Adding fractions
Adding fractions with the same denominator is straightforward: add the numerators and place the sum over the common denominator. To add 1/7 + 2/7 + 3/7, add the numerators: 1 + 2 + 3 = 6, keeping the denominator 7, to get 6/7. For mixed numbers, add the whole number parts and fraction parts separately, then combine. This Grade 7 math skill from Saxon Math, Course 2 is the foundation for all fraction arithmetic and is prerequisite for adding fractions with different denominators, a key skill in algebra and real-world measurement.
Key Concepts
Property When adding fractions that have the same denominators, we add the numerators and write the sum over the common denominator.
Examples To add $\frac{1}{7} + \frac{2}{7} + \frac{3}{7}$, we add the numerators: $1+2+3=6$. The sum is $\frac{6}{7}$. Adding mixed numbers works the same way: $1 \frac{1}{8} + 1 \frac{1}{8} = (1+1) + (\frac{1}{8}+\frac{1}{8}) = 2 \frac{2}{8}$. How much is $\frac{1}{4}$ of a dollar plus $\frac{3}{4}$ of a dollar? $\frac{1}{4} + \frac{3}{4} = \frac{4}{4}$, which equals one whole dollar!
Explanation Imagine adding pizza slices! If your fractions share a denominator, it means all the slices are the same size. You just have to count up the numerators to find out how many slices you have altogether. The size of the slice, the denominator, stays the same. Simple as that!
Common Questions
How do I add fractions with the same denominator?
Add the numerators and keep the denominator the same. For example, 3/8 + 2/8 = 5/8. The denominator tells you the size of the pieces; adding numerators counts how many you have.
How do I add mixed numbers with the same denominator?
Add the whole number parts together and the fractional parts together separately. For 1 and 3/8 + 2 and 1/8: whole numbers 1 + 2 = 3, fractions 3/8 + 1/8 = 4/8 = 1/2, total = 3 and 1/2.
What do I do if the sum of the fractions exceeds 1 when adding mixed numbers?
Convert the improper fraction to a mixed number and add it to the whole number part. For fractions summing to 9/8: 9/8 = 1 and 1/8, add that to the whole number sum.
Why can you only add fractions directly when they have the same denominator?
Fractions with the same denominator represent same-sized pieces. Adding them is like adding apples to apples. Different denominators represent different-sized pieces that cannot be combined directly.
When do students learn to add fractions with common denominators?
Adding fractions with same denominators is introduced in Grade 3-4 and reviewed in Grade 7. Saxon Math, Course 2 covers it in Chapter 5 before extending to unlike denominators.
What is the first step if the fractions have different denominators?
Find a common denominator (the LCM of both denominators), convert each fraction to an equivalent fraction with that denominator, then add the numerators.
What is the difference between adding fractions and multiplying fractions?
Adding fractions requires common denominators — you add numerators and keep the denominator. Multiplying fractions does not require common denominators — you multiply numerators together and denominators together.