How do you add 6/5 + 1/4? Thank you

Question

I am adding/ Subtracting with fractions. I am helping my daughter with her 6th grade homework. Thank you

Answer 1

When adding/subtracting fractions, the fractions must have a common denominator. 

For this problem:     6/5 + 1/4 ,  

         the least common denominator is the least common multiple of the denominators in the fractions you are adding. Here, the two denominators are 4 and 5. Let's make a list of the multiples of 4 and the multiples of 5 and find the least common multiple of the two:

Multiples of 4:   4, 8, 12, 16, 20, 24, 28, 32, .....

Multiples of 5:   5, 10, 15, 20, 25, 30, 35, ..... 

We find that the least common multiple of 4 and 5 is 20. So we change the two fractions in the problem above to generate two fractions with a common denominator of 20.

      6/5 + 1/4          multiply the first fraction by 4/4 and the second fraction by 5/5 

    (6/5)*(4/4) + (1/4)*(5/5) = (6*4)/(5*4) + (1*5)/(4*5)

                                          = 24/20 + 5/20

                                          = (24 + 5)/20

                                          = 29/20

   29/20 = 20/20 + 9/20 = 1+ 9/20 = 1 ⁹/₂₀

Thus,    6/5 + 1/4 = 24/20 + 5/20 = 29/20  OR  1 ⁹/₂₀      

Answer 2

6/5 + 1/4 = N

As a student you know that mathematics is one long word. The word itself is .... maybe because of its length.

MATH short for MATHEMATICS

M - MENTAL

A - ACCURATE

T - TALENTED

H - HELPFUL

As a student you know some attributes to or about MATH.

A CLOSER LOOK AT THE QUESTION

6/5 + 1/4 = N

You are adding what looks like 2 fractions where 6 is the numerator and 5 is the denominator for the first fraction and given for one fraction and the other you have numerator of 1 and a denominator of 4. How do you add fractions? Well? MATHEMATICS requires that you follow a set of rules or operations. I assume your teacher has taught you adding, subtracting, multiplication, or division.

LET US LOOK AT RULES FOR YOUR QUESTION 6/5 + 1/4 = N IN WHICH IS ADDING 2 FRACTIONS.

HOW DO YOU ADD FRACTIONS?

FIRST YOU MUST CHECK FOR COMMON DENOMINATORS AS THEY ARE PARTS OF THE FRACTIONS AND THIS ALLOWS US TO ADD NUMERATORS AS WE ADD TO PARTS OF WHOLES IN FRACTIONS MAKING THE ANSWER CLEARER.

IF THE DENOMINATORS ARE NOT EQUAL WE HAVE SEVERAL OPTIONS

OPTION 1

LETS LINE UP THE QUESTION

6/5

+1/4

-------------

AS YOU CAN SEE WE CANNOT JUST ADD NUMERATORS BECAUSE DENOMINATORS WHICH ARE THE EQUAL PARTS THE FRACTIONS ARE DIVIDED.

IT ALSO SEEMS LIKE WE HAVE 2 TYPES OF FRACTIONS.

1 TYPE OF FRACTION? 6/5 IMPROPER

2 TYPE OF FRACTION? 1/4 PROPER

LET US FIND A COMMON DENOMINATOR

HOW? WE MULTIPLY BOTH FRACTIONS DENOMINATORS BY EACH FRACTIONS DENOMINATORS.

1 DENOMINATOR IS 5 AND ANOTHER DENOMINATOR IS 4

HOW DID WE LOCATE THEM?

FRACTION LOOKS LIKE

1/4

NUMERATOR

---------------------

DENOMINATOR

5 MULTIPLIED 4 EQUALS 20

6/5 numerator/20

+ 1/4 numerator/20

-----------

We do not know what the new numerator is and at this point we only know the DENOMINATOR IN COMMON FOR BOTH FRACTIONS IS 20.

WE DIVIDE THE FIRST NEW DENOMINATOR 20 BY OLD DENOMINATOR WHICH IS 5 SO WE CAN FAIRLY SAY OUR FRACTION PROPORTIONAL IS NOW 4 TIMES FROM DENOMINATOR 5 TO DENOMINATOR 20 THUS NOW WE MUST ALSO BE FAIR EVEN DOUGH ITS A FRACTION AND INCREASE PORTION SIZE OF NUMERATOR WHICH WAS HOW MANY PARTS IT HAD 6 BY 4 PARTS INCREASE TO 24.

