Interactive Rational Numbers Worksheet

Chapter 1: Rational Numbers (Moderate Level)

Rational numbers are numbers that can be expressed as pq where p and q are integers and q ≠ 0. Let's explore their properties step by step.

First, let's understand the basic properties of rational numbers.

1. Write the additive inverse of −59.

Awesome! The additive inverse of −59 is 59.

2. Find the product of (−34) and 49.

Great job! (−34) × (49) = −13.

3. Is the number 0.25 a rational number? Justify your answer. YesNo

Perfect! Yes, 0.25 = 14 which is in pq form.

4. Find a rational number equivalent to 711 with denominator 77.

Excellent! 711 = 4977 (multiply both by 7).

5. Write the multiplicative inverse of –2.

Super! The multiplicative inverse of -2 is -1/2.

6. Fill in the blank: If a + b = b + a, then the operation is ? commutativeassociativedistributive

That's correct! This shows the commutative property.

7. What is the result of dividing any non-zero rational number by 1? The number itself01.

Well done! Any number divided by 1 gives the number itself.

8. Write a rational number between −35 and −12. −1120−920−23−710

Brilliant! −1120 lies between −35 and -1/2.

9. The rational number 57 is closedopenundefined under addition.

Perfect! Rational numbers are closed under addition.

10. Find the rational number which when multiplied with −712 gives 1.

Great work! The answer is −127.

Drag each example to the correct property:

Part B: Short Answer Questions (2 Marks Each)

1. Find the value of: [(−56) ÷ (29)] × (35).

To find the value first we have to perform divisionmultiplication.

Let's divide −56 by 29. Division means multiply by .

(−56) ÷ (29) =

Now multiply by 35: (−154) × (35) =

Excellent! The final answer is −94.

2. Show that rational numbers are closed under subtraction.

Perfect! Rational numbers are closed under subtraction.

3. Simplify: (−25 + 25) + (49 + 59).

Final result =

Awesome! The simplified value is 1.

4. Divide: (−78) ÷ (−143) and express in lowest terms.

(−78) ÷ (−143) =

To express a fraction in its simplest form, we need to find the GCDLCMsum of the numerator and denominator

Simplify by dividing by GCD i.e. .

Final answer =

Brilliant! The answer in lowest terms is 316.

Part C: Long Answer Questions (4 Marks Each)

1. Simplify: ((34 + 12) – (58)) × (83).

Perfect! The final answer is 53.

2. Check if subtraction is associative for: 35, −12, and 415.

LHS: (35 - −12) - 415 =

RHS: 35 - (−12 - 415) =

Since LHS ≠= RHS, subtraction is notis associative.

Excellent analysis! Subtraction is not associative.

3. Verify distributive property: A × (B + C) = A × B + A × C where A = −34, B = 25, C = −12.

LHS: A × (B + C) =

RHS: A × B + A × C =

Since LHS RHS, distributive property is verifiednot verified.

Outstanding! The distributive property is verified.

4. Find the correct value of: [(−47) ÷ (23)] × (218).

To find the value first we have to perform divisionmultiplication.

Step 1: Division

(−47) ÷ (23) =

Step 2: Multiplication

(−67) × (218) =

Fantastic! The final answer is −94.

Test your understanding with these multiple choice questions:

For each question, click on the correct answer:

1. The multiplicative inverse of −112 is:

(a) −211 (b) 211 (c) 112 (d) −112

Super job! The multiplicative inverse of −112 is −211.

2. Which satisfies the additive inverse property?

(a) 5 + 0 = 5 (b) 4 × 1 = 4 (c) −67 + 67 = 0 (d) 1 + 1 = 2

Well done! −67 + 67 = 0 shows additive inverse.

3. Value of (−23) × ((45) - (15)):

(a) −615 (b) −25 (c) 615 (d) −815

That's right! (−23) × (35) = −25.

4. Which represents the distributive property?

(a) a + b = b + a (b) (a + b) + c = a + (b + c) (c) a × (b + c) = a × b + a × c (d) a ÷ b = a × 1/b

Correct! a × (b + c) = a × b + a × c is distributive property.

5. Which is not a rational number?

(a) −37 (b) 0 (c) 20 (d) 115

Perfect! 20 is undefined, not a rational number.