How to Use This Page
1. Solve each exercise problem on your own first — attempt every step before looking here. 2. Compare your method with the step-by-step solution shown. 3. If your answer differs, rework from the step where you diverged. 4. Pay special attention to the Common Mistakes section — these are the errors that cost marks in exams. 5. Use the Exam Checklist before your test to ensure you have covered every topic.
Key Concepts (Quick Recap)
Rational Numbers
- Rational number: Any number that can be written as p/q where p, q are integers and q is not 0
- Examples: 3/4, -7/2, 0, 5 (since 5 = 5/1)
- Equivalent fractions: 2/3 = 4/6 = 6/9 = 10/15 (multiply/divide numerator and denominator by same number)
Properties of Rational Numbers
- Closure: a + b, a - b, a × b are all rational (for rational a, b). a ÷ b is rational if b is not 0.
- Commutative: a + b = b + a and a × b = b × a (but NOT for subtraction or division)
- Associative: (a + b) + c = a + (b + c) and (a × b) × c = a × (b × c) (but NOT for subtraction or division)
- Distributive: a × (b + c) = a × b + a × c (multiplication distributes over addition)
- Additive identity: 0 (a + 0 = a)
- Multiplicative identity: 1 (a × 1 = a)
- Additive inverse of a/b: -a/b (a/b + (-a/b) = 0)
- Multiplicative inverse of a/b: b/a (a/b × b/a = 1, provided a is not 0)
Rational Numbers Between Two Numbers
- Mean method: Between a and b, insert (a + b)/2
- n numbers between a and b: a + (b-a)/(n+1), a + 2(b-a)/(n+1), ..., a + n(b-a)/(n+1)
Decimal Representation
- Terminating decimal: Denominator (in lowest terms) has only 2 and 5 as prime factors. E.g., 3/4 = 0.75, 7/20 = 0.35
- Non-terminating repeating decimal: Denominator has prime factors other than 2 and 5. E.g., 1/3 = 0.333..., 2/7 = 0.285714...
- Converting repeating decimal to fraction: Let x = 0.333..., then 10x = 3.333..., 10x - x = 3, 9x = 3, x = 1/3
Powers of Rational Numbers
- (a/b)^n = a^n / b^n for positive integer n
- (a/b)^0 = 1 (provided a/b is not 0)
- (a/b)^(-n) = (b/a)^n
Exercise 1.1 — Rational Numbers: Properties and Operations
Q1. Which of the following are rational numbers? (i) 3/5 (ii) -4 (iii) 0 (iv) sqrt(2) (v) 0.75
(i) 3/5: Yes, it is in p/q form with q is not 0.
(ii) -4: Yes, -4 = -4/1, which is in p/q form.
(iii) 0: Yes, 0 = 0/1, which is in p/q form.
(iv) sqrt(2): No, sqrt(2) is irrational. It cannot be expressed as p/q.
(v) 0.75: Yes, 0.75 = 75/100 = 3/4, which is in p/q form.
Answer: (i), (ii), (iii), and (v) are rational numbers.
Q2. Write the additive inverse of each: (i) 3/7 (ii) -5/9 (iii) 4 (iv) -3/8
(i) Additive inverse of 3/7 = -3/7
(since 3/7 + (-3/7) = 0)
(ii) Additive inverse of -5/9 = 5/9
(since -5/9 + 5/9 = 0)
(iii) Additive inverse of 4 = -4
(since 4 + (-4) = 0)
(iv) Additive inverse of -3/8 = 3/8
(since -3/8 + 3/8 = 0)
Q3. Write the multiplicative inverse (reciprocal) of each: (i) 5/8 (ii) -3/7 (iii) 1 (iv) 0
(i) Reciprocal of 5/8 = 8/5
(since 5/8 × 8/5 = 1)
(ii) Reciprocal of -3/7 = -7/3
(since -3/7 × (-7/3) = 1)
(iii) Reciprocal of 1 = 1
(since 1 × 1 = 1)
(iv) 0 has NO multiplicative inverse (division by zero is undefined)
Q4. Verify the commutative property of addition for 2/5 and 3/7.
a = 2/5, b = 3/7
a + b = 2/5 + 3/7
= (2 × 7 + 3 × 5) / (5 × 7)
= (14 + 15) / 35
= 29/35
b + a = 3/7 + 2/5
= (3 × 5 + 2 × 7) / (7 × 5)
= (15 + 14) / 35
= 29/35
Since a + b = b + a = 29/35, commutative property is verified.
