Q1
1 Mark
What is the sum of 3/4 and 1/4?
A1/2
B1
C3/4
D2/4
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Correct answer: Option 2 — 1
Chapter 6 · Class 7 Mathematics
Fractions and Decimals — Important Questions
SUMMARY: This chapter focuses on understanding and performing operations with fractions and decimals.
KEY TOPICS: types of fractions, addition and subtraction of fractions, multiplication of fractions, division of fractions, decimal representation, addition and subtraction of decimals, multiplication of decimals, division of decimals, conversion between fractions and decimals.
Multiple Choice Questions (MCQs)
5 questions
Q2
1 Mark
Which of the following is an improper fraction?
A2/3
B5/4
C7/8
D1/2
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Correct answer: Option 2 — 5/4
Q3
1 Mark
If you multiply 2/5 by 3/7, what is the result?
A6/35
B5/21
C1/5
D1/2
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Correct answer: Option 1 — 6/35
Q4
1 Mark
Convert 0.75 into a fraction. What is the simplest form?
A3/4
B1/2
C2/3
D4/5
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Correct answer: Option 1 — 3/4
Q5
1 Mark
What is the result of dividing 4.5 by 1.5?
A3
B2.5
C2
D1.5
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Correct answer: Option 1 — 3
Short Answer Questions
5 questions
Q6
3 Marks
What is a proper fraction? Give an example.
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A proper fraction is a fraction where the numerator is less than the denominator. For example, 3/5 is a proper fraction because 3 is less than 5.
Q7
3 Marks
How do you add the fractions 1/4 and 2/3?
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To add 1/4 and 2/3, first find a common denominator, which is 12. Convert the fractions: 1/4 becomes 3/12 and 2/3 becomes 8/12. Then add: 3/12 + 8/12 = 11/12.
Q8
3 Marks
What is the result of multiplying the fractions 2/5 and 3/7?
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To multiply the fractions 2/5 and 3/7, multiply the numerators and the denominators: (2 * 3) / (5 * 7) = 6/35.
Q9
3 Marks
Convert the decimal 0.75 into a fraction and simplify it.
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The decimal 0.75 can be converted to a fraction as 75/100. Simplifying this fraction by dividing both the numerator and denominator by 25 gives 3/4.
Q10
3 Marks
If you divide 5.6 by 0.7, what is the quotient?
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To divide 5.6 by 0.7, you can multiply both the numerator and denominator by 10 to eliminate the decimal, resulting in 56/7. The quotient is 8.
Long Answer Questions
5 questions
Q11
6 Marks
Explain how to add two fractions with different denominators. Provide an example to illustrate your explanation.
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To add two fractions with different denominators, first find a common denominator, which is typically the least common multiple (LCM) of the two denominators. Then, convert each fraction to an equivalent fraction with the common denominator. After that, add the numerators of the converted fractions while keeping the common denominator the same. Finally, simplify the resulting fraction if possible. For example, to add 1/3 and 1/4, the LCM of 3 and 4 is 12. Convert 1/3 to 4/12 and 1/4 to 3/12. Adding these gives 4/12 + 3/12 = 7/12.
Q12
6 Marks
Describe the process of multiplying two fractions. Provide a detailed example to support your explanation.
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To multiply two fractions, simply multiply the numerators together and the denominators together. The product of the numerators becomes the new numerator, and the product of the denominators becomes the new denominator. For example, to multiply 2/5 by 3/4, multiply the numerators: 2 x 3 = 6, and the denominators: 5 x 4 = 20. Therefore, 2/5 x 3/4 = 6/20. This fraction can be simplified to 3/10 by dividing both the numerator and denominator by their greatest common divisor, which is 2.
Q13
6 Marks
How do you convert a fraction to a decimal? Illustrate your explanation with an example.
