class7 maths integer rules ,basics and solving equations

Integers are whole numbers, including positive numbers, negative numbers, and zero.

Imagine a line that goes on forever in both directions. Positive numbers go to the right of zero, and negative numbers go to the left.

A successor is the next number on the number line.

A predecessor is the number just before on the number line.

Absolute value is how far a number is from zero, always positive.

Additive inverses are pairs of numbers that add up to zero, like 3 and -3.

Multiplicative inverses are pairs of numbers that multiply to one, like 1 and 1.

Even numbers can be divided evenly by 2.

Odd numbers cannot be divided evenly by 2.

Add them and keep the same sign.

Subtract and use the sign of the bigger number.

Change the subtraction to addition and follow the rules for adding integers.

The answer is positive.

The answer is negative.

Divide normally and then think about the signs to decide if the answer is positive or negative.
Absolutely, let's simplify further and add more flashcards for each concept related to transposition and solving equations:

Transposition means moving parts of an equation to solve for a variable, changing signs as needed.

To solve, move numbers and variables to different sides of the equation, using opposite operations to keep the equation balanced.

A linear equation involves variables (like \( x \)) with no exponents other than 1 and constants (like \( 3x + 2 = 8 \)).

Balance by doing the same math operations on both sides, such as adding or subtracting, to keep the equation equal.

Variables (like \( x \)) are unknowns, and constants (like \( 5 \)) are fixed numbers in equations.

Transposition helps rearrange equations to find solutions, which is essential for solving problems and understanding math concepts.

Isolate by moving all other terms away from the variable using opposite operations on both sides of the equation.

Inverse operations undo each other, like adding and subtracting or multiplying and dividing, used to solve equations.

In \( 4y - 7 = 5 \), add 7 to both sides, then divide by 4 to find \( y = 3 \).

Verify by substituting the solution back into the original equation to see if both sides are equal.

These flashcards should make it easier to understand the concepts of transposition and solving equations in mathematics.