Chapter Notes: Simple Equations

# Simple Equations Class 7 Notes Maths Chapter 4

 Table of contents Variables What Equation is? How to form Equations using Statements? How to Convert Equation into Statement? Balanced Equation Solving an Equation More Equations Applications of Simple Equations to Practical Situations Word Problems

### Can you solve this riddle?

"I am thinking of a number. When you add 5 to it, you get 12. What is the number?"

The answer is written in the riddle itself!

Think, Think, Think!

Let's call this unknown number 'x'

Adding 5 to this number gives 12. So, let's write down the equation:

x + 5 = 12

The solution to this equation will give us the number. To find x, we need to undo the addition of 5. So, let's subtract 5 from both sides of the equation:

x +5−5 = 12−5

This simplified to:

x =7

The number is 7!

## Variables

A variable is an unknown number that could have a different numerical value. It is called a variable because it can vary. It is represented by different letters like x, y, a, b, etc.

From variables, we form expressions. The expressions are formed by performing operations like addition, subtraction, multiplication, and division of the variables. From x, we formed the expression (x + 5).

Example: 6x + 5 is an algebraic expression.

## What Equation is?

An equation is like a balance scale. It has an equal sign in the middle, which shows that the value on the left side is the same as the value on the right side. The left side is called the LHS, and the right side is called the RHS.
Example:
(i) 4x + 5 = 65

(ii) 10y - 20 = 50

• In equation (i), the LHS is (4x + 5), which means we have 4 times a number (x), and we add 5 to it. The RHS is 65, which means the value on the right side is 65. So, in this equation, the value of (4x + 5) is equal to 65.
• In equation (ii), the LHS is (10y - 20), which means we have 10 times a number (y), and we subtract 20 from it. The RHS is 50, which means the value on the right side is 50. So, in this equation, the value of (10y - 20) is equal to 50.

Question for Chapter Notes: Simple Equations
Try yourself:Which is not an equation?

Important Points Related to the Equation

• One of the expressions must have a variable.
• The LHS (left-hand side) of the equation is equal to the RHS (right-hand side) of the equation.
• An expression does not have an equality sign, but an equation always has an equality sign.
• If we interchange the position of the expression from LHS to RHS or vice versa, the equation remains the same.

Both the above equations are the same.

## How to form Equations using Statements?

1. The sum of four times x and 12 is equal to 35.

2. Half of a number is 3 more than 8.

Example: Write the following statements in the form of equations:
(i) The sum of four times x and 12 is 38.

(ii) If you subtract 4 from 6 times a number, you get 8

(iii) One third of m is 6 more than 9.

(iv) One fourth of a number plus 7 is 10.

Solution:

(i) Four times x is 4x.

Sum of 4x and 12 is 4x + 12. The sum is 38.

The equation is 4x + 12 = 38.

(ii) Let us say the number is z; z multiplied by 6 is 6z.

Subtracting 4 from 6z, one gets 6z – 4. The result is 8.

The equation is 6z – 4 = 8

(iii) One third of m is m / 3. It is greater than 9 by 6.

This means the difference ( m / 3 – 9) is 6.

The equation is (m / 3) – 9 = 6

(iv) Take the number to be n. One fourth of n is n / 4. This one-fourth plus 7 is (n/4) + 7. It is 10. The equation is (n / 4) + 7 = 10

Example: A store sells apples in two types of bags, one small and one large. A large bag contains as many as 6 small bags plus 3 loose apples. Set up an equation to find the number of apples in each small bag. The number of apples in a large bag is given to be 75.

Solution:

Let a small bag contain 'a' number of apples.

A large bag contains 3 more than 6 times 'a', that is, 6a + 3 apples.

But this is given to be 75. Thus, 6a + 3 = 75.

You can determine the number of apples in a small bag by solving this equation.

Question for Chapter Notes: Simple Equations
Try yourself:Write the following statement in the form of an equation:
The sum of three times x and 10 is 13.

## How to Convert Equation into Statement?

• Step 1: Identify the variables in the equation. Variables are represented by letters, such as x, y, a, b, etc.
• Step 2: Determine the operations being performed on the variables. Common operations include addition (+), subtraction (-), multiplication (*), and division (/).
• Step 3: Translate the equation into words, describing the operations in simple terms.
• Step 4: Write the statement in a clear and understandable manner.

Example: Convert the equation into a statement by yourself:

(i) x + 3 = 7

(ii) 4y = 16

(iii) 2a - 5 = 9

(iv) 7b + 3 = 24

Solution:

(i) x + 3 = 7 - Adding 3 to x gives 7.

(ii) 4y = 16 - Four times a number y is equal to 16.

(iii) 2a - 5 = 9 - Subtracting 5 from twice a number a gives 9.

(iv) 7b + 3 = 24 - Adding 3 to seven times a number b results in 24.

## Balanced Equation

When the left-hand side of an equation is equal to its right-hand side, then it is said to be a balanced equation.

