Learn on PengiEureka Math, Grade 4Chapter 26: Addition and Subtraction of Fractions by Decomposition

Lesson 3: Add mixed numbers.

In this Grade 4 Eureka Math lesson, students learn to add mixed numbers by combining like units — whole numbers with whole numbers and fractions with fractions — including cases where the fractional parts sum to more than one whole. Students practice decomposing mixed numbers and applying the arrow way and number line strategies to regroup and simplify sums. The lesson is part of Chapter 26, which focuses on addition and subtraction of fractions by decomposition.

Section 1

Add Mixed Numbers and Regroup the Fractional Sum

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.

Abd+Ced=(A+C)+(bd+ed)A\frac{b}{d} + C\frac{e}{d} = (A+C) + (\frac{b}{d} + \frac{e}{d})

If b+ed≥1\frac{b+e}{d} \geq 1, regroup.

Examples

  • 234+134=(2+1)+(34+34)=3+64=3+124=4242\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}
  • 523+223=(5+2)+(23+23)=7+43=7+113=8135\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.

Section 2

Add Mixed Numbers by Making a Whole

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.

245+125=245+15+115=3+115=4152\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

  • 478+238=(478+18)+228=5+228=7284\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}
  • 323+323=(323+13)+313=4+313=7133\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}
  • 556+446=(556+16)+436=6+436=10365\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.

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Add Mixed Numbers and Regroup the Fractional Sum

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.

Abd+Ced=(A+C)+(bd+ed)A\frac{b}{d} + C\frac{e}{d} = (A+C) + (\frac{b}{d} + \frac{e}{d})

If b+ed≥1\frac{b+e}{d} \geq 1, regroup.

Examples

  • 234+134=(2+1)+(34+34)=3+64=3+124=4242\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}
  • 523+223=(5+2)+(23+23)=7+43=7+113=8135\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.

Section 2

Add Mixed Numbers by Making a Whole

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.

245+125=245+15+115=3+115=4152\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

  • 478+238=(478+18)+228=5+228=7284\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}
  • 323+323=(323+13)+313=4+313=7133\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}
  • 556+446=(556+16)+436=6+436=10365\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.