Learning Material Sheets class 7 ganita prakash

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Learning Material Sheets class 7

Complete Learning Material Sheets: Ganita Prakash Class 7

Chapter 1: Large Numbers Around Us

Core Concepts

  • Number Systems: Understanding the difference between the Indian (Lakh, Crore) and International (Million, Billion) systems of numeration.
  • Estimation: Rounding numbers to the nearest convenient place value (ten, hundred, lakh, etc.) to make calculations easier and to get a quick sense of a quantity’s size.
  • Place Value: Recognizing that the value of a digit depends on its position within a number. This is key to reading, writing, and comparing large numbers.

Solved Example: Reading and Comparing

Question: Write the number 24,68,13,579 in words according to both systems and compare 500 lakhs with 5 million.

Indian System: Twenty-Four Crore, Sixty-Eight Lakh, Thirteen Thousand, Five Hundred Seventy-Nine.
International System: Two Hundred Forty-Six Million, Eight Hundred Thirteen Thousand, Five Hundred Seventy-Nine.
Comparison: 10 lakhs = 1 million. Therefore, 50 lakhs = 5 million. They are equal.

Practice Questions

  1. How many thousands make a lakh?
  2. Round the number 6,72,85,183 to the nearest ten lakh.
  3. Which is greater: 1 Crore or 15 Million?

Chapter 4: Expressions Using Letter-Numbers (Algebra)

Core Concepts

  • Variable: A letter (like x or n) used to represent an unknown or changing number.
  • Algebraic Expression: A mathematical phrase built with variables, numbers, and operations (e.g., 2n + 5).
  • Like Terms: Terms with the exact same variable part (e.g., 7x and -3x). You can combine like terms.
  • Simplifying: Combining all like terms in an expression to make it as short as possible.

Solved Example: Simplifying an Expression

Question: Simplify the expression: (5a + 8b - 2) - (3a - 4b - 7)

Step 1: Remove the brackets. Remember to flip the signs of all terms in the second bracket because of the subtraction sign in front of it.
5a + 8b - 2 - 3a + 4b + 7
Step 2: Group the like terms.
(5a - 3a) + (8b + 4b) + (-2 + 7)
Step 3: Combine the like terms.
2a + 12b + 5

Practice Questions

  1. Write an expression for “a number `y` is multiplied by 10 and then 7 is subtracted from the product.”
  2. If p = 5, what is the value of the expression 4p - 3?
  3. Simplify: 9x + 4y - 5x - y + 3.

Chapter 5: Parallel & Intersecting Lines

Core Concepts

  • Intersecting Lines: Two lines that cross, forming four angles.
  • Vertically Opposite Angles: Angles opposite each other at an intersection. They are always equal.
  • Linear Pair: Two adjacent angles forming a straight line. Their sum is always 180°.
  • Parallel Lines & Transversal: When a line (transversal) crosses two parallel lines:
    • Corresponding Angles are equal.
    • Alternate Interior Angles are equal.
    • Interior Angles on the Same Side add up to 180°.

Solved Example: Finding Unknown Angles

Question: Two parallel lines are cut by a transversal. One of the corresponding angles is 75°. Find the measure of its alternate interior angle.

Step 1: Understand the relationships. Let the given corresponding angle be ∠1 = 75°. Let its vertically opposite angle be ∠3. Let the alternate interior angle be ∠4.
Step 2: Use the properties.
  • ∠1 and ∠3 are vertically opposite, so ∠3 = ∠1 = 75°.
  • ∠3 and ∠4 form a linear pair. No, that’s not right.
  • Let’s rethink. ∠1’s alternate exterior angle is also 75°.
  • The alternate interior angle we want is vertically opposite to the other corresponding angle. Let’s call the other corresponding angle ∠2. So ∠2 = ∠1 = 75°. The alternate interior angle is vertically opposite to ∠2, so it is also 75°.
  • Simpler way: For parallel lines, alternate interior angles are equal to corresponding angles. So if the corresponding angle is 75°, the alternate interior angle is also 75°.

Practice Questions

  1. If two lines intersect and one angle is 110°, what are the other three angles?
  2. Two parallel lines are cut by a transversal. If one interior angle is 60°, what is the measure of the other interior angle on the same side?

Chapter 6: Number Play

Core Concepts

  • Parity: The property of a number being either even or odd.
    • Rules of Addition: O+O=E; E+E=E; O+E=O.
    • Rules of Multiplication: O×O=O; E×Any=E.
  • Magic Squares: Grids where the sum of numbers in each row, column, and diagonal is the same (the “magic sum”).
  • Fibonacci Sequence: A sequence where each number is the sum of the two preceding ones (e.g., 1, 2, 3, 5, 8, 13…).
  • Cryptarithms: Puzzles where letters stand for digits and you must solve the arithmetic problem.

Solved Example: Parity Puzzle

Question: A box contains an odd number of apples and an even number of oranges. Can the total number of fruits be 50?

Step 1: Identify the parity of each group. Apples = Odd. Oranges = Even.
Step 2: Apply the parity rule for addition.
Total Fruit = Number of Apples + Number of Oranges
Total Fruit = Odd + Even = Odd.
Step 3: Compare with the target number. The target is 50, which is an Even number.
Conclusion: No, it is not possible. The total number of fruits must be odd, and 50 is even.

Practice Questions

  1. What is the parity of the product of two odd numbers and one even number?
  2. In a 3×3 magic square using numbers 1-9, what is the magic sum?
  3. What are the next two numbers in the sequence: 1, 2, 3, 5, …?

Chapter 8: Working with Fractions

Core Concepts

  • Multiplication: Multiply the numerators, then multiply the denominators. Simplify by canceling common factors before multiplying. (Numerator × Numerator) / (Denominator × Denominator).
  • Reciprocal: The “flipped” version of a fraction. The reciprocal of a/b is b/a. A number multiplied by its reciprocal equals 1.
  • Division: To divide by a fraction, multiply by its reciprocal. (Known as “Keep, Change, Flip”).

Solved Example: Division of Fractions

Question: A ribbon of length 5 1/2 metres is cut into pieces, each of length 1/4 metre. How many pieces can be cut?

Step 1: Identify the operation. This is a division problem: Total Length ÷ Length per Piece.
Step 2: Write the expression. Convert the mixed number to an improper fraction: 5 1/2 = 11/2.
The problem is: 11/2 ÷ 1/4.
Step 3: Apply the division rule (Keep, Change, Flip).
11/2 × 4/1.
Step 4: Multiply and simplify. We can cancel the 2 and 4.
11/1 × 2/1 = 22.
Conclusion: 22 pieces can be cut.

Practice Questions

  1. Calculate: 3/8 × 4/9.
  2. What is the reciprocal of 7?
  3. Calculate: 4/5 ÷ 2/3.