What if your denominators are 3 and10

Question

Kaitlin buys 9 tenths pound of orange slices. She eats 1 thirds of them and divides the rest equally into 3 bags. How much is in each bag?

Answer 1

 

 

Simply translate words and phrases into math expressions:

  "Kaitlin buys 9 tenths pound of orange slices"     means     9/10 lb

  "She eats 1 thirds of them"      means

              (1/3)       *  (9/10 lb)          [because "of" usually means multiply]

  "divides the rest equally into 3 bags"     means

    ( 9/10  -  (1/3)*(9/10))        /    3         [this is what is not eaten; divided by 3]

 

O.K., "How much are in each bag?"

   Remember P-E-M-D-A-S and start inside the parentheses.

   ( 9/10  - 3/10 )    / 3

   ( 6/10 ) / 3

   (6/10)*(1/3)             [to divide, invert denominator and multiply]

     2/10                      [cancel 3 by dividing it into 6]

     1/5 lb                    [reduce by dividing each number by 2]

 

Answer 2

Hi,

 

First we'd write the weight of the orange slices bought by Kaitlin (9 tenths of a pound [or "lb"]):

 

9/10 lb

 

Then we'd calculate the amount eaten by Kaitlin (1 third of them):

 

9/10 lb * 1/3 = ( 9 * 1 ) / ( 10 * 3 ) lb

 

Here we just multiply the numerators by each other and the denominators by each other to get the new fraction.

 

We can simplify this calculation by noticing that the 3 in the denominator cancels with the 9 in the numerator, leaving 3 in the numerator.

 

( 9 * 1 ) / ( 10 * 3 ) lb = ( 3 * 1 ) / ( 10 * 1 ) lb = 3/10 lb

 

3/10 lb were eaten. Then we'd calculate the amount left by subtracting the amount that were eaten:

 

9/10 lb - 3/10 lb = ( 9 - 3 ) / 10 lb = 6/10 lb

 

The 3/10 can be subtracted from the 9/10 easily because they share the same denominator.

 

So there are 6 tenths left. These are divide equally into 3 bags. So we have to divide by 3.

 

( 6/10 lb ) / 3

 

Another way to represent division is as multiplication by the inverse. The inverse of 3 is 1/3. In general you can get the inverse by writing 1 over the number. So we have:

 

( 6 / 10 lb ) * ( 1 / 3 ) = ( 6 * 1 ) / ( 10 * 3 ) lb

 

Again we multiplied numerators together and denominators together. We can simplify this calculation by noticing that the 3 in the denominator cancels with the 6 in the numerator, leaving 2 in the numerator.

 

( 6 * 1 ) / ( 10 * 3 ) lb = ( 2 * 1 ) / ( 10 * 1 ) lb = 2/10 lb

 

We can simplify this fraction by noticing that 2 goes into both the numerator and the denominator, giving this answer:

 

1/5 lb

 

The answer for the amount in each bag is 2 tenths of a pound or 1/5 of a pound (which is the same thing).