Fraction Addition and Subtraction: Problem Type 2

Hello =)

In my previous post, we discussed how to add and subtract fractions with like denominators.  Now we will learn how to add and subtract fractions with unlike denominators, which is not difficult if you practice! Lets proceed with an example: Add 3/4 + 5/12.  First, we simply notice that we have unlike denominators, that is, our bottom numbers are different.  Second, we have to find the least common denominator of the two fractions.  That is, what number can you multiply the one denominator to to get the other denominator, or what number can you multiply to both denominators to get the least common denominator (LCD).  The easiest way to approach this is to list the first few multiples of 4 and 12 and scanning from left to right, we want the smallest multiple that both have.  So, multiples of 4 include: 4, 8, 12, 16, 20.  Multiples of 12 include: 12, 24, 36, 48, 60.  In this example, we are lucky because we have found the least common multiple, which is 12, because scanning from left to right, it is the first common multiple that both have.  So, changing both of our denominators to 12, we now have to find our numerators.  Looking at 3/4, what do we multiply 4 by to get 12? 3.  Now, since we multiplied 4 by 3 to get 12, we have to multiply our numerator, 3, by 3, which is 9.  We are done with our first fraction, and our second fraction does not need to be changed because our denominator is already 12.  So, now our problem is: 9/12 + 5/12 = 14/12. 

Let's try another example.  Subtract the following: 2/5 - 1/8.  We first notice that we have unlike denominators, so we must list the first few multiples of both 5 and 8.  Multiples of 5 include: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, ...  Multiples of 8 include: 8, 16, 24, 32, 40, 48, 56, 64, 72, ... If you notice, there is a common multiple of 40 for both.  Hint: Once you have been practicing with these problems and you cannot think of a common multiple of each of your denominators readily, then just multiple your denominators together, and use that as your least common denominator.  The only disadvantage is that you may have to simplify your answer at the end because you did not choose a smaller multiple.  Okay, now that I gave you that hint, we can proceed with our problem =).  So, our first fraction: 2/5 will change into ?/40?  We multiply 5 by 8 to get 40, so we must also multiply our numerator by 8 to get our new numerator: 16.  Now looking at our second fraction, we must multiply our denominator by 5 to get 40, so we must multiply our numerator by 5 to get our new numerator: 5.  Finally, our problem is: 16/40 - 5/40 = 11/40.

Let's do one more example.  Solve 4/15 + 7/3.  If you list your multiples of 15 and 3, you should see that your least common multiple of the two is 15.  Our first fraction stays the same because it already has a 15 for its denominator, but our second fraction must change from 7/3 to ?/15? If you guessed 35/15 you were correct!! =).  Since we had to multiply our denominator by 5 to get 15, we had to multiply our numerator, 7, by 5, which is 35. 

Remember: Whatever you have to multiply to your bottom number by to get the new denominator, you must also multiply to the top.    

For more instruction, watch these video to help you: adding fractions with unlike denominators and
subtracting fractions with unlike denominators
You can also go to this website for help with fractions: subtracting fractions

If you have any questions, do not hesitate to ask!

Fraction Addition and Subtraction: Problem Type 1

Hi, today's post will be a lesson on fractions.  That is, we will learn how to add and subtract fractions with the same denominator.  First of all, we must consider whole numbers.  Every whole number can be written as a fraction.  For instance, 4 can be written as 4/1, and be the same number.  This works for any whole number.  Second of all, lets define fractions.  A fraction consists of a top and bottom number, with the top number known as the numerator and the bottom number known as the denominator.  When adding and subtracting fractions, you may want to keep this in mind.  In order to show you how to go about adding fractions with the same denominator, let me give you an example.  To add 2/7 + 3/7, you first notice that your denominators are the same, which are 7's.  So, all you need to do is add your numerators 2 and 3 together.  So your answer is 5/7.  It's very simple!  How about 1/6 + 3/6? You will add your 3 and 1 and then keep your 6.  So your answer will be 4/6, or if you simplify further, you notice that 2 is divisible by both 4 and 6, and so you can reduce 4/6 to 2/3.  Make sense? 
So, overall, here is the key to adding fractions with the same denominator: Add your numerators and keep your denominator.  Do not add your denominators together.  In order to subtract fractions with the same denominator, you take the same steps as you did to add fractions with like denominators, but you SUBTRACT!  Let's do one example to make sure that you are confident in yourself when you work on these example problems provided at the end of this post.  Tell me what 7/15 - 5/15 is.  All you have to do is subtract 7-5 and keep your denominator since both denominators are the same.  So, your final answer should be 2/15!

