Fraction Test: Review of Fraction Concepts Worksheet for 6th - 7th ... - Free Printable

Here are the step-by-step solutions for each problem on the worksheet.

1. Convert to a mixed number: $\frac{21}{8}$
* Divide 21 by 8.
* $8 \times 2 = 16$.
* $21 - 16 = 5$ (remainder).
* The whole number is 2, and the remainder is the numerator over the original denominator.
* Answer: $2 \frac{5}{8}$

2. Convert to a mixed number: $\frac{38}{9}$
* Divide 38 by 9.
* $9 \times 4 = 36$.
* $38 - 36 = 2$ (remainder).
* Answer: $4 \frac{2}{9}$

3. Convert to a mixed number: $\frac{67}{10}$
* Divide 67 by 10.
* $10 \times 6 = 60$.
* $67 - 60 = 7$ (remainder).
* Answer: $6 \frac{7}{10}$

4. Convert to an improper fraction: $3 \frac{5}{8}$
* Multiply the whole number (3) by the denominator (8): $3 \times 8 = 24$.
* Add the numerator (5): $24 + 5 = 29$.
* Keep the same denominator (8).
* Answer: $\frac{29}{8}$

5. Convert to an improper fraction: $8 \frac{3}{10}$
* Multiply the whole number (8) by the denominator (10): $8 \times 10 = 80$.
* Add the numerator (3): $80 + 3 = 83$.
* Keep the same denominator (10).
* Answer: $\frac{83}{10}$

6. Convert to an improper fraction: $7 \frac{5}{12}$
* Multiply the whole number (7) by the denominator (12): $7 \times 12 = 84$.
* Add the numerator (5): $84 + 5 = 89$.
* Keep the same denominator (12).
* Answer: $\frac{89}{12}$

7. Calculate: $4\frac{1}{5} + 8\frac{3}{5}$
* Add the whole numbers: $4 + 8 = 12$.
* Add the fractions: $\frac{1}{5} + \frac{3}{5} = \frac{4}{5}$.
* Combine them.
* Answer: $12 \frac{4}{5}$

8. Calculate: $7\frac{2}{9} + 6\frac{1}{9}$
* Add the whole numbers: $7 + 6 = 13$.
* Add the fractions: $\frac{2}{9} + \frac{1}{9} = \frac{3}{9}$.
* Simplify the fraction $\frac{3}{9}$ by dividing top and bottom by 3, which gives $\frac{1}{3}$.
* Answer: $13 \frac{1}{3}$

9. Calculate: $8\frac{5}{7} - 2\frac{2}{7}$
* Subtract the whole numbers: $8 - 2 = 6$.
* Subtract the fractions: $\frac{5}{7} - \frac{2}{7} = \frac{3}{7}$.
* Answer: $6 \frac{3}{7}$

10. Calculate: $6\frac{3}{8} + 1\frac{1}{8}$
* Add the whole numbers: $6 + 1 = 7$.
* Add the fractions: $\frac{3}{8} + \frac{1}{8} = \frac{4}{8}$.
* Simplify the fraction $\frac{4}{8}$ by dividing top and bottom by 4, which gives $\frac{1}{2}$.
* Answer: $7 \frac{1}{2}$

11. Calculate: $7\frac{5}{6} - 6\frac{1}{6}$
* Subtract the whole numbers: $7 - 6 = 1$.
* Subtract the fractions: $\frac{5}{6} - \frac{1}{6} = \frac{4}{6}$.
* Simplify the fraction $\frac{4}{6}$ by dividing top and bottom by 2, which gives $\frac{2}{3}$.
* Answer: $1 \frac{2}{3}$

12. Calculate: $1\frac{2}{5} + 6\frac{1}{5}$
* Add the whole numbers: $1 + 6 = 7$.
* Add the fractions: $\frac{2}{5} + \frac{1}{5} = \frac{3}{5}$.
* Answer: $7 \frac{3}{5}$

13. Calculate: $4\frac{2}{7} + 4\frac{3}{7}$
* Add the whole numbers: $4 + 4 = 8$.
* Add the fractions: $\frac{2}{7} + \frac{3}{7} = \frac{5}{7}$.
* Answer: $8 \frac{5}{7}$

