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.
Arizona Academic Standards 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 Arizona
In the Arizona 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.
Source: Arizona 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 ratio of cats to dogs at an animal shelter is 7:4. There are 42 cats. How many dogs are there?
answer box
24
Hint: 42 cats is 7 × 6. Keep the ratio equivalent: multiply 4 by 6 too.
Question 2
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 3
Which is greater: 11/6 or 1 5/6?
- They are equal
- 1 5/6
- 11/6
They are equal
Hint: Write the mixed number as an improper fraction with denominator 6: 1 5/6 = 11/6. Then compare the numerators.
Question 4
What is the ratio of sunflowers to all the items?
🌻🌻🌻🌷🌷🌷🌷🌷- 3:8
- 5:8
- 5:3
- 3:5
3:8
Hint: A part-to-whole ratio compares one group with everything. Count the sunflowers, then count all the items.
Question 5
The table shows equivalent ratios. What number replaces the ?
Pancake recipe Cups of flour Eggs 4 5 8 10 12 15 32 ? answer box
40
Hint: Find what the known number in the last row was multiplied by, compared with the ratio 4:5. Multiply the other number by the same amount.
Question 6
Which mixed number belongs at the ? on the number line?
- 2 1/4
- 2 1/2
- 2 1/5
- 3 1/4
2 1/4
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.