SOLUTION: 1.Combine: 3/48-12/75+ 4/12

1.Combine: 
3/48-12/75+ 4/12

  3     12      4
———— - ———— + ———— 
 48     75     12

Reduce the fractions first

3/48 will reduce to 1/16, so replace 3/48 by 1/16

  1     12      4
———— - ———— + ———— 
 16     75     12

12/75 will reduce to 4/25, so replace 12/75 by 4/25

  1      4      4
———— - ———— + ———— 
 16     25     12

4/12 will reduce to 1/3, so replace 4/12 by 1/3

  1      4     1 
———— - ———— + ——— 
 16     25     3

Now since there are no common factors of 16, 25 and 3 other
than 1, we multiply them all together to find the LCD
16×25×3 = 1200

To make the first fraction have denominator 16×25×3 we 
multiply 1/16 by the fraction (25×3)/(25×3) which equals 1
and multiplying by 1 will not change the value 1/16.

  1    25×3     4     1 
———— × ———— - ———— + ——— 
 16    25×3    25     3

To make the second fraction have denominator 16×25×3 we 
multiply 4/25 by the fraction (16×3)/(16×3) which equals 1
and multiplying by 1 will not change the value 4/25.

  1    25×3     4    16×3    1 
———— × ———— - ———— × ———— + ——— 
 16    25×3    25    16×3    3

To make the third fraction have denominator 16×25×3 we 
multiply 1/3 by the fraction (16×25)/(16×25) which equals 1
and multiplying by 1 will not change the value 1/3.

  1    25×3     4    16×3    1    16×25
———— × ———— - ———— × ———— + ——— × —————
 16    25×3    25    16×3    3    16×25

Indicate the multiplications of numerators and denominatore
in all three cases:

      1×25×3     4×16×3   1×16×25
     ——————— - ———————— + ———————
     16×25×3    25×16×3   3×16×25
 
Now multiply as indicated:

          75     192    400
         ———— - ———— + ————
         1200   1200   1200

Now combine numerators over the LCD 1200

         75 - 192 + 400
         ——————————————
              1200

Combining the numerator terms:

              283
             ————
             1200

Edwin
AnlytcPhil@aol.com