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.
Minnesota K-12 Academic Standards benchmark: 6.3.6.5; 6.3.6.6 · comparing quantities with ratios and solving ratio problems
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 Minnesota
In the Minnesota K-12 Academic 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.
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
Which is greater: 33/8 or 4 1/8?
- They are equal
- 4 1/8
- 33/8
They are equal
Hint: Write the mixed number as an improper fraction with denominator 8: 4 1/8 = 33/8. Then compare the numerators.
Question 2
Which mixed number is equal to 19/5?
- 3 4/5
- 4 3/5
- 3 1/5
- 2 4/5
3 4/5
Hint: Divide 19 by 5. The quotient is the number of wholes. The remainder becomes the numerator of the fraction part, over 5.
Question 3
The table shows equivalent ratios. What number replaces the ?
Bracelet pattern Red beads White beads 3 5 6 10 9 15 15 ? answer box
25
Hint: Find what the known number in the last row was multiplied by, compared with the ratio 3:5. Multiply the other number by the same amount.
Question 4
Write the mixed number 4 1/8 as an improper fraction.
answer box
33/8
Hint: Multiply the whole number by the denominator, then add the numerator: 4 × 8 + 1. Keep the denominator, 8.
Question 5
Each whole is cut into 6 equal parts. Write the shaded amount as an improper fraction.
answer box
14/6
Hint: Count every shaded part: 2 full wholes are 12 parts, plus 2 more. Put the total over 6.
Question 6
What is the ratio of bananas to apples?
🍎🍎🍎🍎🍎🍌🍌- 5:2
- 2:7
- 5:7
- 2:5
2:5
Hint: Count each group. Write the numbers in the same order as the words: first : second.