14. Calculate: $6\frac{1}{3} - 7\frac{2}{3}$
* Since you cannot subtract a larger number from a smaller one easily with mixed numbers here, convert both to improper fractions first.
* $6\frac{1}{3} = \frac{19}{3}$.
* $7\frac{2}{3} = \frac{23}{3}$.
* Subtract: $\frac{19}{3} - \frac{23}{3} = -\frac{4}{3}$.
* Convert back to a mixed number: $-1 \frac{1}{3}$.
* *Note: If negative numbers haven't been learned yet, check if the question meant $7\frac{2}{3} - 6\frac{1}{3}$. If so, the answer would be $1 \frac{1}{3}$. Based strictly on the order written ($6... - 7...$), the answer is negative.*
* Answer: $-1 \frac{1}{3}$

15. Calculate: $4\frac{1}{4} + 5\frac{2}{4}$
* Add the whole numbers: $4 + 5 = 9$.
* Add the fractions: $\frac{1}{4} + \frac{2}{4} = \frac{3}{4}$.
* Answer: $9 \frac{3}{4}$

16. Calculate: $6\frac{3}{5} + 1\frac{1}{5}$
* Add the whole numbers: $6 + 1 = 7$.
* Add the fractions: $\frac{3}{5} + \frac{1}{5} = \frac{4}{5}$.
* Answer: $7 \frac{4}{5}$

17. Calculate: $9\frac{1}{3} - 3\frac{2}{3}$
* You cannot subtract $\frac{2}{3}$ from $\frac{1}{3}$. You need to borrow from the whole number 9.
* Change $9\frac{1}{3}$ to $8\frac{4}{3}$ (take 1 from 9, making it 8, and add $\frac{3}{3}$ to $\frac{1}{3}$).
* Now subtract whole numbers: $8 - 3 = 5$.
* Subtract fractions: $\frac{4}{3} - \frac{2}{3} = \frac{2}{3}$.
* Answer: $5 \frac{2}{3}$

18. Calculate: $2\frac{1}{2} + 2\frac{1}{2}$
* Add the whole numbers: $2 + 2 = 4$.
* Add the fractions: $\frac{1}{2} + \frac{1}{2} = \frac{2}{2}$, which equals 1.
* Add that 1 to the whole number sum: $4 + 1 = 5$.
* Answer: $5$

19. Complete the equivalent fraction: $\frac{1}{4} = \frac{?}{12}$
* To get from denominator 4 to 12, multiply by 3.
* Do the same to the numerator: $1 \times 3 = 3$.
* Answer: $3$

20. Complete the equivalent fraction: $\frac{3}{5} = \frac{?}{15}$
* To get from denominator 5 to 15, multiply by 3.
* Do the same to the numerator: $3 \times 3 = 9$.
* Answer: $9$

21. Complete the equivalent fraction: $\frac{4}{5} = \frac{20}{?}$
* To get from numerator 4 to 20, multiply by 5.
* Do the same to the denominator: $5 \times 5 = 25$.
* Answer: $25$

22. Complete the equivalent fraction: $\frac{7}{8} = \frac{?}{32}$
* To get from denominator 8 to 32, multiply by 4.
* Do the same to the numerator: $7 \times 4 = 28$.
* Answer: $28$

23. Complete the equivalent fraction: $\frac{2}{3} = \frac{4}{?}$
* To get from numerator 2 to 4, multiply by 2.
* Do the same to the denominator: $3 \times 2 = 6$.
* Answer: $6$

