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3 years ago

Find the greatest 3 digit number which when divided by 75,45 and 60 leaves no remainder and the remainder 4 in each case

1 answer:

7 0

LCM of 75,45 and 60 is 900.
The divisor of 75,45 and 60 must be a multiple of their LCM.
75×900=67500 )⤵
45×900=40500 )↪ not a 3 digits no.
60×900=54000 )⤴
Since they are not 3 digits no..the greatest 3 digits no exactly divisible by 75,45,60 must be the LCM itself i.e. 900 >>Ans

Now,the next question is very simple.As the 900
greatest divisor of all given no., add 4 to get remainder 4 when divided by 75,60 and 45.
So, ans=904

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leva [86]

Answer: The correct answer is:

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→ Choice: [C]: " $\frac{2}{1} * \frac{7}{-2}$ " .

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Step-by-step explanation:

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Note that this problem contains multiplication and division.

WIth multiplication and division;

the order of operations we perform is from "left side to right side" in the expression; in the order in which the operation occurs:

As such:

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The given problem:

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" $\frac{-3}{4} * \frac{7}{-2}$ ÷ $\frac{3}{-8}$ " ;

Is treated as:

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" $(\frac{-3}{4} * \frac{7}{-2})$ ÷ $\frac{3}{-8}$ " ;

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So, we start with:

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" $\frac{-3}{4} * \frac{7}{-2}$ " ;

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→ $\frac{-3}{4} * \frac{7}{-2} = \frac{(-3*7)}{[4*(-2) ]} = \frac{-21}{-8}$ ;

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Simplify:

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" $\frac{-21}{-8} = \frac{(-1)*21}{(-1) *8}$ " ;

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→ The "(-1)'s " cancel out:

{since: "(-1)/(-1) = 1 "} ;

→ And we have: " $\frac{21}{8}$ " ;

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Now, continue with the problem, and divide this value by: " $\frac{3}{-8}$ " ;

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" $\frac{21}{8}$ ÷ $\frac{3}{-8}$ " ;

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Note that dividing by a number is the same as multiplying by the reciprocal of that said number:

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The reciprocal of " $\frac{3}{-8}$ " ; is: " $\frac{-8}{3}$ : l

As such:

" $\frac{21}{8}$ ÷ $\frac{3}{-8}$ " ;

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= " $\frac{21}{8} * \frac{-8}{3}$ "

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Now, let us simplify:

Note: The "8" and the "-8" ;

The "8" can be changed to "1" ; and the "-8" can be changed to "-1" ;

since: "-8 ÷ 8 = 1 " ; and since: "8 ÷ 8 = 1 " ;

Note: The "3" and the "21" ;

The "3" can be changed to "1"; and the "21" can be changed to "7" ;

since: "21 ÷ 3 = 7 " ; and since: "3 ÷ 3 = 1 " ;

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And we can we rewrite the expression:

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→ " $\frac{7}{1} * \frac{-1}{1}$ " ;

which equals: " 7 * -1 " ; which equals " - 7 ".

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Now, the problem has 4 (four) answer choices. Which expression [i.e. which answer choice] is equal to: " -7 " ??

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Consider Choice [A]: " $\frac{1}{2} * \frac{7}{2}$ " ; which equals: " $\frac{(1*7)}{(2*2)} = \frac{7}{4} = 1\frac{3}{4}$ " ;

" $1\frac{3}{4} \neq -7$ ."

Rule out: "Choice [A]."

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Consider Choice: [B]: " $\frac{2}{1} * \frac{7}{2}$ " ; which equals: " $\frac{(2*7)}{(1*2)} = \frac{14}{2} = 7$ ; " $7\neq -7$ ."

Rule out: "Choice: [B]."

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Consider Choice: [C]: " $\frac{2}{1} * \frac{7}{-2}$ " ; which equals: " $-7$ ; " $-7 = -7$ ".

Choice [C]: seems correct!

______________

Consider Choice: [D]: " $\frac{-1}{2} * \frac{7}{-2}$ " ; which equals:

" $\frac{(-1*7)}{(2*-2)} = \frac{-7}{-4} = \frac{(-1)*7}{(-1)*4}$ ;

→ cancel out the "(-1)'s" ;

→ {since: "(-1) / (-1) = 1 " ;

to get:

→ " $\frac{7}{4}$ " ; which equals:

→ " $1\frac{3}{4}$ " ; " $1\frac{3}{4} \neq -7$ . "

Rule out: "Choice: [D]."

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The correct answer is:

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Choice: [C]: " $\frac{2}{1} * \frac{7}{-2}$ " .

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Hope this is helpful to you!

Wishing you the best!

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Amy can run 1/10 mile in a minute how many minutes will it take amy to run 3 miles

german

She will have to have run for 30 minutes to have run 3 miles.

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Step-by-step explanation:

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