Fractions · Learner pages

Lesson 1 · Rename the same fraction

Create equivalent fractions by dividing every part in the same way.

Name or initials: ____________   Date: ____________

A fraction names equal parts of one whole. Keep the whole the same when comparing pictures.

1. Start with one half. Shade one of two equal parts of a strip.
2. Split every part in two. The whole now has four equal parts; two of them are shaded.
3. Read the new name. The shaded amount did not change: 1/2 = 2/4.
4. Check the rule. Multiply both numbers by 2: (1 × 2)/(2 × 2) = 2/4. Scaling only one number changes the fraction.

Worked example: 2/3 = 4/6 because each third splits into two sixths. Multiply both 2 and 3 by 2. Four sixths cover the same amount as two thirds.

1. Which is equivalent to 2/5?

   1. 2/10 · 2. 4/10 · 3. 4/5

2. Which fraction equals 1/2?

   1. 1/4 · 2. 3/4 · 3. 3/6

3. To rename 3/4 with denominator 8, use…

   1. 6/8 · 2. 3/8 · 3. 4/8

Discuss: Draw a strip showing why 3/4 = 6/8. Explain what happened to each old part.

Lesson 2 · Compare using equal-sized parts

Compare fractions by renaming them with a common denominator.

Name or initials: ____________   Date: ____________

Numerators can be compared directly only when the parts have the same size.

1. Notice different part sizes. Compare 2/3 and 3/4 of the same whole. Thirds and quarters are not the same size.
2. Rename in twelfths. Split each third into four: 2/3 = 8/12. Split each quarter into three: 3/4 = 9/12.
3. Compare the numerators. Nine twelfths is greater than eight twelfths because each part is now the same size.
4. State and check. 3/4 > 2/3. The difference in the diagrams is one twelfth of the whole.

Worked example: Compare 3/5 and 1/2. Rename them as 6/10 and 5/10. Since 6 > 5, 3/5 > 1/2.

1. Which is greater: 1/3 or 1/4 of the same whole?

   1. 1/4 · 2. They are equal · 3. 1/3

2. Compare 3/8 and 5/8.

   1. 3/8 < 5/8 · 2. 3/8 > 5/8 · 3. They are equal

3. Which is greater: 2/3 or 1/2?

   1. 1/2 · 2. 2/3 · 3. They are equal

Discuss: Compare 2/3 and 1/2 using sixths. Explain why your answer needs the same whole.

Lesson 3 · Add equal-sized fraction parts

Add fractions after making the part sizes match.

Name or initials: ____________   Date: ____________

Adding fractions combines amounts. The denominator names the size of a part.

1. Start with the amounts. Add 1/2 and 1/4 of the same whole. The parts have different sizes.
2. Rename the half. 1/2 = 2/4. Now both amounts use quarters.
3. Combine the quarters. Two quarters plus one quarter gives three quarters.
4. Write the calculation. 1/2 + 1/4 = 2/4 + 1/4 = 3/4. The denominator stays 4 because the pieces are still quarters.

Worked example: 2/3 + 1/6 = 4/6 + 1/6 = 5/6. First rename two thirds as four sixths, then add the numerators because the parts match.

1. What is 2/7 + 3/7?

   1. 5/7 · 2. 5/14 · 3. 6/7

2. What is 1/2 + 1/4?

   1. 2/6 · 2. 3/4 · 3. 2/4

3. What is 1/3 + 1/6?

   1. 2/9 · 2. 1/6 · 3. 1/2

Discuss: A jug has 1/4 litre of water and you add 2/4 litre. Find the total, then explain why it is less than one litre.

Final check · Set 1

Try one set after the lessons. Use the other set after reviewing any errors.

1. Which equals 3/5?

   6/10 / 3/10 / 6/5

2. What number completes 1/3 = ?/9?

   1 / 3 / 6

3. Which is greater, 3/4 or 2/3?

   2/3 / They are equal / 3/4

4. Compare 5/8 and 3/8.

   5/8 > 3/8 / 5/8 < 3/8 / They are equal

5. What is 2/5 + 1/5?

   3/10 / 3/5 / 2/10

6. What is 1/2 + 1/6?

   2/8 / 1/3 / 2/3

Final check · Set 2

Try one set after the lessons. Use the other set after reviewing any errors.

1. Which equals 4/6?

   4/3 / 2/3 / 2/6

2. What number completes 2/3 = ?/12?

   2 / 6 / 8

3. Which is smaller: 1/5 or 1/2 of the same whole?

   1/5 / 1/2 / They are equal

4. Which is greater, 3/5 or 1/2?

   1/2 / 3/5 / They are equal

5. What is 3/8 + 2/8?

   5/16 / 6/8 / 5/8

6. What is 1/4 + 1/2?

   3/4 / 2/6 / 1/4