Explain how knowing 50 times 4 =200 helps you find 500 times 400.
Answers
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 : usecommutative, associative properties and place value
500 times 400
Further explanation
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
Learn more
the place value: 12,354,897
place-value patterns
Keywords : place value, digit, number, times , commutative, associative
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The length of the opposite side is the same as the length of the hypotenuse (they are the same side in this case), the ratio is:
sin(90 degrees) = 1 / 1 = 1
Thus, sin(90 degrees) equals 1.
In trigonometry, the sine function (abbreviated as sin) is defined based on the angles of a right-angled triangle.
Specifically, for a given angle θ in a right-angled triangle, the sine of θ is defined as the ratio of the length of the side opposite θ to the length of the hypotenuse (the longest side of the triangle, which is always opposite the right angle).
In a standard coordinate system, consider a right-angled triangle where one of the angles is 90 degrees (a right angle).
This angle is often denoted as π/2 radians in radians or 90 degrees in degrees.
In this triangle, the side opposite the angle θ (the side opposite the right angle) is the vertical side, and the hypotenuse is the longest side.
For a right-angled triangle with a 90-degree angle, the sine of θ is defined as:
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Since the length of the opposite side is the same as the length of the hypotenuse (they are the same side in this case), the ratio is:
sin(90 degrees) = 1 / 1 = 1
Thus, sin(90 degrees) equals 1.
In radians, sin(π/2 radians) is also equal to 1 since it is the same angle as 90 degrees but measured in radians.
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Because the "opposite segment " is actually the hypotenuse of the triangle we get the fraction