Question 4084

You have...


1/2
1/9 ∙ 3
1/24 ∙ 3 


3 is nothing other than 3/1, so you have...


1/2
1/9 ∙ 3/1
1/24  ∙ 3/1



Step # 1
Multiplying the given fractions:


1/2
1/9 ∙ 3/1 = 3/9 (rule for multiplication: numerator ∙ numerator, denominator ∙ denominator)
1/24  ∙ 3/1 = 3/24



Step # 2
Finding a common denominator:


You need to add these fractions together later on. In order to add  fractions together, all of them must have the same denominator. The least common denominator for those 3 fractions is 72...


1/2  ∙ 36/36 = 36/72
3/9  ∙ 8/8 = 24/72
3/24  ∙ 3/3 = 9/72



Step # 3
Adding fractions together:


Now as all 3 fractions have the same denominator, you can add them together...


36/72 + 24/72 + 9/72 = 69/72 (rule for addition: numerator + numerator, denominator stays unchanged)



Step # 4
Finding the difference between 69/72 and “the whole” (72/72):


69/72 = the amount Mr. Haller gave to his wife, children and grand children 
72/72 = the whole amount his estate is worth
the difference between 69/72 and 72/72 = the remaining $ 18,000 he gave to his favorite charity


In order to find the difference you subtract 69/72 from 72/72...


72/72 – 69/72 = 3/72 (rule for subtraction: numerator – numerator, denominator stays unchanged)


3/72 = the remaining $ 18,000 he gave to his favorite charity



Step # 5
Dividing 69 (from 69/72) by 3 (from 3/72):


69 : 3 = 23



Step # 6
Multiplying 18,000 by 23 in order to find the amount of “the whole” (72/72):


18,000 ∙ 23 = 414,000


Answer: The value of his estate was $ 414,000. (72/72 = 414,000)