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Neko [114]
3 years ago
8

Find the greatest number that will divide 63, 45 and 69 so as to leave the same remainder.

Mathematics
1 answer:
jeka57 [31]3 years ago
7 0

Answer:

6

Step-by-step explanation:

Let n be unknown divisor and a be the same remainder, then

63=q_1\cdot n+a\\ \\45=q_2\cdot n+a\\ \\69=q_3\cdot n+a

Subtract a from all equalities:

63-a=q_1\cdot n\\ \\45-a=q_2\cdot n\\ \\69-a=q_3\cdot n

Subtract them:

63-45=(q_1-q_2)n\Rightarrow 18=(q_1-q_2)n\\ \\69-63=(q_3-q_1)n\Rightarrow 6=(q_3-q_1)n\\ \\69-45=(q_3-q_2)n\Rightarrow 24=(q_3-q_2)n

The greatest number is 6. When you divide numbers 63, 45, 69 by 6, you'll get remainders 3, 3, 3, respectively.

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4 = 2 * 2

Multiplying by 2 is the same a doubling.
Since 4 is 2 * 2, to multiply a number by 4, double the number twice.

Example:
What is 4 * 100?
Double 100 to get 200.
Double 200 to get 400.
Therefore, 4 * 100 = 400.
By doubling twice, we do the same as multiplying by 4.
4 0
3 years ago
1 cup is equal to 8 fluid ounces. How many fluid ounces are in 3 cups, 3 fluid ounces?
Gnesinka [82]

Answer:

If one cup is 8 then 3 cups is 24

Step-by-step explanation:

This can be solved by multiplying:

1*8=8

3*8=24

4 0
3 years ago
2.
andrew11 [14]

Answer:

the digit two is in tens... so a) is the answer

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3 years ago
Problemas de proporcion calidad inversa
Nata [24]

Answer:

A)the answer is 21

B)the answer is 22 days

C)the answer is 71 hours

3 0
3 years ago
The average person in the United States drinks 767 cups of coffee annually. How many quarts of coffee is that? Show your work. (
My name is Ann [436]

Answer: 191.75 quarts.

Step-by-step explanation:

We know that:

1 quart = 4 cups.

Then:

1 cup = 1/4 quarts.

this means that 1 cup, is equal to 1/4 quarts.

Then 767 cups is equal to 767 times 1/4 quarts.

The change of units is simply:

767 cups = 767*( 1/4 quarts) = 191.75 quarts.

7 0
3 years ago
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