\frac{2}{7}$ , not $3\frac{2}{7}$ . Always double-check your problem setup!

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