Adding, subtracting, and simplifying fractions with the same denominator

Adding and subtracting fractions with the same denominator

The denominator tells how many equal pieces the whole is split into, and the numerator tells how many of those pieces you have. When the denominators are the same, the pieces are the same size, so you only add or subtract the numerators and keep the denominator as it is.

2/7 + 3/7 puts together 2 pieces and 3 pieces out of 7, which makes 5 pieces: 2/7 + 3/7 = 5/7.

Simplifying

When the numerator and denominator can both be divided by the same number, as in 4/6, you can divide them to write a simpler fraction. This is called simplifying (or reducing). 4 and 6 can both be divided by 2, so 4/6 = 2/3. A fraction like 5/5, where the numerator and denominator are the same, equals 1.

This unit in the app shows answers in simplest form. If your child has not learned simplifying yet, introduce it simply as “a simpler way to write the same amount.”

Why children find it hard

• As with adding whole numbers, it is easy to think the denominators should be added too.
• To simplify, they need to find a number that divides both the numerator and the denominator, so if the times tables are slow, they miss it.
• Children sometimes write the numerator and denominator in the wrong places, especially when they enter them in separate boxes. Have them check which number goes on top, for example in 3/8.

Steps

1. Check that the denominators are the same. In this unit, they always are.
2. Add or subtract the numerators. Do not change the denominator; write it as it is.
3. If the numerator and denominator are the same, write 1. 5/5 and 4/4 are both 1.
4. See whether it can be simplified. Find a number (2, 3, 4 …) that divides both the numerator and the denominator, and keep dividing until you cannot anymore.
5. Check with a drawing. Split a bar into as many parts as the denominator and shade as many as the numerator to see whether the answer is right.

Common mistakes

• Adding the denominators too. For example, 2/7 + 3/7 = 5/14, where the denominator was worked out as 7 + 7. Show with a drawing that the size of the pieces stays the same.
• Subtracting the denominators in subtraction. Working out the denominator of 6/7 − 4/7 as 7 − 7 and writing 0 (the correct answer is 2/7).
• Not simplifying all the way. In 7/8 − 3/8 = 4/8, dividing by 2 only once and stopping at 2/4. Dividing once more gives 1/2. The app grades 2/4 as correct too, so check simplifying yourself.

10 practice problems

Same format as this unit in the app (denominators 2 to 9, adding and subtracting with the same denominator). Answers are written in simplest form. Tap to see each answer.

1. 2/7 + 3/7 = ?
   Answer

   5/7

2. 1/5 + 2/5 = ?
   Answer

   3/5

3. 1/6 + 3/6 = ?
   Answer

   2/3 (before simplifying: 4/6)

4. 3/8 + 3/8 = ?
   Answer

   3/4 (before simplifying: 6/8)

5. 2/5 + 3/5 = ?
   Answer

   1 (before simplifying: 5/5)

6. 5/9 − 2/9 = ?
   Answer

   1/3 (before simplifying: 3/9)

7. 6/7 − 4/7 = ?
   Answer

   2/7

8. 7/8 − 3/8 = ?
   Answer

   1/2 (before simplifying: 4/8)

9. 4/4 − 1/4 = ?
   Answer

   3/4

10. 4/5 − 2/5 = ?
    Answer

    2/5

Practicing this unit in the app

1. Open the Create tab at the bottom of the app. If you have not added your child yet, add them in the Children tab first.
2. Under 📚 Select Level, tap Lv.8 (Ages 10-11), then under 📖 Select Unit choose “Add, subtract & simplify fractions”. If numerators and denominators are still confusing, start with “Fraction basics”.
3. Set the number of problems with the − and + buttons on the unit card, or tap ✏️ to type a number. 5 to 10 problems is an easy start.
4. Choose your child under 👶 For whom? and create the problems. Your child can solve them on their own device, or tap Solve on this phone now right after creating to solve on your phone. The numerator and denominator go in separate boxes.
5. When your child submits, open the worksheet and tap ✅ Grade Now. The correct answer and your child's answer are shown for each problem, so you can also see here whether any answers were not simplified.
6. If any answers are wrong, tap ❌ Retry Wrong Answers on the results in your child's screen. The correct answers are shown only after they submit again.
7. Check the accuracy for each unit in the Progress tab. 90% or higher is shown as Good, 70-89% as Average, and below 70% as Weak.