1. If we add the same number to both sides.: We can add the same number on both sides of a balanced equation, the equation will remain the same.
2. If we subtract the same number from both sides.: We can subtract the same number from both sides of a balanced equation, the equation will remain the same.
3. If we multiply the same number on both sides: We can multiply the same number on both sides of a balanced equation, the equation will remain the same.

## Solving an Equation

Any value of the variable that satisfies the equation is the solution of the equation.

There are two methods to solve an equation:

1. By adding or subtracting the same number to both sides of the equation.

Example: x + 11 = 35

Solution:

Subtract 11 from both sides.
x + 11 – 11 = 35 – 11

x = 24

Here, x = 24 is the solution of the given equation.

2. By multiplying or dividing by the same non-zero number to both sides of the equation.

Example : 25y = 125

Solution:

Divide both sides by 25.

y = 5

## More Equations

In this method, we transpose the numbers from one side of the equation to the other side so that all the terms with variables come on one side and all the constants come on another side.

While transposing the numbers, the sign of the terms will get changed. i.e. Negative will become positive and positive will become negative.

Example: x + 11 = 35

Solution:

Now we will transfer 11 from LHS to RHS and its sign will get reversed.

x = 35 – 11

x = 24

Example: Solve 20y + y - 18 = 10y + 2y

Sol:

21y - 18 = 12y

21y -  12y = 18

9y = 18 (By dividing both sides by 9)

y = 2

The digit at the unit's place is y = 2.

And the digit at the tens place is 2y = 2 × 2 = 4

Hence, the required number is 42.

Add/Subtract on both sides Vs Transposing

## Applications of Simple Equations to Practical Situations

From a Solution to the Equation

As we solve the equation to get the solution, we can get the equation also if we have the solution.

Any equation has only one solution but if we make an equation from a solution then there could be many equations.

Example: Sara is twice as old as her brother John. Five years ago, Sara was three times as old as John. How old is Sara now?

Solution:

Let John's current age be x years.

Since Sara is twice as old as John, Sara's current age is 2x years.

According to the problem, five years ago, Sara was three times as old as John. So, we can write the equation:

2x3(x$−5)$

To find their ages, solve for x:

First, simplify the right side of the equation:

2x5=3x15

Next, isolate x by subtracting 3x from both sides:

2x3x5=15

x15

Add 5 to both sides to isolate x:

10

Multiply both sides by -1:

x=10

So, John is 10 years old.

Since Sara is twice as old as John:

2x=2×10=20

Therefore, Sara is 20 years old.

This is not the only possible equation. There could be other equations also.

Question for Chapter Notes: Simple Equations
Try yourself:18 is taken away from 8 times of a number is 30. Find the number.

## Word Problems

Example 1: Radha’s Mother’s age is 5 years more than three times Shikha’s age. Find Shikha’s age, if her mother is 44 years old.

Solution:

Let Shikha’s age = y years

Her mother’s age is 3y + 5 which is 44.

Hence, the equation for Shikha’s age is 3y + 5 =44

3y + 5  = 44

3y = 44 – 5 (by transposing 5)

3y = 39

y = 13 (by dividing both sides by 3)

Hence, Shikha’s age = 13 years

Example 2: A number consists of two digits. The digit in the tens place is twice the digit in the units place. If 18 is subtracted from the number, the digits are reversed. Find the number.

Solution:

Let the digit at units place = y

So, the digit in the tens place = 2y

So, the number is (2y) y.

As it is given that if 18 is subtracted from the number, the digits are reversed.

So, we have

(2y) y - 18 = y(2y)

10 × (2y) + 1 × y - 18 = 10 × y + 1 × (2y)

The document Simple Equations Class 7 Notes Maths Chapter 4 is a part of the Class 7 Course Mathematics (Maths) Class 7.
All you need of Class 7 at this link: Class 7

## Mathematics (Maths) Class 7

76 videos|345 docs|39 tests

## FAQs on Simple Equations Class 7 Notes Maths Chapter 4

 1. What are variables in the context of simple equations?
Ans. In simple equations, variables are symbols that represent unknown quantities or values that can change in an equation.
 2. How do you form equations using statements?
Ans. To form equations using statements, you need to identify the unknown quantity in the problem and represent it with a variable. Then, create an equation that describes the relationship between the known quantities and the unknown quantity.
 3. How can you convert an equation into a statement?
Ans. To convert an equation into a statement, simply substitute the values of the variables in the equation with the actual numbers given in the problem. This will provide a statement that is true when the equation is satisfied.
 4. What is a balanced equation in the context of simple equations?
Ans. A balanced equation is an equation where both sides have the same value when simplified. This means that the equation is true and represents a balance between the quantities on both sides.
 5. How do you solve an equation in the context of simple equations?
Ans. To solve an equation, you need to isolate the variable by performing the same operations on both sides of the equation until the variable is alone on one side. This will give you the solution to the equation.

## Mathematics (Maths) Class 7

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