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How do you subtract a number from a mixed number?

Published in Math Subtraction 2 mins read

Subtracting a number from a mixed number involves a few different approaches, depending on whether you're subtracting a whole number or a fraction. Here's a breakdown:

Subtracting a Whole Number from a Mixed Number

This is the simpler case. You simply subtract the whole number from the whole number part of the mixed number.

Example:

5 1/4 - 2 = (5 - 2) 1/4 = 3 1/4

Subtracting a Fraction from a Mixed Number

This requires a bit more attention.

  1. Check if the fraction you are subtracting is less than the fractional part of the mixed number. If it is, simply subtract the fractions:

    • Example: 3 2/5 - 1/5 = 3 (2/5 - 1/5) = 3 1/5. According to the reference, you subtract the numerators and keep the common denominator. In this case, 2-1 = 1, so the answer is 3 1/5.

  2. If the fraction you're subtracting is larger than the fractional part of the mixed number, you'll need to borrow. This involves:

    • Borrowing 1 from the whole number part of the mixed number.
    • Converting that 1 into a fraction with the same denominator as the existing fraction.
    • Adding that fraction to the existing fraction.
    • Then you can subtract.

    Example: 4 1/3 - 2/3

    • We can't subtract 2/3 from 1/3, so we borrow 1 from the 4.
    • This turns the 4 into a 3.
    • The borrowed 1 becomes 3/3 (since our denominator is 3).
    • We add 3/3 to the existing 1/3, giving us 4/3.
    • Now we have: 3 4/3 - 2/3 = 3 (4/3 - 2/3) = 3 2/3

Subtracting a Mixed Number from a Mixed Number

  1. Subtract the whole numbers.
  2. Subtract the fractions. If the fraction you're subtracting is larger than the fraction you're subtracting from, you'll need to borrow as described above.

Example: 5 1/2 - 2 1/4

  1. Find a common Denominator: You will need to convert 1/2 into 2/4. The problem now becomes: 5 2/4 - 2 1/4.

  2. Subtract the whole numbers: 5 - 2 = 3.

  3. Subtract the fractions: 2/4 - 1/4 = 1/4.

  4. Combine: The answer is 3 1/4.

Converting to Improper Fractions (Alternative Method)

Another method is to convert both the mixed number and the number being subtracted into improper fractions. Then perform the subtraction, and convert the result back into a mixed number if necessary.

Example: 3 1/4 - 1/2

  1. Convert to improper fractions: 3 1/4 = 13/4 and 1/2 = 2/4.
  2. Subtract: 13/4 - 2/4 = 11/4
  3. Convert back to a mixed number: 11/4 = 2 3/4

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