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san4es73 [151]
3 years ago
9

Reduce 6/12 to its simplest form

Mathematics
2 answers:
Vlad1618 [11]3 years ago
7 0

Answer:

1/2

Step-by-step explanation:

6/12

3/6

1/2

Nuetrik [128]3 years ago
3 0

Answer: 1/2

Step-by-step explanation: To write the fraction 6/12 in lowest terms,

we divide the numerator and the denominator by the

greatest common factor of 6 and 12.

Since the factors of 6 are 1, 2, 3, and 6

and the factors of 12 are 1, 2, 3, 4, 6, and 12,

the greatest common factor of 6 and 12 is 6.

So we divide the numerator and the denominator of 6/12 by 6.

6 divided by 6 is 1 and 12 divided by 6 is 2.

So 6/12 written in lowest terms is 1/2.

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One non-negative number is the reciprocal of another number. The sum of the two numbers is a minimum. What are the two numbers
Troyanec [42]

The two numbers are 1 and 1.

Let the non-negative number be x and its reciprocal be y = 1/x

The sum of the two numbers is f(x,y) = x + y

= x + 1/x

= f(x)

For f(x) to be minimum, we differentiate it with respect to x and equate it to zero to find the value of x at which irt is minimum.

So, df(x)/dx = d(x + 1/x)/dx

= dx/dx + d(1/x)/dx

= 1 - 1/x²

Equating it to zero, we have

1 - 1/x² = 0

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x² = 1

Taking square-root of both sides, we have

x = ±√1

x = ±1

Since x is non-negative x = + 1

We differentiate f(x) again to determine if this value gives a minimum for f(x).

So, d²f(x)/dx² = d(1 - 1/x²)/dx

= d1/dx - d(1/x²)/dx

= 0 - × (-2/x³)

= 2/x³

Substituting x = 1 into the equation,

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So x = 1 is a minimum point for f(x)

Since x = 1 and y = 1/x, y = 1/1 = 1

So, the two numbers are 1 and 1.

Learn more about sum of two numbers here:

brainly.com/question/13854139

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