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Given the following equation, what is x?)
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ACT Aspire Math: Knowing (and Using) the Rules of Divisibility 13 Views
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Description:
Place one of the following numbers into the ones digit of the number 428, while moving the other digits so that the 4 is in the position of the thousands digit. What ones digit would make the number 428 divisible by 6 and 9?
Transcript
- 00:03
Okay Aspiring math people moving on another drill for you
- 00:07
Place one of the following numbers into the ones digit
- 00:10
of the number of four Twenty eight while moving the
- 00:12
other digits so that the four is in the position
- 00:16
of the thousands digit What one's digit would make the
Full Transcript
- 00:19
number for twenty eight divisible by six and by nine
- 00:27
Well the problem asked us to shift all digits to
- 00:30
the left and then tack on one more number to
- 00:32
the end But which number gets to join the group
- 00:35
here Well we can't just let any old number join
- 00:37
the club There are standards to solve this problem We
- 00:40
need to divide and conquer kind of there's division involved
- 00:43
anyway at least conquering that's So think of visibility rules
- 00:48
How does that work How do they work to be
- 00:50
divisible by six evenly a number must be divisible by
- 00:54
two and three and even number is divisible by two
- 00:58
duck and a number is divisible by three If the
- 01:01
digits add up to a multiple of three what we
- 01:04
mean by that is like four plus two plus a
- 01:07
That's fourteen is that divisible by three so much and
- 01:11
the rule for visibility by nine is similar If the
- 01:13
digits add up to a multiple of nine like they
- 01:17
some toe eighteen or twenty seven or thirty six like
- 01:20
that then it's all good We're also particularly fund of
- 01:23
this helpful little rule Nine is a multiple of three
- 01:25
So if a number is divisible by nine then of
- 01:28
course it must be divisible by three as well In
- 01:30
other words there's no need to check the rules for
- 01:33
both three and nine So if you have a niner
- 01:35
there the three work In short our number needs to
- 01:38
be divisible by both six and nine In other words
- 01:40
it needs to be even like in a c t
- 01:44
And the digits need to add up to a multiple
- 01:47
of nine Well the on ly answer that satisfies both
- 01:50
is four So uh that's c right there It gives
- 01:54
us four thousand two hundred eighty for if we adam
- 01:57
up for post to hiss six plus aids for eighteen
- 02:00
plus four there is eighteen eighteen of his wine nine
- 02:04
and then by definition by three as well So that's
- 02:07
it That's the answer It's see you'd stick up for
- 02:10
there in the thousands place and be done with this 00:02:12.578 --> [endTime] thing
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