NCERT Solutions for Class 7 Maths Chapter 4 – Simple Equations
NCERT Solutions for Class 7 Maths Chapter 4 is about Simple Equations, the start of algebra. In this chapter, there are a total of 4 exercises and 14 questions. The Chapter 4 of NCERT Solution for Class 7 covers the concept of equations, formulation of Simple Equations and some practical applications
Class 7 NCERT Solutions for Chapter 4 ‘Simple Equations’ is based on the latest syllabus approved by CBSE. At Instasolv, we provide the most reliable study material for Class 7 Maths. Chapter-wise Solutions of NCERT Class 7 Maths Book are also provided that help you in understanding the concepts of each exercise better.
Chapter 4 Simple Equations, of CBSE NCERT Class 7 Maths Book introduces you to basic algebraic concepts that will be applied often in practical use. For the Maths subject in Class 7, we explain the important elements and summarise each part and subpart of the Chapter. The same sequence as in the book will be followed so that it becomes easy to understand and help as a reference. You will be able to strengthen your concepts of simple equations for class 7 NCERT and score high marks in the exams.
NCERT Solutions for Class 7 Maths Chapter 4: Important Topics of Each Exercise
In NCERT Solutions for Class 7 Maths Chapter 4 you will find exercise-wise solutions to all the 4 exercises that carries 19 questions in total. These exercises are based on the topics discussed below:
- A Mind-Reading Game
Tell your friend to think of any number, multiply by 2 and then subtract 5 from the product. Now tell your friend to tell the result and you will tell him the number he had initially thought of. Does it not look like magic or as though you have read your friend’s mind? This game is the introduction of the chapter because the answer lies in Simple Equations.
- Setting Up of an Equation
Let us consider the same example we took above. Suppose the number your friend thought of was A. The first thing you did was tell him to multiply by 2 so the result is 2A.
Now you said subtract 5 from the product so the result is 2A – 5. Suppose your friend says the result he got is 15. The equation then is 2A – 5 = 15. You can now tell him the number he had thought of is 10. Put 10 in the simple equation in place of A and check for yourself.
- Review of What We Know
From the above, we can infer that a simple equation is formed or set up when a condition on a variable is applied. The variable is not fixed and can take any different numerical value. We generally denote a variable with an alphabet.
- What Equation is?
In an equation, there is always an equality sign. The expression on the Left Hand Side (LHS) of the equality sign is equal to the expression on the Right Hand Side (RHS) of the equality sign. In totality LHS, equality sign and RHS together form a simple equation. Let us summarise:
- An equation is a condition on a variable
- The condition is that two expressions, LHS and RHS, should have equal value or in other words LHS = RHS
- Since both sides are equal, interchanging the expressions will make no difference.
- Note that the variable should be there in at least one of the expressions.
- Solving an Equation
– Since LHS is equal to RHS, the equation will still hold if we add the same number to both sides. In other words, we add the same number to both LHS and RHS.
– By the same logic, the equation still holds if we subtract the same number from both sides.
– This is true even if we multiply or divide by the same number on both sides provided it is a non-zero number.
– Note that these are valid even if there is an unknown variable in the expressions LHS or RHS.
- More Equations
Let us take the same simple equation we took at the beginning 2A – 5 = 15
The equation still holds if we add 5 to both sides.
2A – 5 + 5 = 15 + 5 or 2A = 20
The equation still holds if we divide both sides by the non-zero number 2
2A/2 = 20/2 or A = 10
We can also simplify the process by transposing on either side. Let us use the same example for more clarity.
2A – 5 = 15
Instead of doing the addition function simply transpose so a negative number on one side becomes a positive number on the other side
2A = 15 + 5 or 2A = 20
Now transpose the multiplier of A which is 2. Check whether the multiplier is non-zero. 2 is a non-zero number so the condition holds. A multiplier on one side becomes a divider on the other side.
2A = 20 can now be written as A = 20/2
The answer is the same as before. A = 10.
Note: that just as a negative number one side becomes a positive number on the other side, similarly a positive number on one side becomes a negative number of the other side.
In the same manner, just as a multiplier on one side becomes a divider on the other side, a divider on one side becomes a multiplier on the other side.
- From Solution to Equation
Making the equation from the solution is how we played the mind-reading game. Knowing the solution as 15, we took the variable as A and made the equation just as we had given instructions. 2A – 5 = 15.
Any number of equations can be created. Let us take the same example.
We know A = 10
One equation we created was 2A – 5 = 15
We can create many more.
Add the same divisor on both sides say 2. A/2 = 10/2. Then add the same number on both sides say 5
The new equation created now is A/2 +5 = 10/2 + 5
Solve and check
A/2 + 5 = 5 + 5 or A/2 + 5 = 10
Transpose 5 from LHS to RHS, A/2 = 10 – 5 or A/2 = 5
Transpose 2 from LHS to RHS, A = 5 x 2 or A = 10.
- Application of Simple Equations to Practical Situations
There are several practical situations where Simple Equations can be used. NCERT Class 7 Maths Book has a self-practice exercise that we will use for our understanding.
There are two types of boxes containing mangoes. Each box of the larger type contains 4 more mangoes than the number of mangoes contained in 8 boxes of the smaller type. Each larger box contains 100 mangoes. Find the number of mangoes contained in the smaller box?
Given that each larger box contains 100 mangoes.
Also given that the larger box contains four more mangoes than the smaller box.
We have to find the number of mangoes in the smaller box which we will take as the variable and denote by A
From the above statements, the simple equation is A = 100 – 4 = 96.
Note: that there is extra information given here that there are 8 boxes of smaller type. When your concepts and understanding are clear you will not get confused by added information and use only what is relevant according to the requirement. That is how practical situations are.
Study Tips for NCERT Class 7 Maths Chapter 4: Simple Equations
Every student has an aim to get a high score in the exams. Instasolv recommends that you read chapter 4 Simple Equations of CBSE NCERT textbook for Class 7 Maths. Instasolv has provided a simple explanation and summary of each part.
An example has been used at the beginning and the same example is used to explain all the parts and subparts. All of this can be used to develop a better understanding of all the concepts.
- If any concept is still not understood, ask the experts on the Instasolv app which does not charge any student for this support.
- Do all the 4 exercises, solved examples and self-practice questions on your own before you cross-check from the NCERT Solutions or ask the experts on the Instasolv app.
A practical self-practice example from the CBSE NCERT textbook for Class 7 Maths has been used for explanation. In practical situations, data available can be much more than that required for the question asked. Being able to segregate the required data only is an important step. It is easy for students who have understood the concept and confusing for those who try to learn by rote. Learning by rote is never recommended by the subject matter experts of Instasolv.
Follow the NCERT solutions for class 7 maths chapter 4 and tips provided by Instasolv and score high marks in your Maths exam.