Thanks for reading, and hopefully that the following links and worksheet will help you practice and grasp the concept better =)

Fraction practice game
For more info on subtracting and simplifying fractions

Note: For the second link, only read up until reducing fractions.

      

Practice with rounding numbers to the nearest tens, hundreds, and thousands

The last post that I posted had to do with place values.  Rounding is kind of like learning the different place values.  In order to round, you need to know what place value you are talking about.  When rounding, you are basically bumping up to a higher number or bumping down to a lower number.  When rounding, you are approximating, meaning you are not finding an exact answer, but an estimate.  There are two things that you need to remember in order to round numbers to the nearest ten.  First, if the number ends in one through four, you need to round down to the next number that ends in zero.  For example, if you need to round 63 to the nearest ten, you will round down to 60.  Second, if the number ends in five or greater, you need to round up to the next even ten.  For example, if you need to round 48 to the nearest ten, you would round up to 50, which is the next even ten.  To round numbers to the nearest hundred is not much different.  For example, round 671 to the nearest hundred.  You must look at the digit right next to the hundreds place, which is 7.  Since it is greater than 5, you will round 671 to 700, versus 600.  Another example: round 825 to nearest hundred.  Since the digit next to the hundreds place is less than 5, you will round 825 down to 800, versus 900.

Lets go back to rounding to the tens place with these two previous examples.  For the first, to round 671 to the nearest tens place, you would look at the digit to the right of the tens place, which is a 1.  Since it is less than 5, you will round 671 down to 670.  For the second, to round 825 to the nearest ten, you would look at the digit to the right of the tens place, which is 5.  Since it is a 5, you will round 825 up to 830.

Now that we have looked at examples of how to round to the nearest tens and hundreds place, lets look at how to round to the nearest hundreds place.  We will go ahead and do a few examples: 1.) Round 4,564 to the nearest thousands place.  Looking at the previous place value, which is the hundreds place, we see a 5, meaning we will round 4,564 down or up?  We will round 4,564 up to 5,000.  2.) Round 7,340 to the nearest thousands place.  Looking at the hundreds place, we see a 3, meaning we will round down.  So, 7,340 rounded to the nearest thousands place is 7,000.  And just so we are on the same page, what would 7,340 rounded to the nearest hundreds place be?  Looking at the previous place value, we see a 4, meaning we will round down, correct?  Correct.  So, 7,340 rounded to the nearest hundreds place would be 7,300.

For further assistance, you can comment on my post, or you can visit the following links to practice and build confidence in yourself =)

http://www.ixl.com/math/grade-4/rounding

http://www.myschoolhouse.com/courses/O/1/16.asp 

http://www.superkids.com/aweb/tools/math/round/round6.cgi and for the answers to this worksheet, go to: http://www.superkids.com/aweb/tools/math/round/round6_answer.cgi

Place Value Help!

Today, I am posting examples and resources of place values.  Basically, when thinking about place values, you are looking at the individual digits of a number.  Place values include: ones, tens, hundreds, thousands, ten thousands, hundred thousands, etc.  For example, the number 76 has two digits, and each digit is a different place value.  The first digit, 7, is called the tens place.  The second digit, 6, is called the ones place.  Given another example, 5,671, the 5 is called the thousands place, the 6 is the hundreds place, the 7 is the tens place, and the 1 is the ones place.  When talking about money, for instance if you have $56.47, the 5 is the tens place, the 6 is the ones place, the 4 is the tenths place, and the 7 is the hundredths place.  It's easy to get confused because of the "ths" at the end when you have decimals involved, but just remember to add the "ths" if the digit is to the right of a decimal.  You should also remember that after the decimal point, you will have tenths, hundredths, thousandths, ten thousandths, and so on, versus with whole numbers, it starts with ones, then tens, then hundreds, etc.  Let's try one more example.  What place value is the 8 in the following number: 80,457.60?  The 8 is in the ten thousands place.  What about the place value for 6?  The 6 would be the tenths place.  Got it?  =)  If you need help or want more practice the following resources will definately help!  There are free place value worksheets at http://www.softschools.com/math/worksheets/placevalue_worksheets.jsp.  There is also another worksheet with answers for practice with place values through thousands.  If you go to

http://www.softschools.com/grades/4th_grade/math/, click on find place value of a number under 4th grade math games, and this will be a fun way to practice more.  Last, but not least, if you go to http://www.ixl.com/math/grade-4, click place values under the 1st category called Number Sense.