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To convert a fraction to a decimal, divide the numerator by the denominator using long division or a calculator. The result will be the decimal representation of the fraction. For example, to convert 3/8 to a decimal, divide 3 by 8. Performing the division gives 0.375. Thus, 3/8 is equivalent to 0.375 in decimal form.
Q14
6 Marks
Explain the steps involved in dividing one fraction by another. Use an example to clarify your explanation.
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To divide one fraction by another, you multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by swapping its numerator and denominator. For example, to divide 2/3 by 4/5, first find the reciprocal of 4/5, which is 5/4. Then, multiply 2/3 by 5/4: (2/3) x (5/4) = (2 x 5) / (3 x 4) = 10/12. This can be simplified to 5/6 by dividing both the numerator and denominator by their greatest common divisor, which is 2.
Q15
6 Marks
Discuss the addition of decimals and how it differs from adding fractions. Provide an example to illustrate your points.
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Adding decimals involves aligning the numbers by their decimal points and then adding each column starting from the rightmost side, just like adding whole numbers. If necessary, you can add zeros to ensure that both numbers have the same number of decimal places. For example, to add 2.75 and 1.3, align them as follows: 2.75 + 1.30. Starting from the right, add 5 + 0 = 5, 7 + 3 = 10 (write down 0 and carry over 1), and then add 2 + 1 + 1 (carry) = 4. The result is 4.05. This process differs from adding fractions, where you must first find a common denominator.
Assertion–Reason Questions
5 questions
Q16
1 Mark
Assertion (A): The fraction 3/4 is an example of a proper fraction.
Reason (R): A proper fraction is defined as a fraction where the numerator is less than the denominator.
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Correct answer: Option 1 —
Both A and R are true, and R is the correct explanation of A.
Q17
1 Mark
Assertion (A): When adding the fractions 1/3 and 1/4, the result is 7/12.
Reason (R): To add fractions, we need a common denominator.
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Correct answer: Option 2 —
Both A and R are true, but R is not the correct explanation of A.
Q18
1 Mark
Assertion (A): The product of two fractions is always greater than both fractions.
Reason (R): Multiplying fractions results in a smaller value than either of the original fractions if both are less than 1.
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Correct answer: Option 4 —
A is false, but R is true.
Q19
1 Mark
Assertion (A): 0.75 can be expressed as the fraction 3/4.
Reason (R): The decimal 0.75 is equivalent to 75/100, which simplifies to 3/4.
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Correct answer: Option 1 —
Both A and R are true, and R is the correct explanation of A.
Q20
1 Mark
Assertion (A): Dividing a decimal by a whole number always results in a decimal.
Reason (R): Dividing a decimal by a whole number can result in a whole number if the decimal is a multiple of the whole number.
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Correct answer: Option 3 —
A is true, but R is false.
Statement-Based Questions
5 questions
Q21
1 Mark
Statement 1: A proper fraction has a numerator that is greater than its denominator.
Statement 2: The sum of two fractions with the same denominator is obtained by adding their numerators.
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Correct answer: Option 2 —
Only Statement 1 is true.
Q22
1 Mark
Statement 1: To multiply two fractions, you multiply the numerators and the denominators separately.
Statement 2: The decimal representation of 1/4 is 0.25.
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Correct answer: Option 1 —
Both statements are true.
Q23
1 Mark
Statement 1: When dividing fractions, you multiply the first fraction by the reciprocal of the second fraction.
Statement 2: 0.75 is equivalent to 3/4 as a fraction.
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Correct answer: Option 1 —
Both statements are true.
Q24
1 Mark
Statement 1: The result of adding 0.5 and 0.25 is 0.75.
Statement 2: A mixed fraction can be converted to an improper fraction.
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Correct answer: Option 1 —
Both statements are true.
Q25
1 Mark
Statement 1: The product of two decimals is always greater than either of the decimals.
Statement 2: To convert a decimal to a fraction, you can place the decimal over 1 and multiply by 10 for each digit after the decimal point.
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Correct answer: Option 3 —
Only Statement 2 is true.
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