6th grade · Math · Unit 2 of 17
Mixed Numbers & Ratios
Improper fractions and ratios
What your child practices
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.
Alaska content standards learning standard: 6.RP.1 · ratio language and ratio relationships
How we explain it
Children can open this short lesson before they practice.
- 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
Mixed Numbers & Ratios in Alaska
In the Alaska content standards, this is unit 2 of 17 in 6th grade Math, after Facts & Factors and before Decimal × and ÷.
Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.
Source: Alaska Department of Education and Early Development
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 5 2 10 4 15 6 40 ? answer box
16
Hint: Find what the known number in the last row was multiplied by, compared with the ratio 5:2. Multiply the other number by the same amount.
Question 2
Which mixed number belongs at the ? on the number line?
- 2 5/6
- 3 5/6
- 1 5/6
- 2 5/7
2 5/6
Hint: Each whole is split into 6 equal jumps, so each jump is 1/6. Find the whole number just before the ?, then count the jumps past it.
Question 3
Each whole is cut into 5 equal parts. Write the shaded amount as an improper fraction.
answer box
6/5
Hint: Count every shaded part: 1 full whole is 5 parts, plus 1 more. Put the total over 5.
Question 4
What is the ratio of blue counters to red counters?
🔴🔴🔴🔴🔴🔴🔴🔵🔵🔵🔵🔵- 5:7
- 5:12
- 12:7
- 7:5
5:7
Hint: Count each group. Write the numbers in the same order as the words: first : second.
Question 5
Which mixed number is equal to 25/6?
- 3 1/6
- 5 1/6
- 4 5/6
- 4 1/6
4 1/6
Hint: Divide 25 by 6. The quotient is the number of wholes. The remainder becomes the numerator of the fraction part, over 6.
Question 6
Write the mixed number 3 3/8 as an improper fraction.
answer box
27/8
Hint: Multiply the whole number by the denominator, then add the numerator: 3 × 8 + 3. Keep the denominator, 8.