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

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.

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step-by-step explanation: