Puzzles and stuff for the younger students - please join in.

4 and 2
4 times 2 = 8
4+ 2 = 6

Hard one!
The sum of a 5-term arithmetic sequence is 100. If all terms are positive integers, what is the smallest possible value for a term?

Soup » Sun Jan 05, 2014 7:26 am
Hard one!
The sum of a 5-term arithmetic sequence is 100. If all terms are positive integers, what is the smallest possible value for a term?

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2 + 11 + 20 + 29 + 38 =100
(difference of 9)
possible value for a term is 2

EXCELLENT WORK FROM
WEIRD
SOUP
and
PUZZLED
I'm impressed!

Soup, just a little suggestion, maybe you could have explained what an AP was so that some of our younger bright sparks could have a go.
I am really pleased that you posted this puzzle and I'm glad that Soup gave you a reasonable quick reply. thanks to both of you.
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A not very hard puzzle. So long as you have done some negative numbers at school you could have a proper go at this one.
Weird, you gave a great answer last time, can you do this one?
What are 2 numbers that add to 0 and multiply to -9

3, -3
3*-3 = -9
-3+3 = 0 ^_^

Thanks special, well done.

if 2 number multiply to give a positive number what can you tell me about their signs?

Both of the integers would be negative.

(-)*(-)=+
(-)*+=(-)
+*+=+

or positive actually, now that i already posted my answer

Excellent answer mystery songbird


How about this question. I am looking for 2 numbers.
they multiply to give 12 and add to give -7
what would the signs be, and what would the numbers be?

Melody:

Excellent answer mystery songbird


How about this question. I am looking for 2 numbers.
they multiply to give 12 and add to give -7
what would the signs be, and what would the numbers be?

Well because we know that a negative times a negative is a positive we can say negative 4 times negative 3. This would get the positive 12, but when added it would equal negative 7.
or
-4 * -3 = 12
-4 + -3 = -7

These questions could also help to factor out binomials into their polynomial forms before combined like terms for instance, using some of the same terms:

Say this is your binomial x^2 - 16 to un-combine like terms you would need to find the two numbers that when multiplyed receive 16 and when added receive 0.

You could work it out completely into (x-4)(x+4) or the polynomial x^2 - 4x + 4x - 16 I'm assuming this is some of what Melody is helping out with, I hope this was helpful to someone lol(:

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Thank you Warped Tour Girl,
That is exactly what i was thinking
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I would really like for one of our younger students to answer this.

This is a diagram of rectangular yards. They are adjacent which means they share a fence. They are measured in metres.
The area of anything is how many squares will fit inside.
The areas of these yards will be measured in metres squared (or square metres) m ²
a) I want you to tell me the area of each of the yards separately
then
b) I want you to tell me the area of both the yards put together.

You can do this a few different ways. How many ways can you think of ?

So I want the answers but I want to know how you got the answers. More than one method would be good.

140118 adjacent rectangles.JPG

How about this question. I am looking for 2 numbers.
they multiply to give 12 and add to give -7
what would the signs be, and what would the numbers be?

The number are

-3 + -4 = -7
-3 * -4 = -12

Should I put () around these numbers? It looks funny when I type them with out them.

2 times 4 equals 8
2 plus 4 equals 6

The areas of these yards will be measured in metres squared (or square metres) m2
a) I want you to tell me the area of each of the yards separately
then
b) I want you to tell me the area of both the yards put together.

You can do this a few different ways. How many ways can you think of ?

So I want the answers but I want to know how you got the answers. More than one method would be good

Big yard is 5*4 = 20 square meters
small yard is 3*5 = 15 square meters

15 + 20 square meters is 35 square meters total

or

(5+7)*5 = 35 square meters total


I thougt meters squared was different than square meters
because if it was 35 meters square then it would be 35*35 = 1225 square meters

I thougt meters squared was different than square meters
because if it was 35 meters square then it would be 35*35 = 1225 square meters

You have to be very careful Puzzled,
They are both the same
think about if 35 metres square is written 35m ².
that wouldn't be a square with a side length of 35m would it! that might be a rectangle 5m by 7m.

If you are talking about a square with a side length of 35m you need to use the extra words.

Good work on the solutions Serjio and Puzzled. It is good to see people get involved.