Add and subtract fractions

What is this skill?

In fourth grade children add and subtract fractions that have the same denominator, and they add mixed numbers like 4 1/3 + 2 2/3. When the pieces are the same size, the work is counting pieces: 2/5 + 2/5 is four fifths, and 10/12 − 2/12 is eight twelfths. The denominator names the size of the piece and stays the same. The numerator counts how many pieces.

Mixed numbers add in two steps: add the wholes, then add the fractions. In 4 1/3 + 2 2/3 the wholes make 6 and the thirds make 3/3, which is one more whole, so the total is 7. This idea of “making a whole” is central. Children also learn that a fraction can be broken up (5/6 is 2/6 + 3/6), which is the base for decomposing fractions and for the later work with unlike denominators.

Why it matters

Fractions appear in measurement, cooking and time, and adding them is the most common thing people do with them. Understanding why the denominator stays the same prevents the most common misconception in this topic, which is adding the bottoms.

This is also the stepping stone to fifth grade, where denominators differ and children must first rewrite fractions with equivalent ones. If the like-denominator case is clear, with a picture in mind for every step, the harder case is a short step instead of a leap.

Common mistakes

• Adding the denominators too, so 2/5 + 2/5 becomes 4/10. The pieces stay fifths.
• Not turning an improper fraction into a whole number when the fractions add past one whole. In 4 1/3 + 2 2/3 the thirds add to 3/3, which is one more whole, so the answer is 7 and not 6 3/3.
• Subtracting the smaller numerator from the larger one in the wrong order.
• Adding the wholes and ignoring the fractions, or the other way around.
• Not reducing or converting, such as leaving 7/3 when the problem asked for a mixed number.

How to help at home

• Use a measuring cup. Pour 1/4 cup twice and talk about how many quarters you have, then pour a third time.
• Cut a pizza or a paper circle into equal slices and describe the amounts eaten and left, with fractions that add to the whole.
• Say the unit when you say the fraction: “three fifths plus one fifth is four fifths,” the same way you would say “three apples plus one apple.”
• Practice making a whole: ask “how many eighths do I need with 5/8 to make one?”
• Draw bars for each fraction and shade them, then put the shaded parts together.

Worked examples

These are real questions from the Tutorsaurus add and subtract fractions practice, with the answers worked out.

1. Example 1

   10/12 − 2/12 = ? (write as a fraction)

   Answer: 8/12. Same denominator: subtract the tops. 10 − 2 = 8, so 8/12.

2. Example 2

   4/5 − 2/5 = ? (write as a fraction)

   Answer: 2/5. Same denominator: subtract the tops. 4 − 2 = 2, so 2/5.

3. Example 3

   2/4 + 1/4 = ? (write as a fraction, like 5/8)

   Answer: 3/4. Same denominator: add the tops. 2 + 1 = 3, so 3/4.