Tam Sayılarla Çarpma ve Bölme İşlemi 📘 7. Sınıf Matematik #2025

Summary

The lesson explains multiplication and division with integers, then applies those rules to order of operations, powers, and several properties of multiplication.

1. Multiplying and dividing integers

For both multiplication and division, determine the sign of the answer by comparing the signs of the numbers:

• Same signs → positive result
  • Examples: (5 \times 4 = 20), ((-5) \times (-4) = 20), and ((-20) \div (-5) = 4).
• Different signs → negative result
  • Examples: (5 \times (-4) = -20), ((-5) \times 4 = -20), and (20 \div (-5) = -4).

After deciding the sign, calculate using the numbers’ absolute values.

2. Order of operations

The instructor reviews the order for evaluating expressions:

1. Calculate powers.
2. Evaluate parentheses.
3. Do multiplication and division, working from left to right.
4. Do addition and subtraction, working from left to right.

In the example expression, the division is completed first. The remaining subtraction and addition are then handled left to right, using the rule that subtracting a number is equivalent to adding its opposite. The terms ultimately cancel, giving 0.

3. Powers of negative numbers

A power means multiplying the base by itself the indicated number of times. For a negative base:

• An even exponent gives a positive result: ((-3)^2 = 9) and ((-3)^4 = 81).
• An odd exponent gives a negative result: ((-3)^3 = -27) and ((-2)^5 = -32).

Parentheses matter:

• ((-3)^2 = (-3) \times (-3) = 9).
• (-3^2 = -(3 \times 3) = -9): without parentheses, the exponent applies to the 3, and the minus sign remains outside.

The lesson also uses powers such as ((-5)^3 = -125), then combines signed results. For example, (-32 + 81 - 125 = -76).

4. Applying the rules to challenges

The practice questions ask students to use sign rules, exponent parity, and integer addition together. The instructor also highlights that every power of 1 equals 1, regardless of the exponent.

In one challenge, an inequality leaves the integers from (-7) through (8) as possible values. Counting them gives 16.

5. Properties of multiplication

The lesson reviews these properties:

• Commutative property: The order of factors can change without changing the product. Example: ((-5) \times 2 = 2 \times (-5)).

• Associative property: Factors can be grouped differently without changing the product.

• Identity element: Multiplying by (1) leaves a number unchanged.
• Absorbing element: Multiplying by (0) gives (0).
• Distributive property: Multiplication can be distributed over addition or subtraction. For example, (a(b + c) = ab + ac).

A symbol puzzle uses these properties to infer values, and later exercises use opposite numbers to simplify sums. For instance, pairs such as (7 + (-7)) cancel to (0).

The lesson concludes that the sum of the integers strictly between (-10) and (8) is (-17): the opposite pairs cancel, leaving (-9) and (-8).

Speakers and sources featured

• Instructor/teacher: Presents and explains the mathematics, with a humorous teaching style.
• Tonguç/Tonguş: A student character addressed by the instructor and used in the lesson’s back-and-forth examples.
• Tonguç Dershane: The branded presenter named in the opening and closing.
• Music and applause: Non-speaking audio cues in the intro and outro.