Q5. Verify the associative property of multiplication for 1/2, 2/3, and 3/4.
a = 1/2, b = 2/3, c = 3/4
(a × b) × c = (1/2 × 2/3) × 3/4
= (2/6) × 3/4
= 1/3 × 3/4
= 3/12
= 1/4
a × (b × c) = 1/2 × (2/3 × 3/4)
= 1/2 × (6/12)
= 1/2 × 1/2
= 1/4
Since (a × b) × c = a × (b × c) = 1/4, associative property is verified.
Q6. Verify the distributive property: a × (b + c) = a × b + a × c for a = 1/3, b = 2/5, c = 1/5.
LHS: a × (b + c) = 1/3 × (2/5 + 1/5)
= 1/3 × 3/5
= 3/15
= 1/5
RHS: a × b + a × c = (1/3 × 2/5) + (1/3 × 1/5)
= 2/15 + 1/15
= 3/15
= 1/5
Since LHS = RHS = 1/5, distributive property is verified.
Q7. Add: 3/4 + (-7/8)
LCM of 4 and 8 = 8
3/4 = (3 × 2)/(4 × 2) = 6/8
3/4 + (-7/8) = 6/8 + (-7/8)
= (6 - 7)/8
= -1/8
Answer: -1/8
Q8. Subtract: 5/6 - 3/4
LCM of 6 and 4 = 12
5/6 = 10/12
3/4 = 9/12
5/6 - 3/4 = 10/12 - 9/12
= 1/12
Answer: 1/12
Q9. Multiply: (-3/5) × (10/9)
(-3/5) × (10/9) = (-3 × 10)/(5 × 9)
= -30/45
= -2/3
Answer: -2/3
Q10. Divide: (-4/7) ÷ (8/3)
Division: multiply by the reciprocal.
(-4/7) ÷ (8/3) = (-4/7) × (3/8)
= (-4 × 3)/(7 × 8)
= -12/56
= -3/14
Answer: -3/14
Q11. Is subtraction commutative for rational numbers? Verify with 5/7 and 2/7.
a = 5/7, b = 2/7
a - b = 5/7 - 2/7 = 3/7
b - a = 2/7 - 5/7 = -3/7
Since a - b is not equal to b - a (3/7 is not equal to -3/7), subtraction is NOT commutative.
Q12. Is division associative for rational numbers? Verify with 1/2, 2/3, and 3/4.
a = 1/2, b = 2/3, c = 3/4
(a ÷ b) ÷ c = (1/2 ÷ 2/3) ÷ 3/4
= (1/2 × 3/2) ÷ 3/4
= 3/4 ÷ 3/4
= 3/4 × 4/3
= 12/12
= 1
a ÷ (b ÷ c) = 1/2 ÷ (2/3 ÷ 3/4)
= 1/2 ÷ (2/3 × 4/3)
= 1/2 ÷ 8/9
= 1/2 × 9/8
= 9/16
Since 1 is not equal to 9/16, division is NOT associative.
Q13. Find five rational numbers between 1/4 and 1/2.
Method: Find equivalent fractions with denominator large enough.
1/4 = 1/4 and 1/2 = 1/2
Make denominators such that there are enough numbers between them.
1/4 = 6/24 and 1/2 = 12/24
Five rational numbers between 6/24 and 12/24:
7/24, 8/24, 9/24, 10/24, 11/24
Simplified: 7/24, 1/3, 3/8, 5/12, 11/24
Answer: 7/24, 1/3, 3/8, 5/12, 11/24
Q14. Find ten rational numbers between -3/5 and 1/5.
Make denominators such that there are enough numbers between them.
-3/5 = -15/25 and 1/5 = 5/25
Ten rational numbers between -15/25 and 5/25:
-14/25, -13/25, -12/25, -11/25, -10/25, -9/25, -8/25, -7/25, -6/25, -5/25
Simplified: -14/25, -13/25, -12/25, -11/25, -2/5, -9/25, -8/25, -7/25, -6/25, -1/5
Answer: -14/25, -13/25, -12/25, -11/25, -2/5, -9/25, -8/25, -7/25, -6/25, -1/5
Q15. Simplify: 2/3 + (-4/5) + 1/3 - (-2/5)
= 2/3 + 1/3 + (-4/5) + 2/5
= 3/3 + (-4/5 + 2/5)
= 1 + (-2/5)
= 1 - 2/5
= 5/5 - 2/5
= 3/5
Answer: 3/5
Q16. Simplify: (-3/4) × (8/-12) × (-16/24)
(-3/4) × (8/-12) × (-16/24)
Step 1: Simplify each fraction where possible.
