What is a unit fraction?
A unit fraction is a fraction where the top number (numerator) is always 1. The bottom number (denominator) tells how many equal parts make up one whole.
- 12 (one-half)
- 14 (one-fourth)
- 18 (one-eighth)
- 13 (one-third)
Think of the word “unit” meaning “one.” A unit fraction is exactly one part of a whole that has been split into equal pieces.
What does it mean to add unit fractions?
Adding unit fractions means combining two or more fractions that each have a numerator of 1. When you add them, you are finding how many of those equal parts you have in total.
- 14 + 14 = 24
- 16 + 16 + 16 = 36
If the denominators are the same, you simply add the numerators (all 1’s) and keep the denominator the same. This works just like adding whole numbers: 1 apple + 1 apple = 2 apples.
Adding unit fractions with like denominators
Like denominators means the bottom numbers are the same. To add unit fractions with like denominators, add the numerators (which will be 1 + 1 + 1 …) and write that sum over the common denominator.
- 15 + 15 = 25
- 13 + 13 + 13 = 33 = 1 whole
- 110 + 110 + 110 + 110 = 410
When the numerator becomes equal to the denominator, the fraction equals 1 whole. For example, 55 = 1. When the numerator is larger than the denominator, you have more than one whole.
Adding unit fractions with unlike denominators
Unlike denominators means the bottom numbers are different. To add unit fractions with unlike denominators, you must first rename them so they have a common denominator. The easiest way is to find the least common denominator (LCD).
- 12 + 14 → common denominator 4 → 24 + 14 = 34
- 13 + 16 → common denominator 6 → 26 + 16 = 36 = 12
- 15 + 110 → common denominator 10 → 210 + 110 = 310
To find a common denominator, multiply the two denominators. Then rewrite each unit fraction by multiplying the numerator and denominator by the same number. Always check if your answer can be simplified.
Simplifying sums of unit fractions
Simplifying means writing a fraction in its smallest possible numbers. A fraction is simplified when the numerator and denominator have no common factors other than 1.
- 24 simplifies to 12 (divide top and bottom by 2)
- 36 simplifies to 12 (divide top and bottom by 3)
- 48 simplifies to 12 (divide top and bottom by 4)
When you add two unit fractions with different denominators, the answer is often not a unit fraction. For example, 12 + 13 = 56. That is a non-unit fraction.
Adding more than two unit fractions
You can add three, four, or even more unit fractions. The process is the same: find a common denominator, convert each fraction, then add all the numerators.
- 12 + 14 + 18 → common denominator 8 → 48 + 28 + 18 = 78
- 13 + 13 + 16 → common denominator 6 → 26 + 26 + 16 = 56
When adding many unit fractions, it often helps to add two at a time. First, add the first two, then add that result to the next unit fraction.
Writing sums greater than 1
When you add enough unit fractions, the total can be greater than 1. This is called an improper fraction (numerator larger than denominator). You can also write it as a mixed number.
- 13 + 13 + 13 + 13 = 43 = 113
- 12 + 12 + 12 = 32 = 112
- 14 + 14 + 14 + 14 + 14 = 54 = 114
To 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 over the same denominator.
Real-world word problems with unit fractions
Adding unit fractions helps solve everyday problems. You might share pizza slices, measure ingredients for a recipe, or divide a length of ribbon.
- Pizza problem: Luis ate 18 of a pizza. Maya ate 18. How much did they eat together? 18 + 18 = 28 = 14.
- Juice problem: A recipe calls for 14 cup of juice and another 12 cup. Total = 14 + 24 = 34 cup.
- Distance problem: Jana ran 15 mile, then another 15 mile, then 15 mile. Total = 35 mile.
Always read the problem carefully. Ask: “Are the denominators the same? Do I need to find a common denominator? Does my answer make sense?”
Checking your work when adding unit fractions
Always check your addition to avoid mistakes. A good habit is to estimate first, then check if your sum is reasonable.
- For 13 + 16, estimate: 13 is about 0.33, 16 is about 0.17, sum ≈ 0.5. Exact: 26 + 16 = 36 = 12. Correct.
- For 14 + 14 + 14, count the 1’s: three copies of 14 = 34.
Another way to check: use fraction circles or number lines. Draw a picture to see if your sum is correct. Visual models help catch errors.
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.D – Solve word problems involving addition 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 and CCSS.MATH.CONTENT.4.NF.B.3.D.
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