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3 years ago

Is 112 between 10 and 11?

Mathematics

2 answers:

jasenka [17]3 years ago

6 0

I’m gonna go on a limb and say no

qaws [65]3 years ago

4 0

Answer:

Step-by-step explanation:

112 is not between 10 and 11

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Raina must choose a number between 55 and 101 that is a multiple of 2, 8 and 10. Write all the numbers that she could choose. If

Aleonysh [2.5K]

Answer:

The only possible number is $80$ .

Step-by-step explanation:

The number in question needs to be a multiple of all three of $2$ , $8$ , and $10$ . As a result, it must also be a multiple of the least common multiplier (lcm) of the three number.

Start by finding the least common multiplier of the three numbers.

Factor each number into its prime components:

$2$ is a prime number itself.
$8 = 2^3$ .
$10 = 2 \times 5$ .

The only prime factors are $2$ and $5$ .

The greatest power of $2$ among the three numbers is $3$ .
The greatest power of $5$ among the three numbers is $1$ .

Therefore, the least common multiplier of the three number should be the product of $2^3$ and $5$ . That's equal to $2^3 \times 5 = 8 \times 5 = 40$ .

In other words, the number (or numbers) in question could be written in the form $40\, k$ , where $k$ is an integer.

The question requires that this number be between $55$ and $101$ . In other words,

$55 \le 40\, k \le 101$ .

The goal is to find the possible values of $k$ . Note that from integer division by $40$ ,

$55 = 1 \times 40 + 15$ , and
$101 = 2 \times 40 + 21$ .

The inequality becomes:

$1 \times 40 + 15 \le 40\, k \le 2 \times 40 + 21$ .

However,

$1 \times 40 < 55 = 1 \times 40 + 15$ , and
$2 \times 40 + 21 = 101 < 3 \times 40$ .

Hence,

$1 \times 40 < 1\times 40 + 15 \le 40\, k \le 2 \times 40 + 21 < 3 \times 40$ .

$1 \times 40 < 40\, k < 3 \times 40$ .

Divide by the positive number $40$ to obtain:

$1 < k < 3$ .

Since $k$ is an integers, $k = 2$ .

Indeed, $40 \, k = 80$ is between $55$ and $101$ .

Therefore, $80$ is the number in question.

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4 years ago

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What's 10 3/4 - 7 1/4?

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$10 \frac{3}{4} - 7 \frac{1}{4} \\ \\ \frac{10 \times 4 + 3}{4} -7 \frac{1}{4} \\ \\ \frac{43}{4} - y \frac{1}{4} \\ \\ \frac{43}{4} - \frac{7 \times 4 + 1}{4} \\ \\ \frac{43}{4} - \frac{29}{4} \\ \\ \frac{43-29}{4} \\ \\ \frac{14}{4} \\ \\ \frac{7}{2} \\ \\ 3 \frac{1}{2} \\ \\ Answer: \fbox {3 \ 1/2} \ or \ \fbox {3.5}$

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