8/-12 = -8/12 = -2/3
-16/24 = -16/24 = -2/3
Step 2: Multiply all.
= (-3/4) × (-2/3) × (-2/3)
Step 3: Multiply numerators and denominators.
= ((-3)(-2)(-2)) / (4 × 3 × 3)
= (-12) / 36
= -1/3
Answer: -1/3
Q17. The product of two rational numbers is -15/28. If one of them is 3/7, find the other.
Let the other number be x.
3/7 × x = -15/28
x = (-15/28) ÷ (3/7)
x = (-15/28) × (7/3)
x = (-15 × 7) / (28 × 3)
x = -105/84
x = -5/4
Answer: -5/4
Q18. By what number should -4/9 be multiplied to get 2/3?
Let the number be x.
(-4/9) × x = 2/3
x = (2/3) ÷ (-4/9)
x = (2/3) × (9/-4)
x = (2 × 9) / (3 × (-4))
x = 18/(-12)
x = -3/2
Answer: -3/2
Exercise 1.2 — Rational Numbers Between Two Numbers
Q1. Find three rational numbers between 1/3 and 1/2.
1/3 = 4/12 and 1/2 = 6/12
Need more numbers, so use larger denominator:
1/3 = 8/24 and 1/2 = 12/24
Three numbers: 9/24, 10/24, 11/24
Simplified: 3/8, 5/12, 11/24
Answer: 3/8, 5/12, 11/24
Q2. Find four rational numbers between -1 and 0.
Write with enough denominator: -1 = -5/5 and 0 = 0/5
But we need more room. Use -1 = -8/8 and 0 = 0/8.
Four numbers: -7/8, -6/8, -5/8, -4/8
Simplified: -7/8, -3/4, -5/8, -1/2
Answer: -7/8, -3/4, -5/8, -1/2
Q3. Find six rational numbers between 2/5 and 3/5.
LCM of denominators = 5
2/5 = 14/35 and 3/5 = 21/35
Six numbers: 15/35, 16/35, 17/35, 18/35, 19/35, 20/35
Simplified: 3/7, 16/35, 17/35, 18/35, 19/35, 4/7
Answer: 3/7, 16/35, 17/35, 18/35, 19/35, 4/7
Q4. Find the mean of 3/8 and 5/12. Verify it lies between them.
Mean = (3/8 + 5/12) / 2
LCM of 8 and 12 = 24
3/8 = 9/24, 5/12 = 10/24
Mean = (9/24 + 10/24) / 2
= (19/24) / 2
= 19/48
Verification: 3/8 = 18/48 < 19/48 < 20/48 = 5/12
Answer: 19/48 lies between 3/8 and 5/12.
Q5. Between any two distinct rational numbers, there are infinitely many rational numbers. Justify.
Let a and b be two distinct rational numbers with a < b.
The mean method: m = (a + b)/2 gives a rational number between a and b.
Now we have a < (a + b)/2 < b.
Applying the mean method again between a and (a+b)/2:
m' = (a + (a+b)/2)/2 = (3a + b)/4, which is between a and (a+b)/2.
This process can be repeated infinitely many times, generating a new rational number each time.
Therefore, between any two distinct rational numbers, there exist infinitely many rational numbers.
Q6. Insert 8 rational numbers between -5/7 and 9/7.
-5/7 and 9/7 have the same denominator.
-5/7 = -5/7 and 9/7 = 9/7
Multiply numerator and denominator to create more space:
-5/7 = -50/70 and 9/7 = 90/70
Eight numbers between -50/70 and 90/70:
-40/70, -30/70, -20/70, -10/70, 0/70, 10/70, 20/70, 30/70
Simplified: -4/7, -3/7, -2/7, -1/7, 0, 1/7, 2/7, 3/7
Answer: -4/7, -3/7, -2/7, -1/7, 0, 1/7, 2/7, 3/7
Q7. Find the rational number that is exactly midway between 1/4 and 3/8.
