Explain how knowing 50 times 4 =200 you find 500 times 400.

Given -

50 times 4 =200

Find out the  values of 500 times 400.

To prove

As given in the question

50 times 4 =200

i.e the above also written in the form as follows.

50 × 4 = 200

Now find out for 500 times 400.

500 times 400 is also written in the form as follows .

500 × 400 = 200000

Therefore the 500 times 400 is 200000.

Hence proved

To find 500 times 400 from 50 times 4 =200 : use commutative, associative properties and place value

500 times 400

There are 3 properties in arithmetic operations that can be applied to arithmetic operations, namely: commutative, associative , and distributive properties

Commutative properties are mathematical operations of two numbers that are exchanged and produce the same results

a + b = b + a = c

a x b = b x a = c

this property applies to addition and multiplication operations.

Associative properties are mathematical operations of 3 numbers by grouping 2 numbers with parentheses and the location of the grouping is exchanged with the result that remains the same

(a + b) + c = a + (b + c) = d

(a × b) × c = a × (b × c) = d

Distributive properties are mathematical operations with 2 different arithmetic operations, by distributing numbers grouped in parentheses.

a × (b + c) = (a × b) + (a × c) = d

In the digit system, the value of a number depends on its place, or position, in the number.

Each digit is different place value.

the place value of the digits in a number: hundred thousands, ten thousands, one thousands, hundreds, tens, ones, decimal points, tenths, hundredths, thousandths, ten thousandths, hundred thousandths

From the task:

use the previous problem (50 times 4 = 200) to help solve 500 times 400.

50 times 4 = 200

in the form of arithmetic operations

50 x 4 = 200

or in place value

5 tens x 4 ones = 2 hundreds

we can use associative and commutative properties

so multiplication can be expressed in an interchangeable form because it has the same value

So to complete 500 x 400:

multiplying the whole numbers first then the zeros

The difference between first number operations and second number operations is the place value unit

 500 x 400

= 5 hundreds x 4 hundreds

= 5 x100 x 4 x 100 (there are 4 times of 10)

= (5 x 4 x 10) x 10 x 10 x 10

⇒ (5 x 4 x 10) = from previous problem

= 200 x 10 x 10 x 10

the place value: 12,354,897

link

link

place-value patterns

link

Keywords : place value, digit, number, times , commutative, associative

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