Add Mixed Numbers by Making a Whole
Add Mixed Numbers by Making a Whole is a Grade 4 math skill that teaches an efficient addition strategy: decompose one addend to provide just enough to complete the other addend to the nearest whole number, then add the remaining fractional part. For example, to add 2 3/4 + 1 1/2, use 1/4 from 1 1/2 to make 2 3/4 into 3, then add the remaining 1 1/4 to get 4 1/4. Covered in Chapter 24: Fraction Addition and Subtraction in Eureka Math Grade 4, this strategy mirrors the make-a-ten strategy for whole numbers and builds flexible computation with mixed numbers.
Key Concepts
Property Decompose one addend to make the next whole number with the other addend. This is also known as the "make a whole" or "make one" strategy. $$2\frac{4}{5} + 1\frac{2}{5} = 2\frac{4}{5} + \frac{1}{5} + 1\frac{1}{5} = 3 + 1\frac{1}{5} = 4\frac{1}{5}$$.
Examples $4\frac{7}{8} + 2\frac{3}{8} = (4\frac{7}{8} + \frac{1}{8}) + 2\frac{2}{8} = 5 + 2\frac{2}{8} = 7\frac{2}{8}$ $3\frac{2}{3} + 3\frac{2}{3} = (3\frac{2}{3} + \frac{1}{3}) + 3\frac{1}{3} = 4 + 3\frac{1}{3} = 7\frac{1}{3}$ $5\frac{5}{6} + 4\frac{4}{6} = (5\frac{5}{6} + \frac{1}{6}) + 4\frac{3}{6} = 6 + 4\frac{3}{6} = 10\frac{3}{6}$.
Explanation This strategy simplifies addition by focusing on creating whole numbers, which are easier to work with. To use this method, identify how much the first mixed number needs to become the next whole number. Then, decompose the second mixed number to provide that amount, and add the remaining part to the new whole.
Common Questions
How does the make-a-whole strategy work for adding mixed numbers?
Identify how much fraction is needed to make the first addend a whole number. Take that amount from the second addend, make the whole, then add the remaining part of the second addend. This transforms a harder addition problem into a simpler one.
How do I use make-a-whole to add 2 3/4 + 1 1/2?
Ask: how much does 2 3/4 need to become 3? It needs 1/4 more. Take 1/4 from 1 1/2, leaving 1 1/4. Now add 3 + 1 1/4 = 4 1/4. The strategy uses decomposition to eliminate the need for regrouping at the end.
How is make-a-whole similar to make-a-ten for whole numbers?
Both strategies work by completing a round number (10 for whole numbers, the next whole for fractions) before adding the remainder. The underlying structure is the same: decompose one addend to bring the other to a convenient benchmark, then add what is left.
When is the make-a-whole strategy most useful?
Make-a-whole is most efficient when one mixed number is close to the next whole number. If 2 3/4 needs only 1/4 to become 3, and the other addend has at least 1/4, the strategy avoids regrouping and simplifies computation.
What are other strategies for adding mixed numbers in Grade 4?
Other strategies include adding whole number parts and fraction parts separately (then regrouping if the fractions sum to more than 1), and converting both to improper fractions. The make-a-whole strategy is typically the most elegant when applicable.
What chapter covers adding mixed numbers in Eureka Math Grade 4?
Chapter 24: Fraction Addition and Subtraction in Eureka Math Grade 4 covers multiple strategies for adding and subtracting mixed numbers, including the make-a-whole (or make-a-benchmark) approach.