Grade 7 Mathematics Worksheet: Common Fractions - Free Printable

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

1.1 Which one of the following is the same as $\frac{5}{6}$ divided by $\frac{1}{2}$?
* Step 1: To divide by a fraction, you multiply by its reciprocal (flip the second fraction upside down).
* Step 2: The reciprocal of $\frac{1}{2}$ is $\frac{2}{1}$.
* Step 3: So, $\frac{5}{6} \div \frac{1}{2}$ becomes $\frac{5}{6} \times \frac{2}{1}$.
* Conclusion: This matches option (c).

1.2 A quarter of a half is equal to:
* Step 1: "A quarter" means $\frac{1}{4}$. "A half" means $\frac{1}{2}$.
* Step 2: "Of" in math usually means multiplication. So we calculate $\frac{1}{4} \times \frac{1}{2}$.
* Step 3: Multiply the top numbers ($1 \times 1 = 1$) and the bottom numbers ($4 \times 2 = 8$).
* Result: $\frac{1}{8}$. This matches option (b).

1.3 A third squared, is equal to:
* Step 1: "A third" is $\frac{1}{3}$. "Squared" means multiplying the number by itself.
* Step 2: Calculate $\frac{1}{3} \times \frac{1}{3}$.
* Step 3: $1 \times 1 = 1$ and $3 \times 3 = 9$.
* Result: $\frac{1}{9}$. This matches option (a).

1.4 Subtract $\frac{2}{5}$ from $\frac{2}{3}$:
* Step 1: The order is important. "Subtract A from B" means $B - A$. So, $\frac{2}{3} - \frac{2}{5}$.
* Step 2: Find a common denominator for 3 and 5, which is 15.
* Step 3: Convert the fractions: $\frac{2}{3} = \frac{10}{15}$ and $\frac{2}{5} = \frac{6}{15}$.
* Step 4: Subtract: $\frac{10}{15} - \frac{6}{15} = \frac{4}{15}$.
* Result: $\frac{4}{15}$. This matches option (d).

1.5 The square root of the numerator in $\frac{4}{9}$:
* Step 1: Identify the numerator (the top number) of the fraction $\frac{4}{9}$. The numerator is 4.
* Step 2: Find the square root of 4.
* Step 3: $\sqrt{4} = 2$ (because $2 \times 2 = 4$).
* Result: 2. This matches option (b).

1.6 Which one of the following is an equivalent fraction for $2\frac{5}{6}$?
* Step 1: Convert the mixed number $2\frac{5}{6}$ into an improper fraction.
* Step 2: Multiply the whole number by the denominator and add the numerator: $(2 \times 6) + 5$.
* Step 3: $12 + 5 = 17$. Keep the denominator the same (6).
* Result: $\frac{17}{6}$. This matches option (a).

1.7 A fifth divided by 2 =
* Step 1: "A fifth" is $\frac{1}{5}$.
* Step 2: Divide $\frac{1}{5}$ by 2. This is the same as multiplying by $\frac{1}{2}$.
* Step 3: $\frac{1}{5} \times \frac{1}{2} = \frac{1 \times 1}{5 \times 2} = \frac{1}{10}$.
* Note: Looking at the options provided in the image, none seem to match $\frac{1}{10}$ exactly based on standard calculation. However, let's re-read carefully. Usually, these questions have a clear answer. Let's look at option (c) $\frac{2}{5}$? No. Option (d) $1\frac{1}{2}$? No. Option (a) 10? No.
* *Self-Correction/Check:* Is it possible the question meant "2 divided by a fifth"? $2 \div \frac{1}{5} = 10$. That would be option (a). But the text says "A fifth divided by 2".
* Let's check the other visible options again. Option (b) is cut off. It is highly likely the correct answer $\frac{1}{10}$ is option (b), or there is a typo in the question/options. Given the visible options, if I must choose the most likely intended "trick" question where students flip the wrong number, they might get 10. But mathematically, $\frac{1}{5} \div 2 = \frac{1}{10}$.
* *Alternative interpretation:* If the question was "How many fifths in 2?", the answer is 10.
* *Let's assume the question text is strictly correct:* Answer is $\frac{1}{10}$. Since option (b) is obscured/cut off in the watermark, it is the only logical place for the correct answer. If forced to pick from visible wrong answers, there isn't one. However, often in these tests, if the text is "A fifth divided by 2", the answer is $\frac{1}{10}$.
* *Wait, looking closer at 1.7 options:*
a) 10
b) [Obscured]
c) $\frac{2}{5}$
d) $1\frac{1}{2}$
* If the question was actually "2 divided by a fifth", the answer is 10 (Option a). This is a very common type of question. Given "10" is a prominent option, it is highly probable the question intends for the student to calculate $2 \div \frac{1}{5}$ or the student is expected to identify that $\frac{1}{5} \div 2$ results in a smaller number, and perhaps option (b) is $\frac{1}{10}$. Without seeing (b), I will provide the mathematically correct answer for the text written: $\frac{1}{10}$. If (b) is not $\frac{1}{10}$, there is an error in the worksheet.
* *Decision:* I will provide the strict mathematical answer. $\frac{1}{5} \div 2 = \frac{1}{10}$.

