Solve Mixed Number Subtraction: 7¼ - 3½ Step-by-Step

Mixed Number Subtraction with Borrowing

714324= 7\frac{1}{4}-3\frac{2}{4}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:07 Convert mixed fraction to improper fraction
00:14 Convert whole number to proper fraction
00:29 Add using common denominator
00:34 Use the same method for the second fraction
00:38 Convert whole number to proper fraction
00:55 Add using common denominator
01:08 Subtract using common denominator
01:20 Break down 15 into 12 plus 3
01:26 Break down the fraction into whole number and remainder
01:33 Convert proper fraction to whole number, and combine with mixed number
01:38 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

714324= 7\frac{1}{4}-3\frac{2}{4}=

2

Step-by-step solution

To solve the subtraction of the mixed numbers 714324 7\frac{1}{4} - 3\frac{2}{4} , we follow these steps:

  • Step 1: Subtract the whole numbers:
    73=4 7 - 3 = 4 .
  • Step 2: Subtract the fractions:
    1424 \frac{1}{4} - \frac{2}{4} results in 14 \frac{-1}{4} , because the numerators give 12=1 1 - 2 = -1 .
  • Step 3: Combine these results, we initially have 414 4\frac{-1}{4} . Since we can't leave a negative fraction in this form, we adjust by borrowing 1 from the whole number:
    • Convert 1 1 (borrowed from 4) into 44 \frac{4}{4} which combines with the fraction: 4414=34 \frac{4}{4} - \frac{1}{4} = \frac{3}{4} .
  • Step 4: Adjusting the whole number:
    Remove 1 from 4 to account for the adjustment: 41=3 4 - 1 = 3 .

Therefore, combining these parts, the mixed number resulting from the subtraction is 334 3\frac{3}{4} .

Thus, the final result is 334 3\frac{3}{4} .

3

Final Answer

334 3\frac{3}{4}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Subtract whole numbers first, then fractions with same denominators
  • Technique: When 1424=14 \frac{1}{4} - \frac{2}{4} = \frac{-1}{4} , borrow 1 from whole number
  • Check: Convert answer back: 334=3+34=154 3\frac{3}{4} = 3 + \frac{3}{4} = \frac{15}{4}

Common Mistakes

Avoid these frequent errors
  • Leaving negative fractions in final answer
    Don't write 414 4\frac{-1}{4} as your final answer = incorrect mixed number form! Negative fractions must be resolved by borrowing from the whole number. Always borrow 1 from the whole number and add it to the fraction part.

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 2 from 1 in the fractions?

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You can subtract them: 12=1 1 - 2 = -1 . But mixed numbers don't have negative fraction parts. That's why we need to borrow from the whole number to fix this!

How do I borrow from the whole number?

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Take 1 from the whole number and convert it to a fraction with the same denominator. So 1 becomes 44 \frac{4}{4} , then add: 44+14=34 \frac{4}{4} + \frac{-1}{4} = \frac{3}{4} .

What if the fractions have different denominators?

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First find a common denominator before subtracting! In this problem, both fractions already have denominator 4, so we can subtract directly.

Can I convert to improper fractions instead?

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Yes! Convert both mixed numbers to improper fractions: 294144=154 \frac{29}{4} - \frac{14}{4} = \frac{15}{4} , then convert back to 334 3\frac{3}{4} .

How do I know when I need to borrow?

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You need to borrow whenever the first fraction is smaller than the second fraction. Since 14<24 \frac{1}{4} < \frac{2}{4} , borrowing is necessary here.

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