Check Your Skills Answer Key

1. : The denominator stays the same. Add the numerators.
   

2. or : The denominator 4 is already a multiple of the denominator 2. Because only one of the fractions needs to change, use the traditional method to solve this one.

   
   

3. : This time, the 3 and the 8 don’t share any factors, so the double-cross is the best way to proceed.

   

   Here is the traditional approach:

   

4. : The denominators of the two fractions are the same, but the numerator 5 is greater, so
5. : The numerators of the two fractions are the same, but the denominator of is smaller, so . Alternatively, you could double-cross.

   

   39 is greater than 30, so  is the greater fraction.

6. : The denominator 6 goes into 11 just once, so the quotient is 1 and the remainder is 11 − 6 = 5. Alternatively, split the numerator into two parts.
   
7. : Think of multiples of 11. How close can you get to 100 without going over? 11 × 9 = 99, with 1 left over.
   

8. : The shortcut is . Here’s the full path:
   
9. : The shortcut is . The full path is:
   

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13. : When a factor in the numerator cancels to 1, do still write it down; in this problem, the numerator simplifies to 1. It’s safe to ignore a 1 only when a factor in the denominator cancels to 1.
    

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15. 6:
    

16. :
    

17. (A): Split the fraction into two.
    

18. (B): Don’t split the denominator!
    

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20. :