15 4.NF.B.3a Math.4.NF.3a 4.NF.B.3.A 4.NR.4.4 4.NF.3.a 4.NF.B.3.a 4.NF.B.3.a 4.NF.3a 4.NF.3.a 4.NF.B.3.a 15.b 4.NF.B.3c Math.4.NF.3c 4.NF.B.3.C 4.NR.4.6 4.NF.3.c 4.NF.3c 4.NF.3.c 4.NF.3.c 4.NF.B.3.c 4.NF.B.3.c CC.2.1.4.C.2 M04.A-F.2.1.1 M04.A-F.2.1.3 MA.4.FR.2.2 MA.4.FR.2.3 MA.4.AR.1.2 4.NR.4.6 4.NR.5.1 4.CAR.5

Add & Subtract Fractions & Mixed Numbers 4th Grade

Alabama Course of Study Standards: 15
Model and justify decompositions of fractions and explain addition and subtraction of fractions as joining or separating parts referring to the same whole.
Arizona Academic Standards: 4.NF.B.3a Common Core State Standards: Math.4.NF.3a or 4.NF.B.3.A Kentucky Academic Standards (KAS): 4.NF.3.a Mississippi College- and Career-Readiness Standards: 4.NF.3a
Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
Georgia Math and ELA Standards: 4.NR.4.4
Represent whole numbers and fractions as the sum of unit fractions.
Louisiana Academic Standards: 4.NF.B.3.a
Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Example: 3/4 = 1/4 + 1/4 + 1/4.
Massachusetts Curriculum Frameworks: 4.NF.B.3.a
Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. (The whole can be a set of objects.)
North Carolina - Standard Course of Study: 4.NF.3.a
Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
Tennessee Academic Standards: 4.NF.B.3.a
Decompose a fraction into a sum of fractions with the same denominator in more than one way (e.g., 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 21/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8), recording each decomposition by an equation. Justify decompositions by using a visual fraction model.
Alabama Course of Study Standards: 15.b
Add and subtract fractions and mixed numbers with like denominators using fraction equivalence, properties of operations, and the relationship between addition and subtraction.
Arizona Academic Standards: 4.NF.B.3c
Add and subtract mixed numbers with like denominators (e.g., by using properties of operations and the relationship between addition and subtraction and/or by replacing each mixed number with an equivalent fraction).
Common Core State Standards: Math.4.NF.3c or 4.NF.B.3.C Kentucky Academic Standards (KAS): 4.NF.3.c Mississippi College- and Career-Readiness Standards: 4.NF.3c
Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.
Georgia Math and ELA Standards: 4.NR.4.6
Add and subtract fractions and mixed numbers with like denominators using a variety of tools.
North Carolina - Standard Course of Study: 4.NF.3.c
Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.
New York State Next Generation Learning Standards: 4.NF.3.c
Add and subtract mixed numbers with like denominators. e.g., replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction
Tennessee Academic Standards: 4.NF.B.3.c
Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction.
Wisconsin Academic Standards: 4.NF.B.3.c
Add and subtract fractions, including mixed numbers, with like denominators (e.g., 3/8 + 2/8) and related denominators (e.g., 1/2 +1/4, 1/3 + 1/6) by using visual fraction models (e.g., tape diagrams and number lines), properties of operations, and the relationship between addition and subtraction.
Pennsylvania Core Standards: CC.2.1.4.C.2
Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Pennsylvania Core Standards: M04.A-F.2.1.1
Add and subtract fractions with a common denominator (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100; answers do not need to be simplified; and no improper fractions as the final answer).
Pennsylvania Core Standards: M04.A-F.2.1.3
Add and subtract mixed numbers with a common denominator (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100; no regrouping with subtraction; fractions do not need to be simplified; and no improper fractions as the final answers).
Florida - Benchmarks for Excellent Student Thinking: MA.4.FR.2.2
Add and subtract fractions with like denominators, including mixed numbers and fractions greater than one, with procedural reliability.
Florida - Benchmarks for Excellent Student Thinking: MA.4.FR.2.3
Explore the addition of a fraction with denominator of 10 to a fraction with denominator of 100using equivalent fractions.
Florida - Benchmarks for Excellent Student Thinking: MA.4.AR.1.2
Solve real-world problems involving addition and subtraction of fractions with like denominators, including mixed numbers and fractions greater than one.
Georgia Math and ELA Standards: 4.NR.4.6
Add and subtract fractions and mixed numbers with like denominators using a variety of tools.
Georgia Math and ELA Standards: 4.NR.5.1
Demonstrate and explain the concept of equivalent fractions with denominators of 10 and 100, using concrete materials and visual models. Add two fractions with denominators of 10 and 100.
Arkansas Academic Standards: 4.CAR.5
Add and subtract fractions, including mixed numbers, with like denominators, using visual fraction models and equations. Fractions include: denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100

A mixed number is made up of a whole number and a fraction.

One way to add and subtract mixed numbers is to
convert the mixed numbers to improper fractions.

First, convert

1 \frac{3}{8}

to an improper fraction.
Write 1 as an improper fraction

(\frac{8}{8})

, and add it to

\frac{3}{8}

\frac{8}{8} + \frac{3}{8} = \frac{11}{8}

Next, convert

2 \frac{1}{8}

to an improper fraction.
Write 2 as an improper fraction

(\frac{16}{8})

, and add it to

\frac{1}{8}

\frac{16}{8} + \frac{1}{8} = \frac{17}{8}

Then, add the improper fractions.

