Add and subtract like fractions within one whole

What you will learn

• Add and subtract like fractions within one whole

Models used: number sentences, stories, tables.

Before you start

• Compare like fractions with denominators up to 12

Join and remove pieces of the same size

One fifth of a strip is shaded. Shade two more fifths. What fraction is shaded now?

1. Each strip is one whole of the same size. Count all the equal parts, then count the shaded parts.

   The whole strip has five equal parts. One part is shaded: one fifth.

   1/5

   Three quarters and one quarter are counts of the same-sized piece. Unlike pieces first need a common name.

2. Each strip is one whole of the same size. Count all the equal parts, then count the shaded parts.

   Shade two more parts of the same size. Count the shaded fifths: one, two, three.

   1/5 + 2/5 = 3/5

   The size of a fraction depends on both numbers: how many equal parts make the whole, and how many of those parts we take.

3. Each strip is one whole of the same size. Count all the equal parts, then count the shaded parts.

   We did not cut the strip again, so each piece is still a fifth. That is why the denominator stays five.

   Add the number of fifths: 1 + 2 = 3

   The size of a fraction depends on both numbers: how many equal parts make the whole, and how many of those parts we take.

4. Each strip is one whole of the same size. Count all the equal parts, then count the shaded parts.

   Now remove one shaded fifth. Two fifths remain. Subtraction counts how many of the same-sized pieces are left.

   3/5 − 1/5 = 2/5

   The size of a fraction depends on both numbers: how many equal parts make the whole, and how many of those parts we take.

Worked example: A new example, together

Calculate 7/10 + 3/10.

1. The parts must have the same size. Read each value with the heading above its column.

   Check the whole, rename unequal-sized parts when necessary, then join or remove the counts.

   Adding or subtracting equal-sized fractional parts changes their count, not their size.

   The parts must have the same size

   First amount in equal parts	Second amount in equal parts
   7/10	3/10

2. The parts must have the same size. Read each value with the heading above its column.

   Use common denominator 10.

   The parts must have the same size

   First amount in equal parts	Second amount in equal parts
   7/10	3/10

   Calculate 7/10 + 3/10.

   1

3. The parts must have the same size. Read each value with the heading above its column.

   Use common denominator 10.

   The parts must have the same size

   First amount in equal parts	Second amount in equal parts
   7/10	3/10

4. The parts must have the same size. Read each value with the heading above its column.

   7/10 + 3/10 = 10/10.

   The parts must have the same size

   First amount in equal parts	Second amount in equal parts
   7/10	3/10

5. The parts must have the same size. Read each value with the heading above its column.

   Simplify: 1.

   The parts must have the same size

   First amount in equal parts	Second amount in equal parts
   7/10	3/10

6. The parts must have the same size. Read each value with the heading above its column.

   Check the result against the question we started with.

   10/10 − 3/10 = 7/10.

   We found 1. Adding or subtracting equal-sized fractional parts changes their count, not their size.

   The parts must have the same size

   First amount in equal parts	Second amount in equal parts
   7/10	3/10

Common mistakes to discuss

• Adding the denominators too. The denominator names the size of the piece and does not change. 2/5 + 1/5 = 3/5, not 3/10.

Check your understanding

• Add and subtract like fractions within one whole
• explain why fraction addition and subtraction need equal-sized parts
• check the answer against the original quantities and units

Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.