6th grade · Math · Unit 2 of 21
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.
New York State Learning Standards learning standard: NY-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 New York
In the New York State Learning Standards, this is unit 2 of 21 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 mixed number is equal to 35/8?
- 4 5/8
- 5 3/8
- 3 3/8
- 4 3/8
4 3/8
Hint: Divide 35 by 8. The quotient is the number of wholes. The remainder becomes the numerator of the fraction part, over 8.
Question 2
What is the ratio of soccer balls to basketballs?
⚽⚽🏀🏀🏀🏀🏀- 7:2
- 5:2
- 2:5
- 5:7
2:5
Hint: Count each group. Write the numbers in the same order as the words: first : second.
Question 3
Write the mixed number 4 2/3 as an improper fraction.
answer box
14/3
Hint: Multiply the whole number by the denominator, then add the numerator: 4 × 3 + 2. Keep the denominator, 3.
Question 4
The ratio of wins to losses for a hockey team this season is 7:5. There are 63 wins. How many losses are there?
answer box
45
Hint: 63 wins is 7 × 9. Keep the ratio equivalent: multiply 5 by 9 too.
Question 5
Each whole is cut into 6 equal parts. Write the shaded amount as an improper fraction.
answer box
11/6
Hint: Count every shaded part: 1 full whole is 6 parts, plus 5 more. Put the total over 6.
Question 6
The table shows equivalent ratios. What number replaces the ?
Pancake recipe Cups of flour Eggs 4 3 8 6 12 9 32 ? answer box
24
Hint: Find what the known number in the last row was multiplied by, compared with the ratio 4:3. Multiply the other number by the same amount.