24. Complete the equivalent fraction: $\frac{3}{8} = \frac{1}{?}$
* *Correction/Note:* This problem likely has a typo in standard worksheets because 3 does not divide evenly into 1 to create an integer denominator for an equivalent fraction usually taught at this level. However, if we look at the pattern, maybe it meant $\frac{3}{8} = \frac{?}{24}$ or similar.
* Let's re-read carefully. It says $\frac{3}{8} = \frac{1}{x}$. This implies $3x = 8$, so $x = 8/3$ or $2.66$. This is unlikely for this grade level.
* Looking closer at the image, problem 24 is actually $\frac{3}{8} = \frac{?}{24}$? No, the denominator on the right looks like just a blank line under a 1? Or is it $\frac{?}{8}$?
* Let's look at Problem 24 again. It reads: $\frac{3}{8} = \frac{1}{\square}$. Wait, looking at the very bottom right, problem 25 is $\frac{9}{8} = \frac{18}{\square}$.
* Let's re-examine 24. It looks like $\frac{3}{8} = \frac{\square}{24}$? No, the box is in the denominator position next to a 1? Actually, it looks like $\frac{3}{8} = \frac{1 \frac{1}{2}}{4}$? No.
* Let's assume standard equivalence. If the question is $\frac{3}{8} = \frac{x}{y}$, and one number is 1... perhaps it is $\frac{3}{8} = \frac{1.5}{4}$? Unlikely.
* Let's look at the spacing. It is likely $\frac{3}{8} = \frac{?}{24}$ but printed poorly? Or $\frac{3}{8} = \frac{6}{16}$?
* Actually, looking at crop 6, problem 24 is: $\frac{3}{8} = \frac{1}{\text{box}}$. This is mathematically impossible for integer answers.
* Alternative interpretation: Maybe it is $\frac{3}{9} = \frac{1}{3}$? But the text clearly says 3/8.
* Let's look at Problem 25: $\frac{9}{8} = \frac{18}{\text{box}}$. $9 \times 2 = 18$, so $8 \times 2 = 16$. Answer 16.
* Let's look at Problem 24 again. Is it possible it is $\frac{3}{8} = \frac{?}{16}$? No, the right side has a '1'.
* Is it $\frac{3}{8} = \frac{1 \frac{1}{2}}{4}$?
* Let's assume there is a typo in the book and it meant $\frac{3}{8} = \frac{6}{16}$ or similar. However, if I must solve what is visible:
* If it is $\frac{3}{8} = \frac{1}{x}$, then $x = 2.66$.
* If it is $\frac{3}{8} = \frac{x}{24}$, then $x=9$.
* If it is $\frac{3}{8} = \frac{12}{32}$, etc.
* Let's look really closely at #24. It looks like $\frac{3}{8} = \frac{1 \frac{1}{2}}{4}$ is not it.
* Wait, could it be $\frac{3}{8} = \frac{?}{24}$ and the '?' looks like a 1? No.
* Could it be $\frac{3}{8} = \frac{6}{16}$ and the 6 looks like a 1?
* Let's skip providing a definitive integer for 24 due to likely print error, BUT looking at common worksheets, a very common problem is $\frac{3}{8} = \frac{9}{24}$. Another is $\frac{3}{8} = \frac{6}{16}$.
* Let's look at the shape of the character before the box. It is a vertical line. It is a 1.
* Is it possible the fraction on the left is $\frac{1}{8}$? No, it's a 3.
* Is it possible the fraction on the left is $\frac{3}{9}$? No, it's an 8.
* Okay, let's look at Problem 24 as $\frac{3}{8} = \frac{1.5}{4}$? No.
* Let's assume the question is $\frac{3}{8} = \frac{x}{24}$ and the "1" is actually part of "24" where the 2 is faint? Or maybe it's $\frac{3}{8} = \frac{9}{24}$ and the 9 is written weirdly?
* Actually, let's look at the previous problems. They are all integers.
* There is a possibility that Problem 24 is $\frac{3}{8} = \frac{?}{16}$ and the question mark is missing?
* Let's provide the answer for the most likely intended question which fits the pattern of "multiply denominator by X". If the target denominator was 24, answer is 9. If target numerator was 6, denominator is 16.
* However, looking at the image again, Problem 24 is: $\frac{3}{8} = \frac{1}{\square}$. This is unsolvable with integers. I will note this.
* *Self-Correction*: Often in these scans, a $\frac{3}{8}$ might be a typo for $\frac{1}{8}$. If it were $\frac{1}{8} = \frac{1}{8}$, the box is 8. If it were $\frac{1}{4} = \frac{1}{4}$, box is 4.
* Let's look at Problem 25: $\frac{9}{8} = \frac{18}{\square}$. Denominator is 16.
* Let's look at Problem 24 again. Is it $\frac{3}{8} = \frac{?}{24}$? The character before the box is definitely a '1'. Is it possible it is $\frac{3}{8} = \frac{1 \frac{1}{2}}{4}$? No.
* I will provide the answer for #25 and #24 based on the most logical visual interpretation that allows an integer answer, which is often that the '1' is actually a part of a two-digit number like 16 or 24 where the first digit is faint, OR the numerator on the left is different.
* Actually, looking at the very bottom crop, #24 is $\frac{3}{8} = \frac{1}{\dots}$. Wait, is it $\frac{3}{8} = \frac{?}{8}$? No.
* Let's assume the question is flawed but try to find the "best" fit. If we assume the right side is $\frac{?}{24}$, answer is 9. If we assume the right side is $\frac{6}{?}$, answer is 16.
* Let's look at the space. The box is small.
* I will omit a specific single-number final answer for #24 in the summary if it's ambiguous, but for the sake of the student, I will guess it is a typo for $\frac{3}{8} = \frac{9}{24}$ (answer 9) or $\frac{3}{8} = \frac{6}{16}$ (answer 16). Given the '1' is visible, maybe it's $\frac{3}{8} = \frac{1.5}{4}$? No.
* Let's look at #24 again. Is it $\frac{3}{8} = \frac{?}{16}$? And the '?' is missing?
* Okay, I will solve #25 definitively. For #24, I will flag it as likely having a typo, but if forced, $\frac{3}{8}$ does not equal $\frac{1}{n}$ for any integer n.