1.8 A half added to the product of four and a fifth, is equal to?
* Step 1: Find "the product of four and a fifth". Product means multiply. $4 \times \frac{1}{5} = \frac{4}{5}$.
* Step 2: "A half added to..." means $\frac{1}{2} + \frac{4}{5}$.
* Step 3: Find a common denominator for 2 and 5, which is 10.
* Step 4: $\frac{1}{2} = \frac{5}{10}$ and $\frac{4}{5} = \frac{8}{10}$.
* Step 5: Add them: $\frac{5}{10} + \frac{8}{10} = \frac{13}{10}$.
* Step 6: Convert to a mixed number: $1\frac{3}{10}$.
* Note: None of the visible options (a, c, d) match this. Option (b) is obscured. Option (c) is $20\frac{1}{2}$ (way too big). Option (d) is $\frac{4}{10}$. Option (a) is obscured. The correct answer is $1\frac{3}{10}$ (or $\frac{13}{10}$). This is likely option (b).

1.9 Find the value of x in the number pattern: $\frac{1}{3}; \frac{1}{6}; \frac{1}{12}; x$
* Step 1: Look at how the denominators change: 3, 6, 12.
* Step 2: $3 \times 2 = 6$. $6 \times 2 = 12$. The pattern is multiplying the denominator by 2 (or dividing the whole fraction by 2).
* Step 3: Apply the pattern to the next term: $12 \times 2 = 24$.
* Step 4: So, $x = \frac{1}{24}$.
* Note: Looking at the options:
a) [Obscured]
b) [Obscured]
c) $\frac{1}{36}$
d) $\frac{2}{3}$
The correct answer is $\frac{1}{24}$. This is likely option (a) or (b). Option (c) suggests adding to the denominator ($12+24=36$? No, that's not the pattern established by 3->6). The pattern is clearly geometric ($\times \frac{1}{2}$). Answer is $\frac{1}{24}$.

1.10 If a number is multiplied by $\frac{5}{8}$ the answer is $\frac{1}{4}$. What is the number?
* Step 1: Let the number be $n$. The equation is $n \times \frac{5}{8} = \frac{1}{4}$.
* Step 2: To isolate $n$, divide both sides by $\frac{5}{8}$. This is the same as multiplying by the reciprocal $\frac{8}{5}$.
* Step 3: $n = \frac{1}{4} \times \frac{8}{5}$.
* Step 4: Simplify before multiplying: 4 goes into 8 twice. So, $1 \times \frac{2}{5} = \frac{2}{5}$.
* Result: $\frac{2}{5}$. This matches option (a).

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Final Answer:
1.1: c) $\frac{5}{6} \times \frac{2}{1}$
1.2: b) $\frac{1}{8}$
1.3: a) $\frac{1}{9}$
1.4: d) $\frac{4}{15}$
1.5: b) 2
1.6: a) $\frac{17}{6}$
1.7: $\frac{1}{10}$ (Likely option b, as visible options are incorrect for the text provided)
1.8: $1\frac{3}{10}$ (Likely option b, as visible options are incorrect)
1.9: $\frac{1}{24}$ (Likely option a or b, as visible options are incorrect)
1.10: a) $\frac{2}{5}$