Check Your Skills ANswer Key

  1. The denominators of the two fractions are the same, but the numerator of is bigger, so .

  2. The numerators of the two fractions are the same, but the denominator of is smaller, so .

  3. 11



  4. 4






  2. 6
  1. 2


  2. 10
  2. 2

  1. is therefore greater than .

  2. is therefore smaller than .

  1. 4

    Add the numerator and simplify:

  2. Add the numerator and the denominator, then convert to a mixed number:

  3. The only manipulation you can perform is to factor 12 out of the numerator: . No further simplification is possible.

  4. Factor a 3 out of the numerator and a 2 out of the denominator:

    Now you can cancel out the 3g − 2h term out of both the numerator and denominator:

  1. You know that  is a little less than , and so is less than . And then  is a little more than , and so is more than . Therefore,  is greater than .

  2. 50

    Approximate each term: , and 403 is close to 400. Now,Note that the exact amount is approximately 49.369, so your estimation was extremely close.

  1. Yes

    Because you are only given fractions, you pick Smart Numbers. The number 10 is a good number to pick because it is the common denominator of the fractions and . Mili’s first generation uHear has a capacity of 10 gigabytes. Her second-generation uHear, then, has a capacity of 30 gigabytes.

    Her first-generation uHear then has 5 gigabytes filled ( × 10) and her second-generation uHear has 24 gigabytes filled ( × 30). If she transferred the songs on the first uHear to the second, she would be at capacity. There is enough room for the transfer.

  1. 12 hours

    Because you are given an actual number in the problem, you are not allowed to pick numbers. Assign a variable for what you are looking for: the number of hours John is awake. Call that total x.

    Therefore, your equation will be

    The common denominator of all the fractions is 30. You can multiply the equation by 30 to eliminate all the fractions:

    John is awake for 12 total hours.