4th grade math practice with decimals continued

Learning how to multiply and divide decimals is a bit different from adding and subtracting decimals, but it is easy once you practice!  When adding and subtracting decimals, we brought the decimal point straight down where our answer would be after adding place holders to help us.  When multiplying decimals, you would first multiply your numbers together like you normally would.  When finished, you then have to count how many numbers there are after each decimal point.  Then, you count from the right of your answer to the left however many digits you counted after your decimals, and place your decimal point in your answer.  For example, to multiply 16.58 x 37.2, we would first multiply the numbers together and forget about the decimal points.  So 1658 x 372 = 616776.  Now you look at your original problem and count the number of digits after your decimal points: 16.58 x 37.2.  There are three digits after the decimals.  So we take our answer we got, 616776 and count from the right to the left 3 digits.  So, now our final answer is 616.776.  For a video on how to multiply decimals, go to http://www.youtube.com/watch?v=EDd9xaGNP_Q.  To divide decimals, you first need to use your long division skills! (yes, I know you may hate long division, but we will get through this =)).  We will review an example of a long division problem to begin.  Use long division to divide 54.0 / 2.5.  Which number goes on the outside and inside of the division bar?  The number on the bottom of the fraction, or in our case to the right after the slash, goes on the outside of the division bar.  And our numerator, or number to the left of the slash, always goes on the inside.  So, looking our decimal points, we must move those decimal points to the right.  For our number outside the division bar: 2.5, we would only have to move our decimal over once to the right to make a whole number.  Since we moved the decimal over once in 2.5, we are going to move our decimal over once in 54.0.  Important to note: however many times you move your number's decimal outside the division bar, you must move your number's decimal inside the division bar to the right the same amount of times.  In our case, we would move the decimal in 2.5 over once to the right to make 25. .  Now, in the same manner, move the decimal in 54.0 to the right once to make 540. .  Now we may begin to divide since we got rid of our decimals.  We must find how many times 25 goes into 54, meaning 25 multiplied by what is closest to 54?  25 goes into 54 twice because 25 x 2 = 50, which is closest to 54.  Now write the 2 above the 4, and write 50 underneath 54, then subtract.  Now, bring your zero down and proceed.  Now our question is,  how many times does 25 go into 40?  25 goes into 40 once, so now place your 1 above your zero in 540.  Next, write your 25 underneath your 40 and subtract.  You should get 15.  Now, we must add a place holder to our 540 and bring that down to our 15, making it 150.  Then, we must find how many times 25 goes into 150.  You will find that 25 x 6 = 150 exactly.  Because of this, we are done dividing.  Now we must worry about our decimal in our final answer.  All you have to do is move your decimal up from 540, so our final answer is 21.6.  You can always check your answer by multiplying 21.6 x 2.5.  For more practice, you can visit the video: http://www.youtube.com/watch?v=AZ6fyQDVqEE.  And for more practice with long division, visit: http://www.softschools.com/math/division/long_division/.

These are examples of dividing and multiplying decimals:

                             

4th grade math practice with decimals

Learning how to add, and subtract decimals is as easy as one, two, three!  The first step in solving an addition problem with decimals is to line up the decimals.  For example, if you have to add a number where one number lies after its decimal to another number where two numbers lie after its decimal, then you would simply put a place holder, or a zero, next to your first number's digit that lies after its decimal.  It may sound difficult, but here is an example.  To add 125.2 + 136.58, you would first line the decimals up and then place a zero next to the .2 in the first number, so that you can keep all of your columns nice and neat.  In other words, you will add 125.20 + 136.58.  Your answer should be 261.78.  For more practice, you can complete this worksheet at the following website: http://www.education.com/worksheets/fourth-grade/math/.  The title of the worksheet is called "Dizzy Over Decimals: Addition # 1."  To subtract decimals, you do the exact same procedure as you did before to add decimals.  For example, to subtract 458.961 - 62.54, you would simply add a place holder to your second number: 62.540.  If it helps to place a zero before the 6 in your first number, you can do so: 062.540.  Next, you would drop your decimal down to your answer and start subtracting.  Your answer should be 396.421.  For a video of how to add and subtract decimals, go to http://www.youtube.com/watch?v=Mn3BKVuWVP4.  I hope this helps!

These are examples of adding and subtracting with decimals for further assistance: