6th grade · Math · Unit 4 of 19
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.
Texas Essential Knowledge and Skills (TEKS) teks student expectation: 6.4(C); 6.5(A) · ratios as comparisons of two quantities, and problems with ratio tables
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 Texas
In the Texas Essential Knowledge and Skills (TEKS), this is unit 4 of 19 in 6th grade Math, after Dividing Fractions and before Unit Rates.
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: Texas Education Agency (TEA)
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 ?
Pancake recipe Cups of flour Eggs 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 2
What is the ratio of apples to bananas?
🍎🍎🍎🍎🍌🍌🍌🍌🍌- 5:9
- 9:4
- 4:9
- 4:5
4:5
Hint: Count each group. Write the numbers in the same order as the words: first : second.
Question 3
Which is greater: 15/8 or 2 1/8?
- 2 1/8
- They are equal
- 15/8
2 1/8
Hint: Write the mixed number as an improper fraction with denominator 8: 2 1/8 = 17/8. Then compare the numerators.
Question 4
The ratio of girls to boys in a choir is 1:7. There are 9 girls. How many boys are there?
answer box
63
Hint: 9 girls is 1 × 9. Keep the ratio equivalent: multiply 7 by 9 too.
Question 5
Which mixed number is equal to 19/8?
- 3 3/8
- 2 5/8
- 2 3/8
- 1 3/8
2 3/8
Hint: Divide 19 by 8. The quotient is the number of wholes. The remainder becomes the numerator of the fraction part, over 8.
Question 6
Each whole is cut into 4 equal parts. Write the shaded amount as an improper fraction.
answer box
5/4
Hint: Count every shaded part: 1 full whole is 4 parts, plus 1 more. Put the total over 4.