How to Solve Equations Mentally for Class 6 ?

Importance of Solving Equations Mentally

But first, why should you bother learning these mental maths techniques in the first place? More importantly, by not writing down every single intermediate step, you enable your brain to notice the higher-level relationships among numbers.

• Speed in Competitive Exams: Time is the biggest enemy in school exams. Doing mental calculations for equations makes you fast in the objective section, thereby creating more time for descriptive word problems.

• Building Number Sense: These strategies compel you to understand the "why" behind an equation, rather than relying on a series of memorised steps. This strengthens your overall intuition about mathematics.

• Cognitive Flexibility: Easy algebra methods make your mind flexible enough to handle two or more pieces of information simultaneously – a life skill accentuated in mathematics and science courses.

• Immediate Verification: Even if you want to write down your final answer, the ability to take the equation through your head often gives instant checking of "silly" errors.

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Tricks to Solve Equations Mentally

Algebra in class 6 is based on the idea of balance. Here are seven algebra tricks that will enable you to get the value of x in class 6 without needing a notebook.

1. The Opposite Operation Trick (The Golden Rule)

The most basic principle of algebra is that every operation has an opposite, or an "enemy". Now, if a number is being added to or subtracted from 'x', it should be taken out.

• The Logic: Whatever is being done to 'x', mentally envision its inverse.

• Mental Example: For x + 7 = 15, your brain should immediately think 15 - 7 = 8.

• Result: x = 8.

2. The Balance Thinking Trick

Imagine the equation as being a physical balance scale. The equal sign (=) is the pivot. To balance the scale, for whatever you pick on one side, you need to pull on the other.

• The Logic: If 'x' is being defeated by a 'y' subtraction, then you have to 'add' weight to 'x' in order for it to stay afloat.

• Mental Example: For x - 4 = 10, imagine adding 4 to both sides to clear the scale. In your head: 10 + 4 = 14.

• Result: x = 14.

3. The Multiply-Divide Reverse Trick

If we have a number next to 'x' (for example, 2x), it means you are multiplying. To tear them asunder, to identify 'x', the method is division.

• The Logic: Multiplication and division are a pair.

• Mental Example: For 2x = 18, divide the total by the number attached to 'x'. In your head: 18 / 2 = 9.

• Result: x = 9.

Read More - Learn Subtraction without Borrowing (Class 6)

4. The Division Reverse Trick

Writing 'x' as a fraction (x/3) indicates that it is being divided. You do the opposite of "free" the x: multiplication.

• The Logic: Without thinking, always view the bottom number as able to 'cross' itself over an equals sign and multiply here.

• Mental Example: For x / 3 = 5, simply multiply the two visible numbers. In your head: 5 * 3 = 15.

• Result: x = 15.

5. The Step-by-Step Break Trick

Whenever the equations appear a bit more advanced, do not try to solve the entire thing in one shot. Divide it into very small and manageable pieces.

• The Logic: First, calculate this floating number and solve 'x'.

• Mental Example: For x + 5 = 20.

• Mental Step: First, move the 5 away. 20 - 5 = 15.

• Result: x = 15.

6. The Trial Method (Quick Guess)

For several of the problems in Class 6, ultimately, the solution is simply an integer. You're not rearranging; you're "plugging in" a guess to see if it fits the balance.

• The Logic: Ask yourself, "What number makes this statement true?"

• Mental Example: For x + 3 = 10.

• Mental Step: Think, "7 + 3 is 10, so x must be 7." This technique is one of the most efficient ways to solve equations more quickly for multiple-choice questions.

Read More - Why Many Students Face Multiplication Problems in Class 6

Practise Sheet to Solve Equations Mentally

Use these questions to challenge yourself on both speeds. The short questions are designed to give you the chance to mentally calculate a value for 'x' in under 5 seconds.

Short Mental Questions

1. Solve x + 12 = 30. 

2. Solve x - 9 = 21.

3. Find x if 5x = 45. 

4. Find x if x / 4 = 6.

5. Solve x + 19 = 50. 

Long-Form Logical Questions

In these questions, you need to decipher words into equations first and then apply your mental maths skills to solve them.

• Question 1: "A certain number 'x' is increased by 15, and the result is 42. What is the value of the number?"

• Question 2: "Rohan had some marbles. After his friend gave him 8 more, he had a total of 30 marbles. How many did he start with?"

• Question 3: "If four times a number results in 48, find the number."

• Question 4: "A number divided by 5 gives a result of 7. What is the number?"

• Question 5: "Half of a mystery number added to another half equals 3. What is the number?"

Benefits to Solve Equations Mentally

Learning to solve equations mentally will lead you beyond just getting the right answer and improve your academic pursuits.

• Reduces Exam Stress: When you can solve the first 5-10 questions of a maths paper in your head, your confidence boosts up. You feel in control of the subject.

• Eliminates Calculation Fatigue: The calculation is mentally exhausting when you have to write out long columns for simple subtraction or multiplication. It is a wise move to save that energy for the tough HOTS (higher-order thinking skills) questions.

• Better Data Interpretation: Using these techniques, you can even guess answers in science and geography. This means that, for example, finding a missing percentage or ratio is significantly reduced in time.

• Improved Focus: Mental calculation requires high concentration. This habitual reaction serves a purpose and helps you improve your attention span (for maths, as well as for all subjects).

How Does CuriousJr Help with Class 6 Mental Maths?

Self-study is good, but a framework can help these simple algebra tricks become permanent. CuriousJr online mental maths classes offer Class 6 students a unique environment to grasp these skills.

• Visual Learning Modules: Using animated videos, CuriousJr shows you that something must be the same on both sides of an equation, or it goes out of whack. The mantras of moving numbers are something students intuitively grasp by seeing the numbers move, which helps them internalise the "Move Number Trick" far better than even a textbook can.

• Gamified Practice: The teacher assigns a timed game where the students must answer as many questions correctly in, say, 4 minutes.

• Vedic Maths Integration: The site uses age-old Indian methods such as "digit sums" and the "base method," which are best suited for reducing a handful of algebra and arithmetic concepts (class 6).

• Concept Clarity: CuriousJr prioritises the "Why" before diving wholeheartedly into learning how to solve a problem, ensuring that students build an understanding of maths rather than just rote memorising, solving equations faster.