*Re-evaluating #24*: Could it be $\frac{3}{8} = \frac{12}{32}$? No.
Let's look at the provided solution key logic for similar online worksheets. Often, $\frac{3}{8} = \frac{9}{24}$. The '9' might look like a '1' if printed badly? Unlikely.
What if the left side is $\frac{1}{8}$? Then $\frac{1}{8} = \frac{1}{8}$. Box = 8.
What if the left side is $\frac{1}{4}$? Then $\frac{1}{4} = \frac{1}{4}$. Box = 4.
The number is clearly a 3.
I will provide the answer for #25 and leave #24 with a note.

*Wait*, looking at the full image again. Problem 24 is $\frac{3}{8} = \frac{1}{\square}$.
Problem 25 is $\frac{9}{8} = \frac{18}{\square}$.

Let's solve #25:
Numerator: $9 \times 2 = 18$.
Denominator: $8 \times 2 = 16$.
Answer: 16.

For #24, since I cannot give a clean integer answer, I will assume it might be a typo for $\frac{3}{8} = \frac{9}{24}$ (Answer: 24 in denom? No, box is denom). If box is denom, and num is 1, it's broken.
Actually, could it be $\frac{3}{8} = \frac{?}{16}$ and the question mark is just a vertical line? If so, $3 \times 2 = 6$. Answer 6.
Or $\frac{3}{8} = \frac{?}{24}$? $3 \times 3 = 9$. Answer 9.
I'll bet on it being a typo for $\frac{3}{8} = \frac{9}{24}$ or similar. But without clarity, I'll focus on the clear ones.

Let's double check #14. $6 \frac{1}{3} - 7 \frac{2}{3}$.
Usually, elementary worksheets don't have negative answers.
Did I read the numbers right?
Left: $6 \frac{1}{3}$. Right: $7 \frac{2}{3}$.
Yes.
Did I read the operation right? Minus sign.
Yes.
Is it possible the first number is $8 \frac{1}{3}$? No, looks like 6.
Is it possible the second number is $1 \frac{2}{3}$? No, looks like 7.
I will stick with $-1 \frac{1}{3}$ but add a note.

Final Answer:
1. $2 \frac{5}{8}$
2. $4 \frac{2}{9}$
3. $6 \frac{7}{10}$
4. $\frac{29}{8}$
5. $\frac{83}{10}$
6. $\frac{89}{12}$
7. $12 \frac{4}{5}$
8. $13 \frac{1}{3}$
9. $6 \frac{3}{7}$
10. $7 \frac{1}{2}$
11. $1 \frac{2}{3}$
12. $7 \frac{3}{5}$
13. $8 \frac{5}{7}$
14. $-1 \frac{1}{3}$ (Note: If negative numbers are not allowed, check if the problem was copied incorrectly, e.g., $7 \frac{2}{3} - 6 \frac{1}{3} = 1 \frac{1}{3}$)
15. $9 \frac{3}{4}$
16. $7 \frac{4}{5}$
17. $5 \frac{2}{3}$
18. $5$
19. $3$
20. $9$
21. $25$
22. $28$
23. $6$
24. [Likely Typo in Question] If the question meant $\frac{3}{8} = \frac{9}{24}$, the denominator is 24. If it meant $\frac{3}{8} = \frac{6}{16}$, the denominator is 16. As written ($\frac{3}{8} = \frac{1}{x}$), there is no whole number answer.
25. $16$