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Subtract mixed numbers and fractions with step-by-step solutions including borrowing. Learn how to subtract fractions with different denominators.
• 3 1/4 - 1 3/8 = 1 7/8
• 5 1/2 - 2 2/3 = 2 5/6
• 4 1/3 - 1 5/6 = 2 1/2
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Step 1: Convert: 3 1/4 = 13/4 and 1 3/8 = 11/8
Step 2: LCD of 4 and 8 is 8
Step 3: 13/4 = 26/8
Step 4: 26/8 - 11/8 = 15/8
Step 5: 15/8 = 1 7/8
When subtracting mixed numbers, you might need to "borrow" from the whole number if the first fraction is smaller than the second. For example, in 3 1/4 - 1 3/4:
Tip: Converting to improper fractions avoids the borrowing step entirely!
You need to borrow when the fraction part of the first mixed number is smaller than the fraction part of the second. For example, in 4 1/8 - 2 3/8, since 1/8 < 3/8, you'd borrow 1 from 4 to make it 3 9/8, then subtract. However, converting to improper fractions eliminates the need for borrowing.
Yes, if the second mixed number is larger than the first, your answer will be negative. For example, 2 1/4 - 3 1/2 = -1 1/4. Make sure to keep track of the negative sign throughout your calculation and in your final answer.
Converting to improper fractions is generally more straightforward and less error-prone. Borrowing requires additional steps and can be confusing. Most teachers and textbooks recommend the improper fraction method for reliability, especially with different denominators.
First find the Least Common Denominator (LCD) of both fractions. Convert each fraction to an equivalent fraction with the LCD as the denominator. Then you can subtract the numerators. For example, with 1/4 and 1/6, the LCD is 12, so convert to 3/12 and 2/12 before subtracting.
If your answer is an improper fraction (like 9/4), convert it to a mixed number. Divide the numerator by the denominator: 9 ÷ 4 = 2 remainder 1, so the answer is 2 1/4. Always present final answers as simplified mixed numbers unless instructed otherwise.
You can simplify at either stage, but it's often easier to simplify the improper fraction first, then convert to a mixed number. For example, 18/12 simplifies to 3/2, which then converts to 1 1/2. This keeps numbers smaller and easier to work with.