Can someone please explain how to solve a couple of these questions?  Thank you!

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caledon | High School Teacher | (Level 3) Senior Educator

Posted on

Without the instructions it's difficult to tell what the questions are asking you to determine. I'm going to assume that, based on the blank line between the sets of numbers in each question, that it's asking you to determine which is larger and place the appropriate sign in the blank space, < > or =

All you need to do is to make sure that the numbers on both side are using the same units, at the same size. For example, #26 has the units mm, cm, m and km. We can't add the units in this form; we need them all to be the same. It doesn't really matter which unit you choose, but the standard unit for distances is m, the meter. The other letters tell you whether this unit is larger or smaller than a meter.

1000mm = 1m

100cm = 1m

1000m = 1km (or, .001km = 1m)

You need to apply these conversions to each number.

For example, on the left side we have

10cm + 895km + 442km

None of these units are in the form of meters; we need to convert them. However, since 895km and 442km are in the same units, km, we can just add them right now and save ourselves the trouble of one additional conversion.

So now we have

10cm + 1337km

We need to get both of these numbers in the form of meters.

If 100cm = 1m, then we need to find out how many "hundreds" of cm would fit in the number we have.

10cm/100cm = .1m

Likewise, if we have 1337km, and 1 km is 1000 meters, we need to multiply.

1337km x 1000m = 1,337,000m

Adding them, we get 1337000.1m

Now comparing this to the right side:

51mm + 4956m + 2109m

Combine the two meter measurements:

51mm + 7065m

Convert mm to m:

1000mm are in a meter, how many "1000 mm" are in 51 mm?

51/1000 = .051m

7065.051m

1337000.1m > 7065.051m

There are some very convenient converters that show up on google if you just type "convert X to Y", such as "convert km to m".

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malkaam | Student, Undergraduate | (Level 1) Valedictorian

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In order to explain how to solve these questions, i am solving one below to explain the whole method.

23. 

TAKING LEFT HAND SIDE:

We know that,  1 cl=10ml

Hence, in order to derive an answer we need to convert all the figures into the same units.

Since, cl           ml

          1    =    10` `

       483   =     x

Therefore, on cross multiplying,

1*x = 10*483

x=4830 or 483cl= 4830ml

cl                   ml

1            =     10

26761     =     x

On cross multiplying: 

1x=26761*10

x=267610ml

Therefore, now we take all the values in terms of ml in order to find the answer:

4830+267610+3057

=275497ml

TAKING RIGHT HAND SIDE:

Converting kl into L:

1kl = 1000L

so, 2087kl = xL

On cross multiplying:

1x=2087*1000

x=2087000L

In order to compare the Right and left hand side, we have to brig the values in the same unit, i.e. convert ml into L.

1L=1000ml

So, xL= 275497ml

On cross multiplying: 

x*1000=275497*1

1000x=275497

Dividing by 1000 on both sides:

1000x/1000 = 275497/1000

x=275.497L

HENCE, IT SHOWS THAT LEFT HAND SIDE IS LESS THAN RIGHT HAND SIDE.

275.497 < 2087000

In the same way, the other questions are to be solved by converting the values into the same units as to determine which side is greater or if they are equal.

lauleepops's profile pic

lauleepops | Student, Grade 11 | eNotes Newbie

Posted on

I'm assuming that the questions call for the answer of either <, >, or =. 

24.) 4111m + 5931m + 32mm + 4916m ______ 195km + 52km + 2cm + 689km

To be able to compare the two sides of the equation, you must add up all the numbers in each side. Seeing that they don't all have the same units, however, you'll have to convert some values to match the majority. 

On the left side, you have the values, 4111m, 5931m, 32mm, and 4916m. Since 32mm is the sole value that's in millimeters, you ought to convert it to meters like the other three. 

I have an acronym that I live by in terms of converting units! It goes like this:

King -- kilo-

Henry -- hecto-

Declared -- deca-

May -- meter (unit of measure*)

Dog -- deci-

Cat -- centi-

Month -- milli-

When a unit is to be converted to a greater one, move the decimal point to the left. When a unit is to be converted to a lesser one, move the decimal point to the right.

*May(meter) is the word that corresponds to units of measure, meaning "meter" is not the only unit that can be placed in that position. For example, gram(g) and liter(L) are also applicable. The prefixes (e.g. kilo-, hecto-, deca-) are simply added onto the units. 

So, seeing that 32mm must be converted to m, you just have to adjust the decimal place of 32mm* thrice to the left, since milli-(month) is three places below meter(may). This will leave you with .032m. 

*Since 32 is a whole number, its decimal place is located after its last digit(i.e., 2). 

Now you can add the values 4111m, 5931m, .032m, and 4916m together and get 14958.032m as your sum.

Try getting the sum of 195km + 52km + 2cm + 689km. First, convert 2cm to km like the other three values. You should end up with 936.00002km as your sum.

Now you have 14958.032m and 936.0002km to compare. Let's convert the latter to meters, so you'll see an example of moving decimal places to the right. Since kilo-(king) is 3 places above meter(may), you must adjust the decimal point of 936.00002km thrice to the right to turn it into m. You get 936000.02m.

Finally, compare the two values. 14958.032m < 936000.02m

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