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2

Answer:

-12

Explanation:

Adding and subtracting negative numbers is a pretty tricky thing to learn (trust me, I know!), but if you go through it slowly and use a couple tricks, you can figure it out.
Here's our equation:
#-16 + 9 - 5 = ?#

The first two numbers we are going to deal with are #16# and #9#. Now these aren't just normal #16# and #9#, one is positive and one is negative. I just put some parentheses around them, so that we remember that:
#(-16) + (+9)#

So the easiest way to learn how to do this type of problem is make a number line like this: enter image source here
Obviously, this number line doesn't go far enough, but you could draw it to go all the way to #-16#. Now put your finger at #-16# and count to the right 9 lines. Where is your finger at now? It should be at #-7#.

( If you need extra explanation: You moved 9 spaces to the right because that is that direction positive numbers are. Since 9 is positive, you will get closer to 0, not further away.)

Okay! So now we have:
#-7 - 5 = ?#
#(-7) + (-5) = ?# (I added parentheses again)
Put your finger back on the #-7# and move to the left 5 spaces. Because #5# is negative, we move to the left, or further away from 0.
You should now be at #-12#, which is the answer of this equation.

2

Answer:

#69902# is divisible only by #2# and not by #3,5,9# or #10#. Please see below for details.

Explanation:

Divisibility by #2# can be tested by checking the digit at unit's place. If we have #0,2,4,6# or #8# at unit's place, then the number is divisible by #2#. Here we have #2# at unit's place in #69902#, and hence it is divisible by #2#.

Divisibility by #3# can be tested by checking that sum of all the digits is divisible by #3# or not. Here sum of digit's in #69902# is #6+9+9+0+2=26#, which is not divisible by #3#, therefore #69902# is not divisible by #3#.

Divisibility by #5# can be tested by checking the digit at unit's place. If we have #0# or #5# at unit's place, then the number is divisible by #5#. Here we have #2# at unit's place in #69902#, and hence it is not divisible by #5#.

Divisibility by #9# can be tested by checking that sum of all the digits is divisible by #9# or not. Here sum of digit's in #69902# is #6+9+9+0+2=26#, which is not divisible by #9#, therefore #69902# is not divisible by #9#. Note that if a number is not divisible by #3#, it is also not divisible by #9#.

Divisibility by #10# can be tested by checking the digit at unit's place. If we have #0# at unit's place, then the number is divisible by #10#. Here we have #2# at unit's place in #69902#, and hence it is not divisible by #10#.

2

Answer:

#196=2xx2xx7xx7#

Explanation:

As the last two digits in #196# are divisible by #4#, #196# too is divisible by #4#.

Dividing by #4# we get #49# and hence

#196=4xx49#

but factors of #4# are #2xx2# and that of #49# are #7xx7#. Further #2's# and #7's# are prime numbers and cannot be factorized.

Hence prime factors of #196# are

#196=2xx2xx7xx7#

Note : This method of factorization, in which we first find identifiable factors and then proceed until all prime factors are known is called tree method. This is graphically described below.enter image source here

2

Answer:

#18.024#

Explanation:

Do long division ..

#color(white)(.......l)18.024#
#41|bar739.000#
#color(white)(llllm)ul41" "larr73div 41=1 and 1xx41=41#
#color(white)(llllm)329" "larr43-41 = 32# and bring down the #9#
#color(white)(llllm)ul328" "larr329div41 = 8 and 8 xx41 =328#
#color(white)(llllmlll)100" "larr329-328 = 1# and bring down the #00 #
#color(white)(lllllllllm)ul82" "larr100div41 = 2 and 2 xx41=82#
#color(white)(lllllllllm)180" "larr100-82 = 18# and bring down the #0#
#color(white)(lllllllllm)ul164" "larr100div41 = 4 and 4 xx41=164#

You can continue for as many decimal places as you wish.

Or simply use a calculator if you need the answer immediately.

2

Answer:

#6 " km"#

Explanation:

This is a metric prefix problem. Some of the metric prefixes are:

math.com

In this case, you have:

#=>6"km" = 6 xx10^3 "m" = 6000 "m"#
#=>60 "m"#
#=>600 "cm" = 600 xx 10^(-2) "m" = 6 "m"#
#=>6000 "mm" = 6000 xx 10^(-3) "m " = 6 "m"#

We see that the largest is #6000 "m"#, which corresponds to our #6 "km"#.

2

Answer:

See the construction tips in the explanation.

Explanation:

Tony B

#color(red)("Measuring is counting")#

#color(blue)("Step 1")#

Draw a number line ( A to B) of some easily divisible length. Perhaps 15 lots of #1/2# cm. We will end up counting in #15^("ths")#

Draw the line BG of some length that is easily divided into 5 equal parts. The angle does not matter as long as it is sensible.