Midpoint = (1/4 + 3/8) / 2
LCM of 4 and 8 = 8
1/4 = 2/8
Midpoint = (2/8 + 3/8) / 2
= (5/8) / 2
= 5/16
Verification: 1/4 = 4/16 < 5/16 < 6/16 = 3/8
Answer: 5/16
Q8. Arrange in ascending order: -3/7, 5/-7, -2/3, 1/7
Make all denominators positive first:
-3/7, -5/7, -2/3, 1/7
LCM of 7, 7, 3, 7 = 21
-3/7 = -9/21
-5/7 = -15/21
-2/3 = -14/21
1/7 = 3/21
Ascending order: -15/21, -14/21, -9/21, 3/21
Which is: -5/7, -2/3, -3/7, 1/7
Answer: -5/7 < -2/3 < -3/7 < 1/7
Q9. Which is greater: -7/9 or -5/8?
-7/9 and -5/8
LCM of 9 and 8 = 72
-7/9 = -56/72
-5/8 = -45/72
Since -56/72 < -45/72 (more negative is smaller),
-7/9 < -5/8
Therefore, -5/8 is greater.
Answer: -5/8 is greater than -7/9.
Q10. The sum of two rational numbers is -3/5. If one of them is 2/7, find the other.
Let the other number be x.
x + 2/7 = -3/5
x = -3/5 - 2/7
LCM of 5 and 7 = 35
x = (-21/35) + (-10/35)
x = -31/35
Answer: -31/35
Exercise 1.3 — Decimal Representation
Q1. Express 3/8 as a decimal. Is it terminating or non-terminating?
3/8 = 3 ÷ 8
8 | 3.000
| 0.375
2 4
6 0
5 6
4 0
4 0
0
3/8 = 0.375
The denominator 8 = 2^3. Since the only prime factor is 2,
the decimal is terminating.
Answer: 0.375 (terminating)
Q2. Express 5/12 as a decimal. Is it terminating or non-terminating?
5/12 = 5 ÷ 12
12 | 5.0000
| 0.4166...
4 8
20
12
8 0
7 2
80
72
8
5/12 = 0.41666... = 0.416 (bar on 6)
The denominator 12 = 2^2 × 3. Since there is a prime factor 3
(other than 2 and 5), the decimal is non-terminating repeating.
Answer: 0.41666... (non-terminating repeating, bar on 6)
Q3. Express 7/20 as a decimal.
7/20 = 7 ÷ 20
20 | 7.00
| 0.35
6 0
6 0
0
7/20 = 0.35
The denominator 20 = 2^2 × 5. Prime factors are only 2 and 5.
So the decimal terminates.
Answer: 0.35 (terminating)
Q4. Express 2/11 as a decimal.
2/11 = 2 ÷ 11
11 | 2.00000...
| 0.1818...
1 1
9 0
8 8
2 0
1 1
9
2/11 = 0.181818... = 0.18 (bar on 18)
Answer: 0.181818... (non-terminating repeating, bar on 18)
Q5. Express 0.6 (bar on 6) as a rational number.
Let x = 0.666...
Multiply both sides by 10:
10x = 6.666...
Subtract: 10x - x = 6.666... - 0.666...
9x = 6
x = 6/9 = 2/3
Answer: 2/3
Q6. Express 0.47 (bar on 7) as a rational number.
Let x = 0.4777...
Multiply both sides by 10 (one digit before bar):
10x = 4.777...
Multiply both sides by 10 again (one digit in repeating part):
100x = 47.777...
Subtract: 100x - 10x = 47.777... - 4.777...
90x = 43
x = 43/90
Answer: 43/90
Q7. Express 0.135 (bar on 35) as a rational number.
Let x = 0.1353535...
One digit before the bar: multiply by 10.
10x = 1.353535...
Two digits in the repeating part: multiply by 100.
1000x = 135.353535...
Subtract: 1000x - 10x = 135.3535... - 1.3535...
990x = 134
x = 134/990 = 67/495
Answer: 67/495
Q8. Express 1.27 (bar on 27) as a rational number.
Let x = 1.272727...
No digits before the bar: multiply by 100 (two digits repeat).
100x = 127.2727...
Subtract: 100x - x = 127.2727... - 1.2727...
99x = 126
x = 126/99 = 14/11
Answer: 14/11
Q9. Which of the following have terminating decimal expansions? (i) 3/25 (ii) 7/30 (iii) 11/16 (iv) 17/125
(i) 3/25: 25 = 5^2. Only prime factor is 5. Terminating.
