Decompose a Mixed Number to Regroup for Subtraction
Decompose a Mixed Number to Regroup for Subtraction is a Grade 4 math skill that allows students to subtract a larger fraction from a smaller fractional part in a mixed number by borrowing 1 from the whole number part. The borrowed whole is converted into the equivalent number of unit fractions (for denominator b, that is b/b), added to the existing fraction, and then the subtraction proceeds normally. For example, 4 1/3 becomes 3 4/3 before subtracting 2 3/3. Covered in Chapter 24 of Eureka Math Grade 4, this is the fraction analogue of regrouping in whole number subtraction.
Key Concepts
To regroup a mixed number $W \frac{a}{b}$ to get a larger numerator in the fraction part, you can rewrite it as an equivalent mixed number by taking 1 from the whole number and adding it to the fraction: $$W \frac{a}{b} = (W 1) + 1 + \frac{a}{b} = (W 1) + \frac{b}{b} + \frac{a}{b} = (W 1) \frac{a+b}{b}$$.
Common Questions
How do I regroup a mixed number before subtracting?
When the fraction you need to subtract is larger than the fraction in the minuend, borrow 1 from the whole number. Convert that 1 into a fraction equal to one whole (b/b for denominator b), then add it to the existing fractional part. Now subtract as usual.
How do I rewrite 4 1/3 so I can subtract a fraction larger than 1/3?
Borrow 1 from the 4 to get 3, and convert it to 3/3. Add to 1/3: 3/3 + 1/3 = 4/3. Rewrite as 3 4/3. Now you can subtract any fraction with denominator 3 that is 4/3 or less.
What is the connection between regrouping here and borrowing in whole number subtraction?
Both involve borrowing a unit from a larger place to supplement a smaller one. In whole number subtraction, you borrow a ten to get 10 more ones. In mixed number subtraction, you borrow a whole to get b more unit fractions.
When do I need to decompose a mixed number before subtracting?
Decompose when the fraction part of the number you are subtracting from (the minuend) is smaller than the fraction being subtracted. Without regrouping, you would get a negative fractional part, which is incorrect for this type of problem.
How do I subtract 3 2/5 minus 1 4/5 using regrouping?
Since 2/5 is smaller than 4/5, regroup: 3 2/5 = 2 7/5 (borrow 1 from 3, convert to 5/5, add to 2/5). Now subtract: 2 7/5 minus 1 4/5 = 1 3/5.
What chapter covers regrouping mixed numbers for subtraction in Eureka Math Grade 4?
Chapter 24: Fraction Addition and Subtraction in Eureka Math Grade 4 covers multiple strategies for subtracting mixed numbers including regrouping (decomposing the minuend) and converting to improper fractions.