How do write in simplest form given #7/10-2/15#?

2 Answers
Oct 29, 2016

#17/30#

Explanation:

In order to add or subtract fractions, we have to have common denominators.

  1. List multiples of both numbers.

    #10: 10,20,ul 30,40 ....#
    # 15: 15,ul 30,45,60 ....#

  2. Look for the smallest underlined number (known as the least common multiple, or LCM). This is your common denominator.

    Common denominator: #30#

  3. Multiply the numerator and denominator by the factor that it would take to get to your common denominator…like this:

#7/10 *3/3 = 21/30#

and, #2/15 *2/2 = 4/30#

Now we have both of our fractions with common denominators, so we can subtract! Remember, in a subtraction problem, the numerators subtract but the denominators stay the same. It looks like this:

#7/10-2/15=21/30-4/30=17/30#

Oct 30, 2016

#17/30#

Explanation:

#color(blue)("Initial thoughts")#

Known: #" "2xx15=30" "# and #" "3xx10=30# so both the 'denominators' will divide exactly into 30.

A fraction consist of #" "("numerator")/("denominator")" "->" "("count")/("size indicator")#

You can not directly add or subtract the counts unless the size indicators are the same.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Making the denominators (size indicators) the same")#

#color(brown)("Multiply by 1 and you do not change the value. However 1 comes in many forms")#

#" "[7/10color(red)(xx1)]" " -" "[2/15color(red)(xx1)]#

#" "[7/10color(red)(xx3/3)]" " -" "[2/15color(red)(xx2/2)]#

#" "21/30" "-" "4/30#

#" "17/30#