(ii) 7/30: 30 = 2 × 3 × 5. Has prime factor 3. Non-terminating.
(iii) 11/16: 16 = 2^4. Only prime factor is 2. Terminating.
(iv) 17/125: 125 = 5^3. Only prime factor is 5. Terminating.
Answer: (i) 3/25, (iii) 11/16, and (iv) 17/125 have terminating decimal expansions.
Q10. Classify as terminating or non-terminating repeating: 13/40, 15/24, 19/64, 22/75
(i) 13/40: 40 = 2^3 × 5. Only prime factors 2 and 5. Terminating.
(ii) 15/24: 15/24 = 5/8. 8 = 2^3. Only prime factor 2. Terminating.
(iii) 19/64: 64 = 2^6. Only prime factor 2. Terminating.
(iv) 22/75: 75 = 3 × 5^2. Has prime factor 3. Non-terminating.
Answer: 13/40, 15/24, 19/64 are terminating; 22/75 is non-terminating.
Q11. Express 5.37 (bar on 7) as a rational number in lowest terms.
Let x = 5.3777...
One digit before bar: multiply by 10.
10x = 53.777...
One digit in repeating part: multiply by 10.
100x = 537.777...
Subtract: 100x - 10x = 537.777... - 53.777...
90x = 484
x = 484/90 = 242/45
Answer: 242/45
Q12. Express 3.142 (bar on 42) as a rational number.
Let x = 3.1424242...
One digit before the bar: multiply by 10.
10x = 31.424242...
Two digits in the repeating part: multiply by 100.
1000x = 3142.424242...
Subtract: 1000x - 10x = 3142.4242... - 31.4242...
990x = 3111
x = 3111/990 = 347/110
Answer: 347/110
Exercise 1.4 — Powers and Word Problems
Q1. Find the value of: (2/3)^3
(2/3)^3 = 2^3 / 3^3 = 8/27
Answer: 8/27
Q2. Find the value of: (-3/5)^2
(-3/5)^2 = (-3)^2 / 5^2 = 9/25
Answer: 9/25
Q3. Find the value of: (4/-7)^3
(4/-7)^3 = 4^3 / (-7)^3 = 64/(-343) = -64/343
Answer: -64/343
Q4. Simplify: (1/2)^(-3)
(1/2)^(-3) = (2/1)^3 = 2^3 = 8
Answer: 8
Q5. Simplify: (-3/4)^(-2)
(-3/4)^(-2) = (-4/3)^2 = 16/9
Answer: 16/9
Q6. Simplify: (2^2 × 3^3) / (2^4 × 3)
= 2^2 × 3^3 / (2^4 × 3)
= 2^(2-4) × 3^(3-1)
= 2^(-2) × 3^2
= (1/4) × 9
= 9/4
Answer: 9/4
Q7. Find the value of: 5^0 + (1/3)^0 + (-2)^0
5^0 + (1/3)^0 + (-2)^0
= 1 + 1 + 1
= 3
Answer: 3
Q8. Simplify: [(1/2)^3 × (2/3)^2] ÷ (1/3)^4
Numerator: (1/2)^3 × (2/3)^2 = (1/8) × (4/9) = 4/72 = 1/18
Denominator: (1/3)^4 = 1/81
Division: (1/18) ÷ (1/81) = (1/18) × 81 = 81/18 = 9/2
Answer: 9/2
Q9. The temperature at noon was 5 degrees above zero. It decreased by 3 degrees every hour. What was the temperature after 4 hours?
Initial temperature = 5 degrees
Rate of decrease = 3 degrees per hour
Time = 4 hours
Total decrease = 3 × 4 = 12 degrees
Temperature after 4 hours = 5 - 12 = -7 degrees
Answer: -7 degrees
Q10. A submarine is at -200 m below sea level. It ascends 75 m and then descends 125 m. Find its final position.
Initial position = -200 m
After ascending 75 m: -200 + 75 = -125 m
After descending 125 m: -125 - 125 = -250 m
Answer: -250 m (250 m below sea level)
Q11. In a test, +5 marks are given for each correct answer and -2 marks for each wrong answer. Rahul answered 12 questions correctly and 5 incorrectly. What is his score?