THE NEW FRACTION WAS INCREASED BY 4 PARTS ON BOTH NUMERATOR AND DENONIMATOR

TO

24/20 WHICH DOES SIMPLIFY TO 6/5

1/4 WHEN INCREASED BY 5 PARTS THIS HAPPENED WHEN WE MULTIPLIED BY EACH DENOMINATORS

TO

5 / 20

NOW THAT WE HAVE COMMON DENOMINATORS WE CAN ADD FRACTIONS

24/20 + 5/20 = 29/20

THE ABOVE FRACTION HAS BEEN IDENTIFIED AS AN IMPROPER FRACTION AND IS YOUR ANSWER

IF YOU MUST SIMPLIFY THEN YOU SEARCH OR ASK

HOW TO SIMPLIFY AN IMPROPER FRACTION AND WHY IS IT IMPROPER?

LIKE WE SAID TALKED ABOUT

RULES

INSTRUCTIONS

OPERATIONS

I HOPE I HELPED YOU TODAY

MR SIR

Answer 3

To add or subtract fractions it is important the fractions the same denominators (bottom number). If they have the same denominators, simply add or subtract the numerators (top numbers) accordingly and keep the denominators the same.

As in our case, they do not have the same denominators, then we can change them to be the same.

1. First: find the LCM (lowest common multiple) between the denominators.

For our case of 6/5 + 1/4, we do not have the same denominators, so we will need to find our LCM.

5: 5, 10, 15, 20, 25, 30... 5×4 = 20

4: 4, 8, 12, 16, 20, 24, 28... 4×5 = 20

Our LCM is 20

1. Second: convert the fractions into their equivalent fractions using our new LCM (20) as the denominator. The way to do this is to follow our motto of "what you do to the top, you need to do to the bottom".

to convert 6/5:

We multiplied 5 by 4 to get 20 as our new denominator. ( 5×4 = 20 )

This means we need to multiply by the same number (4) to our current

numerator of 6: to get 6×4 = 24

our new fraction is now 24/20.

to convert 1/4:

We multiplied 4 by 5 to get 20 as our new denominator. ( 4×5 = 20 )

This means we need to multiply by the same number (5) to our current

numerator of 1: to get 5×1 = 5

our new fraction is now 5/20.

1. Third: Now that we have the same denominators, we can add our numerators (the denominators will stay the same):

24/20 + 5/20

add our numerators: 24+5=29

keep the denominators the same: 20

our final answer is 29/20

Answer 4

6/5 + 1/4 =

Change both fractions to the same denominator by identifying the least common multiple which is 20.

5: 5, 10, 15, 20

4: 4, 8, 12, 15, 20

So 6/5= (times 4 for top and bottom to get 20 as denominator) is equivalent to 24/20 and 1/4 (times 5 at top and bottom to get 20 as denominator )is equivalent to 5/20

24/20 + 5/20 = 29/20 or 1 and 9/20

Answer 5

The key is to find the "least common denominator."  This is done by multiplying the denominators (5 and 4) together, this number (20 in this situation) the denominator.  

Now that we know 20 is to be our denominator (from now and in the answer!!) we can move onward to adjust the top number individually by the same manner as follows:

6x4=24.....leading to 24/20

1x5=5......leading to 5/20

See what I meant by 20 being the bottom number ("least common denominator") for BOTH. Good!

Now add the top numbers (numerators) together:

24+5= 29

Answer=29/20 

Multiply bottom numbers to get the "lease common denominator".....use is for both fractions!

remember 29 is Numerator

and 

remember 20 is the denominator (it dominates the bottom!!),   that makes it a little cooler, no?

Answer 6

Dear Luis and daughter:

I agree with both of the other contributors.  However, an easier way to come up with the same answer below.  It involves multiplication and adding.

6/5 + 1/4 = N

Multiply the numerator of the first number (6) times the denominator of the second number (4) and get 24.

Multiply the numerator of the second number(1) times the denominator of the first number (5) and get 5

Add the 24+5 and get 29.

Finally, multiply the two denominators (5 times 4) and get 20.   The denominators remain denominators and form the new denominator of 20.

Place the results of the first equation 29 over 20 for 29/20.  This could be read as 29 over 20 or 29 divided by 20.  Thus, 29/20 (or 1 and 9/20) = N.  

This is much easier and saves you the steps of looking for the common denominator and multiplying inverses, because by multiplying the denominators you create a "common denominator" for both numbers. Then, if it is possible to reduce the denominator further, that process will be simpler.

Let me know how this works for you!  Test it by doing it this way: 7/6 + 2/5 and let me know what you get!

Answer 7

To add fractions with different denominators, the first step is to write them as fractions with a common denominator.  This is done by multiplying both top and bottom of each fraction by 4 and 5, respectively.

6/5 + 1/4 = (6*4)/(5*4) + (1*5)/(4*5) = 24/20 + 5/20.

Now that both fractions have the same denominator, the result is calculated by adding the numerators and placing this over the common denominator, 20.

24/20 + 5/20 = (24+5)/20 = 29/20.

In summary,

6/5 + 1/4 = 24/20 + 5/20 = 29/20.

Hope this helps.