Add Like Units and Regroup an Improper Fraction
This Grade 4 Eureka Math skill teaches students to add a mixed number and a proper fraction with like denominators, regrouping when the sum of the fractional parts forms an improper fraction. Students add the fractions first: if A b/c + d/c produces a fraction where b+d is greater than or equal to c, they regroup by converting the improper fraction to a mixed number and adding the 1 whole to A. For example, 5 and 2/4 + 3/4 = 5 + 5/4 = 5 + 1 and 1/4 = 6 and 1/4. This skill from Chapter 26 of Eureka Math Grade 4 builds on fraction decomposition.
Key Concepts
When adding a mixed number and a fraction with like denominators, add the fractional parts first. If the resulting fraction is improper, regroup it into a whole number and a fraction, then add it to the original whole number. $$A \frac{b}{c} + \frac{d}{c} = A + \frac{b+d}{c}$$.
Common Questions
How do you add a mixed number and a fraction with the same denominator?
Add the fractional parts. If the result is improper, convert it to a mixed number, then add 1 to the whole number of the original mixed number.
Solve 5 and 2/4 plus 3/4.
Add fractions: 2/4 + 3/4 = 5/4. Convert: 5/4 = 1 and 1/4. Add whole: 5 + 1 and 1/4 = 6 and 1/4.
Solve 2 and 5/8 plus 6/8.
Add fractions: 5/8 + 6/8 = 11/8. Convert: 11/8 = 1 and 3/8. Add whole: 2 + 1 and 3/8 = 3 and 3/8.
When is regrouping required when adding a fraction to a mixed number?
Regrouping is required when the sum of the numerators of the fractional parts equals or exceeds the denominator, creating an improper fraction.
What does it mean to add like units in this context?
Like units means the fractions share the same denominator. Since both fractions name the same size parts, you add only the numerators while keeping the denominator constant.