4th Grade Adding and Subtracting Fractions and Mixed Numbers Lesson: Notes and Examples (Free PDF)

Q: What is a unit fraction?

A unit fraction has a numerator of 1, such as \frac{1}{4} or \frac{1}{10}. Every fraction is a sum of unit fractions. For example, \frac{3}{4} equals \frac{1}{4} + \frac{1}{4} + \frac{1}{4}. Seeing this helps explain why adding fractions means counting equal pieces.

Q: How do you subtract a mixed number from a whole number?

Break one whole into equal parts first. To find 6 - 2\frac{3}{5}, rewrite 6 as 5\frac{5}{5}. Then subtract wholes and fractions separately: 5 - 2 = 3 and \frac{5}{5} - \frac{3}{5} = \frac{2}{5}, so the answer is 3\frac{2}{5}.

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This 4th grade adding fractions lesson covers adding and subtracting fractions and mixed numbers (Common Core 4.NF.B.3a, 4.NF.B.3b, 4.NF.B.3c, 4.NF.B.3d), with a free PDF to print.

Key takeaway: This lesson helps fourth grade students add and subtract fractions with like denominators and work with mixed numbers.

Topic: Adding and Subtracting Fractions and Mixed Numbers (4th grade)
Content: One-page lesson with a definition, a worked example and key facts
Standards: 4.NF.B.3a, 4.NF.B.3b, 4.NF.B.3c, 4.NF.B.3d
Answers: Explanations included
Format: Free printable PDF, US Letter, black and white

To add or subtract fractions with the same denominator, add or subtract the numerators and keep the denominator: 2/8 + 3/8 = 5/8. A fraction can be decomposed into a sum of fractions with the same denominator. Mixed numbers can be changed to improper fractions to add or subtract them.

This lesson helps fourth grade students add and subtract fractions with like denominators and work with mixed numbers. It shows why the denominator stays the same: the pieces are all the same size, so only the number of pieces changes.

The lesson covers adding and subtracting like fractions, splitting a fraction into unit fractions, turning mixed numbers into improper fractions and back, and regrouping when a fraction part grows past one whole. Also, each idea is paired with a fraction strip or number sentence. Then, plan about 25 minutes, and try the examples on paper as you read.

Grade 4 · Common Core State Standards: 4.NF.B.3a, 4.NF.B.3b, 4.NF.B.3c, 4.NF.B.3d

Key facts in this 4th grade adding fractions lesson

Key facts

With like denominators, add or subtract the numerators and keep the denominator.
Next, a fraction can be decomposed in more than one way, such as 5/6 = 2/6 + 3/6.
A mixed number such as 2 1/4 equals the improper fraction 9/4.
Then, to add mixed numbers, add the wholes and the fractions, then regroup when the fraction is greater than 1.
To subtract mixed numbers, change them to improper fractions first.

How do like fractions combine?

The fraction $\frac{2}{8}$ tells you there are 2 pieces and each piece is an eighth of a whole. Equal-sized pieces can be counted together, so the top numbers are added and the bottom number is kept.

Adding and subtracting like fractions

$\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}$ and $\frac{a}{c} – \frac{b}{c} = \frac{a – b}{c}$. Pieces keep their size when they are joined or taken away, so the bottom number never changes.

Example: $\frac{2}{8} + \frac{3}{8} = \frac{5}{8}$.

2 eighths plus 3 eighths is 5 eighths.

Taking pieces away works the same way: $\frac{11}{12} – \frac{5}{12} = \frac{6}{12}$.

Can a fraction be split into smaller fractions?

Splitting a fraction into a sum of fractions with the same bottom number is called decomposing. Many splits are possible. For instance,$\frac{5}{6} = \frac{1}{6} + \frac{4}{6}$ and $\frac{5}{6} = \frac{2}{6} + \frac{3}{6}$. Any fraction can also be written as repeated unit fractions: $\frac{3}{4} = \frac{1}{4} + \frac{1}{4} + \frac{1}{4}$.

One strip, two ways to see five sixths.

What are mixed numbers and improper fractions?

A mixed number pairs a whole number with a fraction, such as$2\frac{1}{4}$. An improper fraction has a top number at least as big as the bottom number, such as $\frac{9}{4}$. Both forms describe the same amount.

2 wholes and 1 fourth is 9 fourths.

Mixed to improper: turn the whole number into pieces of the same size: $2 = \frac{8}{4}$.
Put the pieces together:$\frac{8}{4} + \frac{1}{4} = \frac{9}{4}$.
Improper to mixed: divide the top number by the bottom number:$9 \div 4 = 2$ remainder 1, so $\frac{9}{4}$ = $2\frac{1}{4}$.

Can you add and subtract mixed numbers?

Combine the whole numbers and the fractions separately. When the fractions total more than one whole, regroup the extra whole. Example: $2\frac{4}{6} + 1\frac{5}{6} = 3\frac{9}{6} = 4\frac{3}{6}$.

For subtraction, rewrite both mixed numbers as improper fractions first.$3\frac{1}{4} – 1\frac{3}{4} = \frac{13}{4} – \frac{7}{4} = \frac{6}{4} = 1\frac{2}{4}$.

The missing part is 3 $\frac{1}{4}$ minus 1 $\frac{3}{4}$.

4th grade adding fractions lesson: questions and answers

How do you add fractions with the same denominator?

Add the numerators and keep the denominator the same. For 2/8 + 3/8, add 2 + 3 to get 5, so the sum is 5/8.

Why do you keep the denominator the same?

The denominator tells the size of each part. Adding parts of the same size does not change their size, only how many there are.

How do you change a mixed number to an improper fraction?

Write the whole number as a fraction with the same denominator, then add. For 2 1/4, 2 = 8/4, and 8/4 + 1/4 = 9/4.

How do you change an improper fraction to a mixed number?

Divide the numerator by the denominator. The quotient is the whole number and the remainder is the new numerator. For 11/4, 11 divided by 4 is 2 remainder 3, so it is 2 3/4.

What do you do when the fraction part gets too big after adding?

Regroup. Take out whole numbers and keep the rest. For 3 7/5, 7/5 = 1 2/5, so the sum is 4 2/5.

Common mistakes with this 4th grade adding fractions lesson

Students add the denominators too, so $\frac{1}{5} + \frac{2}{5}$ becomes $\frac{3}{10}$. The pieces stay fifths, so keep the denominator and add only the numerators.
Students forget to convert when the fraction part reaches a whole. Instead, if $\frac{9}{8}$ appears in a sum, rewrite it as $1\frac{1}{8}$ and add the extra whole.
Students subtract the smaller fraction from the larger one even when it sits in the wrong spot. In $5\frac{1}{4} – 2\frac{3}{4}$, regroup one whole into fourths first.

How to study this chapter

Draw a fraction strip for any problem that feels confusing. Shading three of eight parts and then two more makes the sum of $\frac{5}{8}$ easy to see.
Practice changing mixed numbers with a short list, such as $1\frac{1}{2}$, $2\frac{1}{3}$, and $3\frac{3}{4}$. Multiply the whole by the denominator, then add the numerator.
Parents can use food at home. Cut a sandwich into fourths and ask what is left after eating three pieces, then write the matching subtraction sentence.

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