Add Mixed Numbers and Regroup the Fractional Sum
This Grade 4 Eureka Math skill teaches students to add mixed numbers with like denominators and regroup when the fractional sum is an improper fraction. Students first add the whole number parts, then the fractional parts separately. When the fractions add to an improper fraction (greater than or equal to 1), they convert it to a mixed number and add the whole number component to the running whole number total. For example, 2 and 3/4 + 1 and 3/4 = 3 + 6/4 = 3 + 1 and 2/4 = 4 and 2/4. This regrouping skill is taught in Chapter 26 of Eureka Math Grade 4.
Key Concepts
Property When adding mixed numbers, first add the whole numbers and then add the fractions. If the sum of the fractions is an improper fraction (greater than or equal to 1), convert it to a mixed number and add it to the sum of the whole numbers. $$A\frac{b}{d} + C\frac{e}{d} = (A+C) + (\frac{b}{d} + \frac{e}{d})$$ If $\frac{b+e}{d} \geq 1$, regroup.
Examples $2\frac{3}{4} + 1\frac{3}{4} = (2+1) + (\frac{3}{4} + \frac{3}{4}) = 3 + \frac{6}{4} = 3 + 1\frac{2}{4} = 4\frac{2}{4}$ $5\frac{2}{3} + 2\frac{2}{3} = (5+2) + (\frac{2}{3} + \frac{2}{3}) = 7 + \frac{4}{3} = 7 + 1\frac{1}{3} = 8\frac{1}{3}$.
Explanation This skill builds on adding like units. You first combine the whole numbers and then the fractions separately. When the sum of the fractions is an improper fraction, you must regroup. To do this, you convert the improper fraction into a mixed number and then add this new whole number to your original sum of whole numbers.
Common Questions
How do you add mixed numbers with the same denominator?
Add whole number parts together, then add the numerators of the fractions while keeping the denominator the same. For example, 2 and 3/4 + 1 and 3/4: whole parts give 3, fraction parts give 6/4.
What do you do when the fractional sum is an improper fraction?
Convert the improper fraction to a mixed number. For example, 6/4 = 1 and 2/4. Then add the whole number part (1) to the existing whole number sum (3) to get 4 and 2/4.
When is regrouping required in mixed number addition?
Regrouping is required whenever the sum of the fractional parts is greater than or equal to 1 — in other words, when the numerator is greater than or equal to the denominator.
Solve 5 and 2/3 + 2 and 2/3 step by step.
Add whole parts: 5+2=7. Add fractions: 2/3+2/3=4/3. Convert: 4/3=1 and 1/3. Add: 7+1 and 1/3=8 and 1/3.
Why must the denominators be the same before adding mixed number fractions?
Fractions represent equal-sized parts. You can only add them directly when the parts are the same size, meaning the denominators must match.