What is a unit fraction?
A unit fraction is a fraction where the top number (the numerator) is always 1. The bottom number (the denominator) tells you how many equal parts make up the whole. A unit fraction represents just one part of that whole.
- 12 (one-half) is a unit fraction.
- 14 (one-fourth) is a unit fraction.
- 18 (one-eighth) is a unit fraction.
- 34 is not a unit fraction because the numerator is 3, not 1.
Think of the word “unit” meaning “one.” A unit fraction always has a numerator of 1. It helps us understand how a whole is broken into equal pieces.
Subtracting unit fractions with the same denominator
When subtracting unit fractions that have the same denominator, the denominator in the answer stays the same. You only subtract the numerators. Since the numerators are both 1, the result will be a numerator of 0. But a fraction with a numerator of 0 is equal to 0, unless the two fractions are the same.
- 13 – 13 = 03 = 0. If you take away one-third from one-third, nothing is left.
- 15 – 15 = 05 = 0. This means the whole part is completely removed.
If you are subtracting one unit fraction from another unit fraction with the same denominator, you are essentially subtracting the same amount. The result is always zero. This concept is key to understanding that fractions represent equal parts, and taking away all the parts leaves nothing.
Subtracting a unit fraction from a whole number
A common problem in fourth grade is subtracting a unit fraction from a whole number. To do this, you must first rewrite the whole number as a fraction with the same denominator as the unit fraction. Remember that any whole number can be written as a fraction by placing it over 1. Then, you find an equivalent fraction with the required denominator.
- 1 – 14 = 44 – 14 = 34
- 2 – 13 = 63 – 13 = 53. This can also be written as 123.
When rewriting a whole number as a fraction, multiply the whole number by the denominator of the unit fraction to get the new numerator. For example, to rewrite 3 as a fraction with a denominator of 8, calculate 3 × 8 = 24, so 3 = 248.
Subtracting a unit fraction from a mixed number
A mixed number contains a whole number and a fraction. To subtract a unit fraction from a mixed number, you may need to “borrow” or regroup from the whole number part if the fraction part is smaller than the unit fraction you are subtracting.
- 112 – 12 = 1. The fraction parts cancel out.
- 114 – 12 = ? First, rewrite 12 as 24. Then, since 14 is smaller than 24, regroup 114 as 44 + 14 = 54. Now subtract: 54 – 24 = 34.
Regrouping is like borrowing in regular subtraction. If the fraction in the mixed number is smaller than the fraction you are subtracting, take one whole from the whole number, convert it to fraction pieces, and add it to the existing fraction.
Using models to subtract unit fractions
Visual models, such as fraction bars or number lines, help you understand what it means to subtract a unit fraction. When you subtract a unit fraction, you are removing one equal part from a whole or from another fraction.
- Imagine a rectangular bar divided into 5 equal parts. If you have 35 shaded and you subtract 15, you remove one shaded part, leaving 25 shaded.
- On a number line from 0 to 1, divided into 4 equal segments, the point at 34 is marked. Subtracting 14 means moving one segment to the left, landing at 24, which simplifies to 12.
Always draw or imagine the model to check your work. Visualizing the parts being removed makes subtraction with fractions more concrete and helps prevent mistakes.
Subtracting unit fractions with different denominators
When subtracting a unit fraction from another fraction that is not a unit fraction, or subtracting two unit fractions with different denominators, you must find a common denominator. A common denominator is a number that both denominators divide into evenly. The least common denominator is the smallest of these numbers.
- 12 – 13 = ? The common denominator is 6. 12 = 36, and 13 = 26. So, 36 – 26 = 16.
- 58 – 14 = ? The common denominator is 8. 14 = 28. So, 58 – 28 = 38.
To find a common denominator quickly, you can multiply the two denominators together. However, always check if you can use a smaller number (the least common denominator) to keep your numbers simple.
Simplifying answers after subtraction
After subtracting fractions, your answer should be written in simplest form. A fraction is in simplest form when the numerator and denominator have no common factors other than 1. For unit fraction subtraction problems, the answer is often another unit fraction or a fraction that can be reduced.
- 12 – 14 = 24 – 14 = 14. This is already in simplest form.
- 34 – 12 = 34 – 24 = 14. Again, the answer is a unit fraction.
- 56 – 13 = 56 – 26 = 36. This simplifies to 12 because both 3 and 6 can be divided by 3.
Always check if your answer can be simplified. A fraction like 24 is not in its simplest form; it should be written as 12. Simplifying makes your answer clear and easy to understand.
Common Core alignment: 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, e.g., by using visual fraction models and equations to represent the problem.
Notes for teachers
This lesson is aligned with CCSS.MATH.CONTENT.4.NF.B.3.D, focusing on subtraction of unit fractions. The content builds from foundational understanding of unit fractions to more complex operations like regrouping and finding common denominators. All content is 100% free, use it for whole-class instruction, independent study and practice, or homework. Encourage students to use visual models and to always simplify their final answers.