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.
Alabama Course of Study content standard: 6.1 · ratio notation and ratio language
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 Alabama
In the Alabama Course of Study, 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: 15/5 or 3 1/5?
- 15/5
- They are equal
- 3 1/5
3 1/5
Hint: Write the mixed number as an improper fraction with denominator 5: 3 1/5 = 16/5. Then compare the numerators.
Question 2
Write the mixed number 4 1/6 as an improper fraction.
answer box
25/6
Hint: Multiply the whole number by the denominator, then add the numerator: 4 × 6 + 1. Keep the denominator, 6.
Question 3
Which mixed number is equal to 35/6?
- 5 5/6
- 5 5/35
- 4 5/6
- 5 1/6
5 5/6
Hint: Divide 35 by 6. The quotient is the number of wholes. The remainder becomes the numerator of the fraction part, over 6.
Question 4
Which mixed number belongs at the ? on the number line?
- 2 5/6
- 3 5/6
- 2 2/3
- 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 5
The ratio of cats to dogs at an animal shelter is 4:7. There are 36 cats. How many dogs are there?
answer box
63
Hint: 36 cats is 4 × 9. Keep the ratio equivalent: multiply 7 by 9 too.
Question 6
Each whole is cut into 6 equal parts. Write the shaded amount as an improper fraction.
answer box
16/6
Hint: Count every shaded part: 2 full wholes are 12 parts, plus 4 more. Put the total over 6.