Adding fractions with the same denominator

1Summary 重點摘要

Same denominator: keep the denominator, just add the numerators.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Step 1: Check the denominatorsBefore adding fractions, look at the denominators. In 15 + 25 both are 5, so you can add directly; different denominators need converting first, which comes later in the course. Checking first is a habit that prevents errors.
2. Step 2: Add the numeratorsAdd the top numbers: 1 + 2 = 3, the numerator of the new fraction. The top counts how many parts were taken, so two takings add their counts; write 3 above the line first.
3. Step 3: Keep the denominatorWrite the denominator 5 unchanged, giving 35. Never add the denominators: 310 would be wrong, because the size of each part never changed, only the number of parts. This is the most common error, so take special care.
4. Step 4: Understand whyOne fifth plus two fifths equals three fifths, just as one sweet plus two sweets equals three sweets; the sweets never changed size. When the fraction units match, adding the counts is all there is to it, and that is the whole idea.
5. Step 5: Simplify if possibleAfter adding, check for simplifying: 18 + 38 = 48, and dividing the top and bottom by 4 gives 12. Simplifying keeps the value but writes it more simply; an answer should end in simplest form.
6. Step 6: Going past 135 + 45 = 75, where the numerator exceeds the denominator, so the sum is more than one whole. Seven fifths is fine as an answer, and later you will learn to write it as the mixed number 1 and 25.
7. Step 7: Adding three fractionsThree like fractions add the same way: 17 + 27 + 37 has numerators 1 + 2 + 3 = 6 with the denominator kept at 7, giving 67. Check the denominators, add the numerators, then look for simplifying — the same routine every time.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Same denominator first
• Add numerators, keep denominator
• Check if the result can be simplified
• The numerator may exceed the denominator, e.g. 35 + 45 = 75
• Three fractions work the same way: add all numerators, keep the denominator