Why do we add fractions with like denominators?

The real reason is due to the definition of the fraction itself, which is a representation of parts of a total which must be the same size. When you add or subtract fractions, you can’t express the result as a fraction if you do not divide the total into equal parts.

Do you need common denominators to add fractions?

In order to add fractions, the fractions must have a common denominator. We need the pieces of each fraction to be the same size to combine them together. These two fractions have the same denominator, so the equal parts that the whole has been split into are the same size.

What is the least common denominator of 5 42 and 7 30?

Steps for adding fractions

Find the least common denominator or LCM of the two denominators: LCM of 42 and 30 is 210.
For the 1st fraction, since 42 × 5 = 210,
Likewise, for the 2nd fraction, since 30 × 7 = 210,
25210 + 49210 = 25 + 49210 = 74210.
74/210 simplified gives 37105.
So, 5/42 + 7/30 = 37/105.

What is a common denominator for 4 and 3?

12
The LCM of 3 and 4 is 12.

What are the rules for adding fractions?

Adding Fractions

Step 1: Make sure the bottom numbers (the denominators) are the same.
Step 2: Add the top numbers (the numerators), put that answer over the denominator.
Step 3: Simplify the fraction (if possible)

How do you solve word problem with fractions?

How to solve Fraction Word Problems using Algebra? (1) The denominator of a fraction is 5 more than the numerator. If 1 is subtracted from the numerator, the resulting fraction is 1/3. Find the original fraction. (2) If 3 is subtracted from the numerator of a fraction, the value of the resulting fraction is 1/2.

How do I add fractions with uncommon denominators?

To add fractions with uncommon denominators, we need to change the fractions to equivalent fractions with common denominators before we find the sum. First, we would need to find the least common denominator (LCD), which is the LCM of the denominators. Next, we write equivalent fractions using the least common denominator.

How do you add fractions with the same denominator?

When you add two fractions that have the same denominator (bottom number), you simply add the numerators (top numbers) together and leave the denominator unchanged. For example, consider the following problem: As you can see, to add these two fractions, you add the numerators (1 + 2) and keep the denominator (5).

Why do you need common denominator to add fractions?

Reasons why it is necessary to have a common denominator before adding or subtracting fractions. This is done because it will become harder to compute and understand in case you are adding or subtracting the denominators. The denominator of a fraction tells you the relative size of the pieces.