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Simple Equations Summary Class 7 NCERT Summary Chapter 4
Equation
- An equation is a condition on a variable. A variable takes on different numerical values; its value is not fixed. Variables are denoted usually by letters of the alphabets, such as x, y, z, l, m, n, p, etc.
- An equation remains the same, when the expressions on the left and on the right are interchanged. This property is useful in solving equations.
Solving an Equation
Systematic Method
- The same quantity can be added to both sides of an equation without changing the equality.
- The same quantity can be subtracted from both sides of an equation without changing the equality.
- Both sides of an equation may be multiplied by the same non-zero number without changing the equality.
- Both sides of an equation may be divided by the same non-zero number without changing the equality.
Transposition Method
- We can transfer (transpose) a term from one side to the other by changing its plus (+) sign to minus (-) sign or from minus sign to plus sign. This does not effect the equality of the statement.
- Transposing a number is the same as adding or subtracting the number from both sides.
- Transposition of an expression can be carried out in the same way as the transposition of a term.
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FAQs on Simple Equations Summary Class 7 NCERT Summary Chapter 4
| 1. What are simple equations? |  |
Simple equations are mathematical statements that contain an unknown value or variable. They involve operations like addition, subtraction, multiplication, and division, and the goal is to find the value of the unknown variable that makes the equation true.
| 2. How do you solve a simple equation? | |
To solve a simple equation, you need to isolate the variable on one side of the equation. This is done by applying inverse operations to both sides of the equation. By performing the same operation on both sides, the equation remains balanced, and you can determine the value of the unknown variable.
| 3. Can you give an example of solving a simple equation? | |
Certainly! Let's solve the equation: 3x + 5 = 17.
First, we want to isolate the variable x. We can start by subtracting 5 from both sides of the equation:
3x + 5 - 5 = 17 - 5
This simplifies to:
3x = 12
Next, we divide both sides of the equation by 3 to solve for x:
3x/3 = 12/3
The equation becomes:
x = 4
Therefore, the value of x that satisfies the equation is 4.
| 4. Are there any specific steps to follow when solving simple equations? | |
Yes, there are general steps to follow when solving simple equations:
1. Simplify both sides of the equation if possible.
2. Use inverse operations to isolate the variable on one side of the equation.
3. Perform the same operation on both sides of the equation to keep it balanced.
4. Continue simplifying until you have the variable alone on one side.
5. Check your solution by substituting the found value back into the original equation.
| 5. Can you provide tips for solving simple equations more efficiently? | |
Certainly! Here are some tips for solving simple equations more efficiently:
1. Always perform operations on both sides of the equation to maintain balance.
2. Use mental math whenever possible to simplify calculations.
3. Combine like terms to reduce the number of steps.
4. Pay attention to signs (+/-) when combining or moving terms.
5. If dealing with fractions, try to eliminate them by multiplying both sides of the equation by the least common denominator.
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