Understanding Rational Numbers

1️⃣ Add: 2/3 + 1/6

• 5/6

• 2/6

• 4/6

• 1/3

Answer explanation

To add 2/3 and 1/6, convert 2/3 to sixths: 2/3 = 4/6. Now add: 4/6 + 1/6 = 5/6. Thus, the correct answer is 5/6.

2️⃣ Subtract: 5/6 − 1/4

• 1/3

• 7/12

• 2/3

• 3/4

Answer explanation

To subtract 5/6 and 1/4, find a common denominator, which is 12. Convert: 5/6 = 10/12 and 1/4 = 3/12. Now, subtract: 10/12 - 3/12 = 7/12. Thus, the correct answer is 7/12.

3️⃣ Multiply: 3/5 × 10/9

• 4/5

• 1/2

• 3/4

• 2/3

Answer explanation

To multiply fractions, multiply the numerators and the denominators: (3 × 10) / (5 × 9) = 30 / 45. Simplifying 30/45 gives 2/3, which is the correct answer.

4️⃣ Divide: 4/7 ÷ 2/5

• 6/14

• 8/14

• 12/14

• 20/14

Answer explanation

To divide fractions, multiply by the reciprocal. Thus, 4/7 ÷ 2/5 = 4/7 × 5/2 = (4×5)/(7×2) = 20/14. The correct answer is 20/14.

5️⃣ Subtract: 7/8 − 1/2

• 2/8

• 3/8

• 1/4

• 5/8

Answer explanation

To subtract 1/2 from 7/8, convert 1/2 to 4/8. Then, 7/8 - 4/8 = 3/8. Thus, the correct answer is 3/8.

6️⃣ Which of the following is a terminating decimal?

• 7/12

• 5/6

• 9/40

• 11/30

Answer explanation

A terminating decimal can be expressed as a fraction where the denominator has only the prime factors 2 and/or 5. The fraction 2/5 meets this criterion, making it a terminating decimal. The other options do not.

7️⃣ What is the standard form of the rational number (−12)/18?

• -2/3

• -5/6

• -3/4

• -1/2

Answer explanation

To simplify (−12)/18, divide both the numerator and denominator by their greatest common divisor, which is 6. This gives us -2/3, making option b) the correct answer.

8️⃣ What is the reciprocal of -4/7?

• 4/7

• -1/4

• -7/8

• -7/4

Answer explanation

The reciprocal of a fraction is obtained by flipping the numerator and denominator. For -4/7, the reciprocal is -7/4, which is option a).

9️⃣ Riya spends 2/3 of her pocket money on books and saves the rest. If she had $30, how much money does she save?

• $5

• $12

• $25

• $10

Answer explanation

Riya spends 2/3 of $30 on books, which is $20. She saves the remaining 1/3, which is $10. Therefore, the amount she saves is $10.

🔟 What is the sum of -1/4 and 3/4?

• 1/2

• 1

• -1/2

• 3/2

Answer explanation

To find the sum of -1/4 and 3/4, add the fractions: -1/4 + 3/4 = (3 - 1)/4 = 2/4 = 1/2. Thus, the correct answer is 1/2.