\frac{11}{8} + \frac{17}{8} = \frac{28}{8}

Another way to add or subtract mixed numbers
is to use properties of operations.

First, write each mixed number as an addition problem.

3 \frac{2}{3} = 3 + \frac{2}{3}

2 \frac{1}{3} = 2 + \frac{1}{3}

Next, subtract the mixed numbers.

(3 + \frac{2}{3}) - (2 + \frac{1}{3}) = 3 + \frac{2}{3} - 2 - \frac{1}{3}

Use the commutative property to rearrange the numbers so that the whole numbers and fractions are together.

3 - 2 + \frac{2}{3} - \frac{1}{3}

Use the associative property to group the whole numbers and fractions.

(3 - 2) + (\frac{2}{3} - \frac{1}{3})

Subtract, then add.

\begin{matrix} (3 - 2) + (\frac{2}{3} - \frac{1}{3}) & = & 1 + \frac{1}{3} \\ = & 1 \frac{1}{3} \end{matrix}

Add & Subtract Fractions & Mixed Numbers

Alabama Course of Study Standards: 15

Model and justify decompositions of fractions and explain addition and subtraction of fractions as joining or separating parts referring to the same whole.

Arizona Academic Standards: 4.NF.B.3a

Common Core State Standards: Math.4.NF.3a or 4.NF.B.3.A

Kentucky Academic Standards (KAS): 4.NF.3.a

Mississippi College- and Career-Readiness Standards: 4.NF.3a

Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

Georgia Math and ELA Standards: 4.NR.4.4

Represent whole numbers and fractions as the sum of unit fractions.

Louisiana Academic Standards: 4.NF.B.3.a

Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Example: 3/4 = 1/4 + 1/4 + 1/4.

Massachusetts Curriculum Frameworks: 4.NF.B.3.a

Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. (The whole can be a set of objects.)

North Carolina - Standard Course of Study: 4.NF.3.a

Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

Tennessee Academic Standards: 4.NF.B.3.a

Decompose a fraction into a sum of fractions with the same denominator in more than one way (e.g., 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 21/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8), recording each decomposition by an equation. Justify decompositions by using a visual fraction model.

Alabama Course of Study Standards: 15.b

Add and subtract fractions and mixed numbers with like denominators using fraction equivalence, properties of operations, and the relationship between addition and subtraction.

Arizona Academic Standards: 4.NF.B.3c

Add and subtract mixed numbers with like denominators (e.g., by using properties of operations and the relationship between addition and subtraction and/or by replacing each mixed number with an equivalent fraction).

Common Core State Standards: Math.4.NF.3c or 4.NF.B.3.C

Kentucky Academic Standards (KAS): 4.NF.3.c

Mississippi College- and Career-Readiness Standards: 4.NF.3c

Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

Georgia Math and ELA Standards: 4.NR.4.6

Add and subtract fractions and mixed numbers with like denominators using a variety of tools.

North Carolina - Standard Course of Study: 4.NF.3.c

Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

New York State Next Generation Learning Standards: 4.NF.3.c

Add and subtract mixed numbers with like denominators.e.g., replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction

Tennessee Academic Standards: 4.NF.B.3.c

Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction.

Wisconsin Academic Standards: 4.NF.B.3.c

Add and subtract fractions, including mixed numbers, with like denominators (e.g., 3/8 + 2/8) and related denominators (e.g., 1/2 +1/4, 1/3 + 1/6) by using visual fraction models (e.g., tape diagrams and number lines), properties of operations, and the relationship between addition and subtraction.

Pennsylvania Core Standards: CC.2.1.4.C.2

Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

Pennsylvania Core Standards: M04.A-F.2.1.1

Add and subtract fractions with a common denominator (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100; answers do not need to be simplified; and no improper fractions as the final answer).

Pennsylvania Core Standards: M04.A-F.2.1.3

Add and subtract mixed numbers with a common denominator (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100; no regrouping with subtraction; fractions do not need to be simplified; and no improper fractions as the final answers).

Florida - Benchmarks for Excellent Student Thinking: MA.4.FR.2.2

Add and subtract fractions with like denominators, including mixed numbers and fractions greater than one, with procedural reliability.

Florida - Benchmarks for Excellent Student Thinking: MA.4.FR.2.3

Explore the addition of a fraction with denominator of 10 to a fraction with denominator of 100using equivalent fractions.

Florida - Benchmarks for Excellent Student Thinking: MA.4.AR.1.2

Solve real-world problems involving addition and subtraction of fractions with like denominators, including mixed numbers and fractions greater than one.

Georgia Math and ELA Standards: 4.NR.4.6

Add and subtract fractions and mixed numbers with like denominators using a variety of tools.

Georgia Math and ELA Standards: 4.NR.5.1

Demonstrate and explain the concept of equivalent fractions with denominators of 10 and 100, using concrete materials and visual models. Add two fractions with denominators of 10 and 100.

Arkansas Academic Standards: 4.CAR.5

Add and subtract fractions, including mixed numbers, with like denominators, using visual fraction models and equations.Fractions include: denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100

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Add and subtract mixed numbers with like denominators.
e.g., replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction

Add and subtract fractions, including mixed numbers, with like denominators, using visual fraction models and equations.
Fractions include: denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100