Adding and subtracting fractions helps students combine parts of a whole, compare quantities, and solve everyday problems with measurements, recipes, and money. This cheat sheet gives a clear process for working with fractions that have the same denominator and fractions that need a common denominator. It is useful for grades 4-7 because it connects visual fraction ideas to reliable step-by-step methods.
The most important idea is that fractions can only be added or subtracted directly when the denominators are the same. For like denominators, combine the numerators and keep the denominator. For unlike denominators, rewrite the fractions as equivalent fractions with a common denominator, then add or subtract.
Answers should usually be simplified, and improper fractions can be changed to mixed numbers when needed.
Key Facts
- For like denominators, add the numerators and keep the denominator: .
- For like denominators, subtract the numerators and keep the denominator: .
- Fractions with unlike denominators need a common denominator before adding or subtracting, such as .
- An equivalent fraction is made by multiplying the numerator and denominator by the same nonzero number: .
- A common denominator can be found by multiplying the denominators, so can use .
- After adding or subtracting, simplify the fraction by dividing the numerator and denominator by their greatest common factor, such as .
- To add or subtract mixed numbers, combine the whole numbers and fractions separately when possible: .
- If the fraction part is not large enough for subtraction, regroup one whole as a fraction, such as .
Vocabulary
- Numerator
- The numerator is the top number in a fraction and tells how many equal parts are being used.
- Denominator
- The denominator is the bottom number in a fraction and tells how many equal parts make one whole.
- Like Denominators
- Like denominators are denominators that are the same, such as the in and .
- Common Denominator
- A common denominator is a shared denominator used to rewrite fractions so they can be added or subtracted.
- Equivalent Fractions
- Equivalent fractions name the same value even though their numerators and denominators are different, such as and .
- Mixed Number
- A mixed number has a whole number and a fraction, such as .
Common Mistakes to Avoid
- Adding denominators, such as writing , is wrong because the denominator names the size of the parts and stays the same for like denominators.
- Combining unlike denominators without rewriting, such as , is wrong because halves and thirds are different-sized parts.
- Changing only the denominator when making equivalent fractions is wrong because the numerator and denominator must be multiplied by the same number, as in .
- Forgetting to simplify, such as leaving instead of , is incomplete because the fraction is not in simplest form.
- Subtracting mixed numbers without regrouping, such as trying directly, is wrong because is smaller than .
Practice Questions
- 1 Find the sum: .
- 2 Subtract and simplify: .
- 3 Add the mixed numbers: .
- 4 Explain why needs a common denominator before the numerators can be combined.