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, fraction strips.

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

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

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

   Count the chosen pieces. Keep their name the same.

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

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

   Use common denominator 10.

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

   Calculate 7/10 + 3/10.

   1

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

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

   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.

   Simplify: 1.

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

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

   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.

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
• add or subtract like-sized fraction pieces
• 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.