Divisibility Rules
Is the number 76,543,210 divisible by 3?
NO.
In order to test if a number is divisible by 3, add up all the digits to get 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28, and then see if 28 is a multiple of 3. In this case, 28 is not a multiple of 3, so the answer is no.
Simplify:
3 - 5 + 7 X 9
61
3 - 5 + 7 X 9
3 - 5 + 63
-2 + 63
61
Perform the multiplication 15.5 X 0.85
13.175
15.5 X 0.85 = 13.175
What is 35% of 45?
15.75
10% of 45 is 4.5
So 30% of 45 is 3 X 4.5 = 13.5
So 5% of 45 is 1/2 X 4.5 = 2.25
Adding yields 13.5 + 2.25 = 15.75
Simplify 1.72
2.89
1.72 = 1.7 X 1.7 = 2.89
Take the number 7,842.
a=1 if the number is divisible by 3. Otherwise, a = 0.
b=1 if the number is divisible by 4. Otherwise, b = 0.
c=1 if the number is divisible by 6. Otherwise, c = 0.
d=1 if the number is divisible by 9. Otherwise, d = 0.
What is the sum of a + b + c + d?
2
To check if 7,842 is divisible by 3, add the digits to get 7 + 8 + 4 + 2 = 21. 21 is divisible by 3, so 7,842 is divisible by 3. So a = 1.
To check if 7,842 is divisible by 4, check the last two digits, 42, but 42 is not a multiple of 4, so 7,842 is not divisible by 4. So b = 0.
To check if 7,842 is divisible by 6, we need to see if this number is divisible by both 2 and 3. It is divisible by 2 because it is even, and it is divisible by 3 based on the work shown above, so 7,842 is divisible by 6. So c = 1.
To check if 7,842 is divisible by 9, add the digits to get 7 + 8 + 4 + 2 = 21. 21 is not divisible by 9, so 7,842 is not divisible by 9. So d = 0.
Adding a + b + c + d = 1 + 0 + 1 + 0 = 2
Simplify:
52 + 5 X 3 + 33
67
52 + 5 X 3 + 33
25 + 15 + 27
40 + 27
67
Perform the division 4/3 divided by 8/11. Keep your answer as a mixed fraction.
11/6
Using Keep-Change-Flip, 4/3 divided by 8/11 is the same as 4/3 multiplied 11/8.4/3 X 11/8 --> 4/8 X 11/3 --> 1/2 X 11/3 = 11/6
55% of a number is 49.5. What is the number?
90
.55 X ___ = 49.5
Divide both sides by 0.55 to get 90
Simplify (2/5)4 minus (3/625)
13/625
(2/5)4 = (2/5) X (2/5) X (2/5) X (2/5) = 16/625
Combining (16/625) - (3/625) = 13/625
The number 5x,069 is divisible by 9, where x is the ten thousands digit of the number. What is the value of x?
x = 7
For a number to be divisible by 9, add its digits to get 5 + x + 0 + 6 + 9 = 20 + x, and for this sum to be a multiple of 9, x = 7 works (because 27 is a multiple of 9).
Simplify:
(4 + (5 - (22)))2
25
(4 + (5 - (22)))2
(4 + (5 - 4))2
(4 + 1)2
52
25
What is 58.72 divided by 0.7? Round your answer to the nearest hundredth.
83.89 (must be correctly rounded)
58.72/0.7 = 83.8857143... ~ 83.89
What percentage of 60 is 80?
Accept any of 133%, 133.3%, 133.33...%, etc.
__% X 60 = 80__% = 80/60
__% = 1.333..., so 133.33...%
Simplify
-10 + 25 - -14.
29
In two steps, -10 + 25 = 15
15 - - 14 = 15 + 14 = 29
Yes
Add the digits:
2(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8) + 9
2(36) + 9
72 + 9
81, which is divisible by 3
Simplify:
1/2 multiplied by 1/3 divided by 1/4 plus 1/5
13/15
1/2 multiplied by 1/3 divided by 1/4 plus 1/5
1/2 X 1/3 = 1/6
1/6 / 1/4 = 1/6 X 4/1 = 4/6 = 2/3
2/3 + 1/5 = 10/15 + 3/15 = 13/15
Multiply -3.4 X -2.1
7.14
-3.4 X -2.1 = +7.14
A pancake is split into quarters for Robert, Carol, Sally and Jamie. Jamie finishes his quarter, but he also eats one quarter of the portion designated for Sally. What is the total percentage of the initial pancake that Jamie has eaten? You can round to the nearest percentage.
Accept 31% or 31.25%
Jamie has eaten
1/4 + 1/4 X 1/4 =
1/4 + 1/16 =
4/16 + 1/16 =
5/16 = 31.25, which rounds to 31%
If 78 = 5,764,801, what is 76?
117,649
78 = 5,764,801, so
76 = 78 / 72 = 5,764,801/49 = 117,649
The number 9,854 is divisible by how many integers between 2 and 9, inclusive of both 2 and 9?
1 integer (the number 2)
Use the divisibility rules on 9,854.
2: Yes, even
3: No, 9 + 8 + 5 + 4 = 26
4: No, 54/4 has a remainder
5: No, does not end in 0 or 5
6: No, is not divisible by 3
7: No, has a remainder when 9,854 is divided by 7, we did not learn the trick so have to do long division
8: No, 854 is not divisible by 8
9: No, 9 + 8 + 5 + 4 = 26
Simplify
(-11 + 44) X (-3 - 4)
-231
(-11 + 44) X (-3 - 4) =
(33) X (-7) =
-231
What is 0.005 divided by 0.02?
0.25
0.005 / 0.02 = 0.25
What is 50% of 40% of 80?
16
10% of 80 is 8, so
40% of 80 is 4 X 8 = 32
Then 50% of 32 is half of 32, or 16
What is the sum of
1 + 4 + 7 + 10 + ... + 292 + 295 + 298?
14,950
By grouping, you can see that 1 and 298 sum to 299, 4 and 295 sum to 299, 7 and 292 sum to 299, etc.
So how many pairs sum to 299?
If you add 3 to every number, the numbers are 3, 6, 9, ...297, 300. Dividing by 3 gets 1, 2, 3...,99,100, so there are 100 numbers. So there are 100/2 or 50 pairs.
Then the sum is 299 X 50 = 14,950