Grade 6 · Math · Unit 3 of 13
Mixed Numbers & Ratios
Improper fractions and ratios
What your child practises
Switching between improper fractions (like 13/5) and mixed numbers (2 3/5), placing them on a number line, and writing and using ratios such as 3:4 in tables and word problems.
Nunavut Curriculum approved guide: Alberta Mathematics K–9 (2007), Number · improper fractions and mixed numbers, and ratio
How we explain it
Children can open this short lesson before they practise.
- To change a mixed number to an improper fraction, multiply the whole by the bottom and add the top.
- A ratio compares two amounts, like 2 to 3.
- Equivalent ratios multiply or divide both parts by the same number.
Example: Write 2 3/4 as an improper fraction. 2 × 4 = 8. 8 + 3 = 11. Keep the bottom: 11/4. Answer: 11/4
Sample questions
A taste of this unit. In the app, questions change every time and get easier or harder to match your child.
Question 1
The table shows equivalent ratios. What number replaces the ?
Pancake recipe Cups of flour Eggs 1 4 2 8 3 12 7 ? answer box
28
Hint: Find what the known number in the last row was multiplied by, compared with the ratio 1:4. Multiply the other number by the same amount.
Question 2
Write the mixed number 5 5/6 as an improper fraction.
answer box
35/6
Hint: Multiply the whole number by the denominator, then add the numerator: 5 × 6 + 5. Keep the denominator, 6.
Question 3
Each whole is cut into 5 equal parts. Write the shaded amount as an improper fraction.
answer box
12/5
Hint: Count every shaded part: 2 full wholes are 10 parts, plus 2 more. Put the total over 5.
Question 4
What is the ratio of sunflowers to tulips?
🌻🌻🌷🌷🌷🌷🌷🌷- 2:6
- 2:8
- 8:2
- 6:8
2:6
Hint: Count each group. Write the numbers in the same order as the words: first : second.
Question 5
Which mixed number belongs at the ? on the number line?
- 2 3/4
- 3 3/4
- 2 1/2
- 1 3/4
2 3/4
Hint: Each whole is split into 4 equal jumps, so each jump is 1/4. Find the whole number just before the ?, then count the jumps past it.
Question 6
Which mixed number is equal to 29/4?
- 7 1/4
- 7 3/4
- 7 1/29
- 6 1/4
7 1/4
Hint: Divide 29 by 4. The quotient is the number of wholes. The remainder becomes the numerator of the fraction part, over 4.