Fractions · Answer guide

Lesson 1 · Rename the same fraction

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

1. Which is equivalent to 2/5?

   Answer: 4/10. Multiply numerator and denominator by 2: 2/5 = 4/10.

2. Which fraction equals 1/2?

   Answer: 3/6. 3/6 divides numerator and denominator by 3 to give 1/2.

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

   Answer: 6/8. Multiply both numerator and denominator by 2.

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

Teaching note: Multiplying only the denominator makes the parts smaller without increasing the selected parts. That is not the same amount. Open responses need discussion; they are not automatically marked.

Lesson 2 · Compare using equal-sized parts

Compare fractions by renaming them with a common denominator.

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

   Answer: 1/3. A third is a bigger part than a quarter of the same whole.

2. Compare 3/8 and 5/8.

   Answer: 3/8 < 5/8. Both use eighths. Three eighths is less than five eighths.

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

   Answer: 2/3. 2/3 = 4/6 and 1/2 = 3/6, so 2/3 is greater.

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

Teaching note: A larger denominator alone does not mean a larger fraction. For unit fractions of the same whole, more equal parts means each part is smaller. Open responses need discussion; they are not automatically marked.

Lesson 3 · Add equal-sized fraction parts

Add fractions after making the part sizes match.

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

   Answer: 5/7. Two sevenths and three sevenths make five sevenths.

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

   Answer: 3/4. Rename 1/2 as 2/4, then add one more quarter.

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

   Answer: 1/2. 1/3 = 2/6, so the sum is 3/6 = 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.

Teaching note: Do not add the denominators. 1/4 + 1/4 is 2/4, not 2/8: the pieces did not become eighths. Open responses need discussion; they are not automatically marked.

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. Multiply numerator and denominator by 2.

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

   3. The denominator was multiplied by 3, so multiply the numerator by 3.

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

   3/4. 3/4 = 9/12 and 2/3 = 8/12.

4. Compare 5/8 and 3/8.

   5/8 > 3/8. Five eighths is more than three eighths.

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

   3/5. Two fifths plus one fifth gives three fifths.

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

   2/3. 1/2 = 3/6; 3/6 + 1/6 = 4/6 = 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?

   2/3. Divide numerator and denominator by 2.

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

   8. Multiply both numbers by 4: 2/3 = 8/12.

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

   1/5. Splitting the same whole into five gives smaller parts than splitting into two.

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

   3/5. 3/5 = 6/10 and 1/2 = 5/10.

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

   5/8. Three eighths and two eighths make five eighths.

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

   3/4. Rename one half as two quarters and add one quarter.