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

4th Grade math lesson: Adding and Subtracting Fractions and Mixed Numbers – Maths PDF

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This grade 4 add subtract fractions lesson for 4th Grade 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.

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.

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 grade 4 add subtract fractions lesson

Key facts

With like denominators, add or subtract the numerators and keep the denominator.
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.
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 \(\frac{3}{4}\).

Grade 4 add subtract 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.

How to use this grade 4 add subtract fractions lesson

Read the definitions first, then follow the worked method line by line and redo the example on paper without looking. When every step makes sense, move on to the worksheet, then check yourself with the quiz.

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