Marks for correct answers = 12 × 5 = 60
Marks for wrong answers = 5 × (-2) = -10
Total score = 60 + (-10) = 50
Answer: 50 marks
Q12. The product of two rational numbers is -8. If one of them is -4/5, find the other.
Let the other number be x.
(-4/5) × x = -8
x = -8 ÷ (-4/5)
x = -8 × (-5/4)
x = 40/4
x = 10
Answer: 10
Q13. A rational number is such that when it is multiplied by 3/5 and added to 1/2, the result is -7/10. Find the number.
Let the number be x.
(3/5) × x + 1/2 = -7/10
3x/5 = -7/10 - 1/2
LCM of 10 and 2 = 10
3x/5 = -7/10 - 5/10
3x/5 = -12/10
3x/5 = -6/5
x = (-6/5) × (5/3)
x = -30/15
x = -2
Answer: -2
Q14. The sum of two rational numbers is 11/24. If one of them is 3/8, find the other.
Let the other number be x.
x + 3/8 = 11/24
x = 11/24 - 3/8
LCM of 24 and 8 = 24
x = 11/24 - 9/24
x = 2/24
x = 1/12
Answer: 1/12
Q15. By what rational number should -8/13 be divided to get 4?
Let the number be x.
(-8/13) ÷ x = 4
(-8/13) × (1/x) = 4
1/x = 4 × 13/(-8) = 52/(-8) = -13/2
x = -2/13
Answer: -2/13
Common Mistakes
1. Sign errors with negative rational numbers — When adding two negative numbers, the result is negative: (-3/5) + (-2/5) = -5/5 = -1, NOT +1. Always track signs carefully through each step.
2. Finding LCM incorrectly for addition/subtraction — To add or subtract fractions, you MUST find the LCM of denominators first. Converting to equivalent fractions with a common denominator that is not the LCM leads to unnecessary simplification. Example: for 1/4 + 1/6, LCM is 12 (not 24).
3. Forgetting to flip the fraction in division — Division by a fraction means multiplying by its reciprocal: a ÷ (b/c) = a × (c/b). A common error is: a ÷ (b/c) = a × (b/c), which is wrong.
4. Confusing additive inverse and multiplicative inverse — The additive inverse of 3/5 is -3/5 (negate the number). The multiplicative inverse (reciprocal) of 3/5 is 5/3 (flip numerator and denominator). These are different operations with different results.
5. Wrong classification of terminating vs non-terminating decimals — A rational number p/q (in lowest terms) has a terminating decimal ONLY if q has no prime factors other than 2 and 5. If q has any other prime factor (3, 7, 11, etc.), the decimal is non-terminating repeating. Example: 7/30 has denominator 30 = 2 × 3 × 5, which includes 3, so it is non-terminating.
6. Errors in converting recurring decimals to fractions — When x = 0.abc(bc repeating), multiply by 10^n where n is the number of non-repeating digits, then by 10^m where m is the number of repeating digits. Subtract the first equation from the second. Many students multiply by 10 only once or subtract incorrectly.
7. Not simplifying the final answer — Always reduce fractions to lowest terms. Example: 6/8 should be written as 3/4. In exam solutions, unsimplified fractions may lose marks.
8. Wrong order in subtraction and division — Both are non-commutative. a - b is NOT equal to b - a, and a ÷ b is NOT equal to b ÷ a. Always keep the correct order.
Exam Checklist
- [ ] I can identify whether a number is rational or irrational
- [ ] I can find the additive inverse and multiplicative inverse of any rational number
- [ ] I can add, subtract, multiply, and divide rational numbers with correct LCM and sign handling
- [ ] I can verify commutative, associative, and distributive properties with rational numbers
- [ ] I can find rational numbers between two given rational numbers (using the mean method)
- [ ] I can insert n rational numbers between two rational numbers
- [ ] I can arrange rational numbers in ascending or descending order
- [ ] I can convert rational numbers to decimal form (terminating or repeating)
- [ ] I can convert a repeating decimal to a fraction
- [ ] I can classify a fraction as having a terminating or non-terminating decimal based on its denominator
- [ ] I can evaluate powers of rational numbers including negative exponents
- [ ] I can solve word problems involving rational numbers
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Frequently Asked Questions
A number that can be expressed in the form p/q where p and q are integers and q is not zero. Examples include 3/4, -2/5, 7 (since 7 = 7/1), and 0 (since 0 = 0/1).