Introduction

Fractions often intimidate students, but they are an essential part of mathematics. With these five simple methods, you’ll be an expert in adding and subtracting fractions easily and accurately. Combining different fractions can be done without stress.

1. Common Denominator Method

Adding or subtracting fractions with the same denominator is quite simple. Just add or subtract the numerators while keeping the same denominator. For example:

(3/8) + (5/8) = (3+5)/8 = 8/8 = 1

(7/12) – (2/12) = (7-2)/12 = 5/12

When dealing with fractions that have different denominators, you’ll first need to find the Least Common Denominator (LCD). Once you have found the common denominator, rewrite both fractions using that denominator and then perform the addition or subtraction.

Example:

(3/4) + (2/3)

The least common multiple of 4 and 3 is 12. Then,

(9/12) + (8/12) = (9+8)/12 = 17/12

2. Cross-Multiply Method

In this method, you’ll cross-multiply the numerators and denominators of the two fractions before adding or subtracting.

Example:

(1/3) + (4/5)

Multiply 1 by 5 and then multiply 4 by 3 → (1×5)/(3×5)+ (4×3)/(5×3)

Simplify → ((1×5)+(4×3))/15 → (5+12)/15 →17

The result is (17/15).

3. Using Mixed Numbers

Another approach for adding or subtracting involves mixed numbers, which combine a whole number with a fraction. To do this, convert the mixed numbers into improper fractions and then apply the methods already discussed. Once you’ve added or subtracted the fractions, convert the result back to a mixed number if necessary.

4. Fraction Strips

A visual method for understanding fractions involves using fraction strips, which are divided into equal parts depending on their denominator. By comparing and overlapping these strips, students can see common denominators or equivalent fractions more readily.

5. Table Method

The table method can help you find common denominators for addition or subtraction. Create a table with each fraction in columns and rows with multiples of their respective denominators. Find the smallest multiple that appears in both columns (the least common multiple) and use that as your common denominator.

Conclusion

Choosing the right method when adding or subtracting fractions depends on your comfort level and the specific problem at hand. Being proficient in these five methods can help anyone add or subtract fractions easily no matter their background in mathematics.