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Number Play - Mental Math

Grade 6CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Rearrangement Property: Using Commutative and Associative properties to group numbers that sum up to multiples of 1010, 100100, or 10001000 for easier addition. For example, a+b+c=(a+c)+ba + b + c = (a + c) + b.

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Distributive Property: Breaking down a multiplier to simplify multiplication, such as a×(b+c)=(a×b)+(a×c)a \times (b + c) = (a \times b) + (a \times c) or a×(b−c)=(a×b)−(a×c)a \times (b - c) = (a \times b) - (a \times c).

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Compensation Method: To add or subtract numbers close to a multiple of 1010, adjust the number to the nearest power of 1010 and then correct the final result.

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Mental Multiplication by 5,25,505, 25, 50: These can be treated as fractions of powers of 1010. For example, n×25=n×1004n \times 25 = n \times \frac{100}{4}.

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Estimation: Approximating the result by rounding numbers to the nearest ten, hundred, or thousand before performing the operation.

📐Formulae

a+b=b+aa + b = b + a

a×(b+c)=(a×b)+(a×c)a \times (b + c) = (a \times b) + (a \times c)

a×(b−c)=(a×b)−(a×c)a \times (b - c) = (a \times b) - (a \times c)

n×5=n×102n \times 5 = \frac{n \times 10}{2}

n×25=n×1004n \times 25 = \frac{n \times 100}{4}

💡Examples

Problem 1:

Calculate 437+215+563437 + 215 + 563 mentally using rearrangement.

Solution:

(437+563)+215=1000+215=1215(437 + 563) + 215 = 1000 + 215 = 1215

Explanation:

By grouping 437437 and 563563, we get a sum of 10001000, making the final addition much simpler.

Problem 2:

Find the value of 15×10315 \times 103 using the distributive property.

Solution:

15×(100+3)=(15×100)+(15×3)=1500+45=154515 \times (100 + 3) = (15 \times 100) + (15 \times 3) = 1500 + 45 = 1545

Explanation:

Breaking 103103 into 100+3100 + 3 allows us to multiply 1515 by each part and sum the results.

Problem 3:

Use the compensation method to solve 745−199745 - 199.

Solution:

745−200=545545+1=546745 - 200 = 545 \\ 545 + 1 = 546

Explanation:

We subtract 200200 (which is 199+1199 + 1) for ease, then add back 11 because we subtracted one too many.

Problem 4:

Perform the following subtraction mentally: 8000−46728000 - 4672.

Solution:

8000−46723328\begin{array}{r} 8000 \\ -4672 \\ \hline 3328 \end{array}

Explanation:

To solve this mentally, subtract in parts: 8000−4000=40008000 - 4000 = 4000, then 4000−600=34004000 - 600 = 3400, then 3400−70=33303400 - 70 = 3330, and finally 3330−2=33283330 - 2 = 3328.

Problem 5:

Multiply 24×2524 \times 25 using the shortcut method.

Solution:

24×1004=24004=60024 \times \frac{100}{4} = \frac{2400}{4} = 600

Explanation:

Multiplying by 2525 is equivalent to multiplying by 100100 and then dividing by 44.