S.4 Add and subtract fractions with like denominators
What are fractions with like denominators?
Fractions represent parts of a whole. The denominator is the bottom number, and it tells us how many equal parts the whole is divided into. When two or more fractions have the same denominator, they are called fractions with like denominators. This common denominator makes adding and subtracting them straightforward because we are working with pieces of the same size.
- The fractions 38 and 58 have like denominators (both are eighths).
- The fractions 25 and 15 have like denominators (both are fifths).
- The fractions 412 and 712 have like denominators (both are twelfths).
When denominators are “like,” the size of the fractional pieces is identical. Think of it like having two pizzas cut into the same number of slices. It is easy to combine or compare the slices.
Adding fractions with like denominators
Adding fractions with like denominators is simple: you add the numerators (the top numbers) and keep the denominator the same. The denominator does not change because you are not changing the size of the fractional parts; you are simply counting how many of those parts you have in total.
- 16 + 46 = 56 (1 sixth + 4 sixths = 5 sixths)
- 310 + 210 = 510 (3 tenths + 2 tenths = 5 tenths)
- 712 + 412 = 1112
- 23 + 23 = 43 (This sum is greater than 1, which we call an improper fraction.)
Always add only the numerators. A common mistake is to add the denominators, too. Remember: the denominator is the name of the part (like “sixths” or “fifths”), and the numerator tells you how many of those parts you have.
Subtracting fractions with like denominators
Subtracting fractions with like denominators follows a similar rule: subtract the numerators and keep the denominator the same. You are removing a certain number of equal-sized parts from a group of those parts.
- 78 – 38 = 48 (7 eighths – 3 eighths = 4 eighths)
- 56 – 16 = 46
- 910 – 710 = 210
- 45 – 45 = 05 = 0
In subtraction, the first fraction must be at least as large as the fraction you are subtracting, otherwise the result would be negative. For fourth grade, we focus on cases where the difference is zero or a positive fraction.
Simplifying fractions
Simplifying fractions (also called reducing fractions) means writing the fraction in its simplest form, where the numerator and denominator have no common factors other than 1. After adding or subtracting fractions, it is considered best practice to simplify the answer.
- 48 simplifies to 12 because both 4 and 8 can be divided by 4.
- 510 simplifies to 12 because both 5 and 10 can be divided by 5.
- 69 simplifies to 23 because both 6 and 9 can be divided by 3.
- 34 is already in simplest form because 3 and 4 share no common factor other than 1.
To simplify, find the greatest common factor (GCF) of the numerator and denominator. Divide both by the GCF. A fraction is simplified when 1 is the only number that divides evenly into both the numerator and denominator.
Improper fractions and mixed numbers
When you add fractions, the sum can sometimes be greater than one whole. This results in an improper fraction, where the numerator is larger than or equal to the denominator. You can rewrite an improper fraction as a mixed number, which has a whole number part and a fractional part.
- 74 is an improper fraction. To convert it: 4 goes into 7 one time (1 whole), with 3 left over. So, 74 = 134.
- Adding: 56 + 56 = 106. This simplifies to 53, which is 123.
- Subtraction: 213 – 23 requires borrowing. You can rewrite 2 13 as 143 to subtract, resulting in 123.
Mixed numbers are often easier to understand in real-world contexts, like “1 and a half pizzas.” However, improper fractions are useful for performing calculations. Knowing how to convert between them is a key skill in fourth grade.
Solving word problems with fractions
Many real-world problems involve adding or subtracting fractions with like denominators. To solve a word problem, identify the operation needed, write the equation, and then perform the addition or subtraction. Always simplify your final answer and include the correct units.
Maya baked a cake. She used 38 of a bag of flour for the batter and 28 of the same bag for the frosting. How much flour did she use in total?
Solution: 38 + 28 = 58. Maya used 58 of the bag of flour.
Liam had a board that was 710 of a meter long. He cut off a piece that was 310 of a meter. How long is the remaining piece?
Solution: 710 – 310 = 410. Simplify: 410 = 25. The remaining board is 25 of a meter long.
When solving word problems, look for keywords: “in all” or “total” often means addition. “How much more,” “how many left,” or “difference” often means subtraction. Always check if your answer makes sense in the context of the problem.
Visual models for fraction addition and subtraction
Using visual models like fraction bars, number lines, or circle graphs can help you understand why adding and subtracting fractions with like denominators works. These models show that you are simply combining or removing pieces of the same size.
To add 25 + 15, imagine a bar divided into 5 equal parts. Shade 2 parts for the first fraction. Then, shade 1 more part for the second fraction. In total, 3 out of 5 parts are shaded, which is 35.
To subtract 56 – 26, mark a number line from 0 to 1 with sixths. Locate 56. Move back 2 jumps (each jump is 16) to land on 36, which simplifies to 12.
Drawing a quick model can help you check your work. If your picture shows a different result than your calculation, it is a sign to review your steps. Visual models build a strong conceptual foundation before moving to abstract rules.
Common Core alignment: CCSS.MATH.CONTENT.4.NF.B.3.A – Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. CCSS.MATH.CONTENT.4.NF.B.3.B – Decompose a fraction into a sum of fractions with the same denominator in more than one way. CCSS.MATH.CONTENT.4.NF.B.3.C – Add and subtract mixed numbers with like denominators. CCSS.MATH.CONTENT.4.NF.B.3.D – Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators.
Notes for teachers
This lesson is aligned with CCSS.MATH.CONTENT.4.NF.B.3 (A, B, C, D), which focuses on adding and subtracting fractions with like denominators, decomposing fractions, and solving word problems. All content is 100% free. Use it for whole-class instruction, independent study and practice, or homework.