Draw the line GA. Then the parallel lines from F,E,D and C

This has provided a full set of #5^("ths")# from A to B

Count #4/5# from A towards B and mark that point (H).
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(blue)("Step 2")#

In the same way as in Step 1 divide AH into 3 parts
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Step 3")#

In the same way divide AB into #15^("th")#. You only need to subdivide AJ to make your point. You will have #4/15# matching:

#4/5-:3->4/5xx1/3= 4/15#

2

Answer:

#color(red)A)# is the fastest.

Explanation:

.

In order to compare, we need to convert all four speeds to a common unit. Let's convert them all to feet per hour:

#color(red)A)# #18# feet in #20# minutes

There are #60# minutes in each hour. We divide #18# by #20# to find the speed as feet per minute. Then we multiply the result by #60# to get feet per hour:

#18/20*60=9/10*60=9*6=# #color(red)("54 feet per hour")#

#color(red)B)# We divide #90# by #2.5# to get feet per hour:

#90/2.5=# #color(red)("36 feet per hour")#

#color(red)C)# There are #3# feet in each yard.

#20# yards is equal to #20*3=60# feet. We divide #60# by #1.5# to get feet per hour:

#60/1.5=# #color(red)("40 feet per hour")#

#color(red)D)# #3(2)/3=11/3#. We multiply #11/3# yards by #3# to get feet:

#11/3*3=11# feet

We divide #11# feet by #15# to get feet per minute and multiply the result by #60# to get feet per hour:

#11/15*60=# #color(red)("44 feet per hour")#

Therefore, #A# is the fastest.

2

Answer:

A teacher will expect the prime number method. Just for the hell of it this is a different approach!

168

Explanation:

We have two numbers ; 24 and 7

I am going to count the 24's. However lets look at this value.

24 can be 'split' into a sum of 7's with a remainder. So each 24 consists of:

#24=(7+7+7+3)#

If we sum columns of these we will get the 3 summing to a value into which 7 will divide exactly. When this happens we have found our least common multiple.

REMEMBER WE ARE COUNTING THE 24's

#" count "color(white)("dd") "The 24's"#
#color(white)("ddd") 1color(white)("ddd")(color(white)(.)7+color(white)(.)7+color(white)(.)7+color(white)(.)3)#
#color(white)("ddd") 2color(white)("ddd")(color(white)(.)7+color(white)(.)7+color(white)(.)7+color(white)(.)3)#
#color(white)("ddd") 3color(white)("ddd")(color(white)(.)7+color(white)(.)7+color(white)(.)7+color(white)(.)3)#
#color(white)("ddd") 4color(white)("ddd")(color(white)(.)7+color(white)(.)7+color(white)(.)7+color(white)(.)3)#
#color(white)("ddd") 5color(white)("ddd")(color(white)(.)7+color(white)(.)7+color(white)(.)7+color(white)(.)3)#
#color(white)("ddd") 6color(white)("ddd")( color(white)(.)7+color(white)(.)7+color(white)(.)7+color(white)(.)3)#
#color(white)("ddd") 7color(white)("ddd")ul( (color(white)(.)7+color(white)(.)7+color(white)(.)7+color(white)(.)3)larr" Add"#
#color(white)("ddddddd.")49+49+49+ubrace(21) #
#color(white)("dddddddddddddddddddd")darr#
#color(white)("dddddddddddddd")" exactly divisible by 7"#

We have a count of 7 so the value is #7xx24 = 168#

4

Answer:

#1# Celsius.

Explanation:

Let's use a number line and start at #-7# Celsius. enter image source here

Now since the temperature rose by 8, we know that it is going to move to the right towards the positive numbers. It is always the same on a number line:

#"moving right = increase"#
#"moving left = decrease"#

Put your finger on the #-7# and move #8# spaces to the #"right"#.

enter image source here

You should be on the #1#.
enter image source here

So the temperature is now #1# Celsius.

2

Answer:

#HCF = 25 and LCM = 4,200#

Explanation:

Write each number as the product of its prime factors.

Then you see what are made up of and what they have in common:

#" "150 = 2color(white)(xxxxxx)xx3xxcolor(blue)(5xx5)#
#" "175 = color(white)(xxxxx.xxxx)xxcolor(blue)(5xx5)xx7#
#" "200 = ul(2xx2xx2color(white)(x..x)xxcolor(blue)(5xx5)" ")#

#" "HCF=color(white)(xxxxx.xxxxx)color(blue)(5xx5)=25#

#" "LCM = 2xx2xx2xx3xx5xx5xx7 = 4,200#