Grade 9 Rational Numbers worksheet
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How to explain it
- A rational number can be written as a fraction.
- To add or subtract, use a common denominator.
- A negative times a negative is positive.
Example: −1/2 + 3/4 = ? Common denominator 4: −2/4 + 3/4. −2 + 3 = 1, so 1/4. Answer: 1/4
Question 1
−1/2 + 1/6 = ?
- -2/3
- -1/3
- -1/6
- 1/3
- 0
-1/3
Hint: Use the common denominator 6: -3/6 + 1/6 = -2/6, which is -1/3 in lowest terms.
Question 2
−1/5 × 5/5 = ?
- -1/5
- -5/26
- -5
- -4/25
- 1/5
-1/5
Hint: Multiply across: −1 × 5 = −5 and 5 × 5 = 25. A negative times a positive is negative. Lowest terms: -1/5.
Question 3
Calculate: 9.8 − 8.8 + 8.8 × 2
answer box
18.6
Hint: Multiply first: 8.8 × 2 = 17.6. Then 9.8 − 8.8 = 1, and add: 18.6.
Question 4
−2.6 + 3.6 = ?
- 6.2
- 1
- -6.2
- -1
1
Hint: Different signs: subtract the sizes, 3.6 − 2.6 = 1. The positive number is farther from zero, so the answer is positive.
Question 5
Write 7/8 as a decimal.
answer box
0.875
Hint: Divide the numerator by the denominator: 7 ÷ 8 = 0.875.
Question 6
What is the value of this expression? Remember BEDMAS.
6 + (-8) × 3 − 12 ÷ 4 = ?
answer box
-21
Hint: Multiply and divide first: (−8) × 3 = -24 and 12 ÷ 4 = 3. Then 6 + (−24) − 3 = -21.
Question 7
Put these rational numbers in order from least to greatest.
- −3/4
- 5/4
- 0.6
- −1.5
−1.5 → −3/4 → 0.6 → 5/4
Hint: Change each to a decimal if it helps: −1.5 ≈ -1.5, −3/4 ≈ -0.75, 0.6 ≈ 0.6, 5/4 ≈ 1.25. Negative numbers farther from zero are smaller.
Question 8
Which fraction gives a non-terminating (repeating) decimal?
- 7/8
- 5/12
- 3/5
- 9/20
5/12
Hint: A fraction in lowest terms ends only if its denominator's prime factors are just 2s and 5s. 12 has a factor of 3.
Question 9
4/5 + 1/4 = ?
- 11/10
- 21/20
- 11/20
- 5/9
- -21/20
21/20
Hint: Use the common denominator 20: 16/20 + 5/20 = 21/20, which is 21/20 in lowest terms.
Question 10
1/5 × 1/4 = ?
- 1/10
- 1/20
- -1/20
- 20
- 1/21
1/20
Hint: Multiply across: 1 × 1 = 1 and 5 × 4 = 20. Positive times positive is positive. Lowest terms: 1/20.
Answer key
- 1. -1/3
- 2. -1/5
- 3. 18.6
- 4. 1
- 5. 0.875
- 6. -21
- 7. −1.5 → −3/4 → 0.6 → 5/4
- 8. 5/12
- 9. 21/20
- 10. 1/20
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