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saul85 [17]
3 years ago
8

What does 5/7 × 2/1 equal? (Please leave an explanation, so I can understand!)

Mathematics
1 answer:
White raven [17]3 years ago
7 0
\bf \cfrac{5}{7}\times \cfrac{2}{1}\implies \cfrac{5\times 2}{7\times 1}\implies \cfrac{10}{7}\implies 1\frac{3}{7}
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There is no smallest positive rational number because, if there were, then it could be divided by two to get a smaller one. EXPL
Gennadij [26K]

Answer:

Since a/2⁽ⁿ ⁺ ¹⁾b <  a/2ⁿb,  we cannot find a smallest positive rational number because there would always be a number smaller than that number if it were divided by half.

Step-by-step explanation:

Let a/b be the rational number in its simplest form. If we divide a/b by 2, we get another rational number a/2b. a/2b < a/b. If we divide a/2b we have a/2b ÷ 2 = a/4b = a/2²b. So, for a given rational number a/b divided by 2, n times, we have our new number c = a/2ⁿb where n ≥ 1

Since \lim_{n \to \infty} \frac{a}{2^{n}b } = a/(2^∞)b = a/b × 1/∞ = a/b × 0 = 0, the sequence converges.

Now for each successive division by 2, a/2⁽ⁿ ⁺ ¹⁾b <  a/2ⁿb and

a/2⁽ⁿ ⁺ ¹⁾b/a/2ⁿb = 1/2, so the next number is always half the previous number.

So, we cannot find a smallest positive rational number because there would always be a number smaller than that number if it were divided by half.

3 0
3 years ago
The depth of a lake is 1,400 meters.What is the depth in kilometers?
lina2011 [118]
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Stels [109]

Answer:

The solution of the system is the ordered pair (-13,-4)

Step-by-step explanation:

we have

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2(a-4b)=2(3)

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substitute the value of b in any equation (i take equation B)

a-4(-4)=3

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Answer:

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