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.
Maine Learning Results learning standard: 6.RP.A.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 Maine
In the Maine Learning Results, 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: Maine Department of Education
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 ?
Bracelet pattern Red beads White beads 4 1 8 2 12 3 32 ? answer box
8
Hint: Find what the known number in the last row was multiplied by, compared with the ratio 4:1. Multiply the other number by the same amount.
Question 2
Which is greater: 11/8 or 1 1/8?
- They are equal
- 11/8
- 1 1/8
11/8
Hint: Write the mixed number as an improper fraction with denominator 8: 1 1/8 = 9/8. Then compare the numerators.
Question 3
Write the mixed number 2 2/3 as an improper fraction.
answer box
8/3
Hint: Multiply the whole number by the denominator, then add the numerator: 2 × 3 + 2. Keep the denominator, 3.
Question 4
Each whole is cut into 8 equal parts. Write the shaded amount as an improper fraction.
answer box
10/8
Hint: Count every shaded part: 1 full whole is 8 parts, plus 2 more. Put the total over 8.
Question 5
Which mixed number is equal to 27/4?
- 5 3/4
- 6 3/27
- 6 3/4
- 6 1/4
6 3/4
Hint: Divide 27 by 4. The quotient is the number of wholes. The remainder becomes the numerator of the fraction part, over 4.
Question 6
The ratio of wins to losses for a hockey team this season is 2:7. There are 12 wins. How many losses are there?
answer box
42
Hint: 12 wins is 2 × 6. Keep the ratio equivalent: multiply 7 by 6 too.