Algebra Know-It-ALL

5. The answers, along with explanations, are as follows:

(a) We have the number 4-7/10. We can convert the integer part, which is 4, into

10ths by multiplying it by 10 and then dividing the result by 10, getting

(4× 10) / 10 = 40/10

The entire number is therefore

40/10+ 7/10 = (40 + 7) / 10

= 47/10

(b) We start with the number −8-7/20. We convert the integer part, −8, into 20ths by

multiplying and then dividing by 20, getting

(− 8 × 20) / 20 =−160/20

The entire number is therefore

−160/20+ (−7/20)= (− 160 − 7) / 20

=−167/20

(c) The number 1/50 is a fraction already, and has been reduced to lowest terms.

There’s nothing further for us to do here!

(d) This situation is the same as in part (c). We already have the final expression in the

form of the starting number, −29/100.

6. The easiest way to work out these problems is to input the numerator into a calculator,
   and then divide by the denominator. When we do that, we get the following results.
   (a) 44/16 = 2.75
   (b)−81/27=− 3
   (c) 51/13 = 3.923076923076923076...
   (d)−45/800=−0.05625
   In case (c), you’ll need a calculator that can display a lot of digits if you want to be certain
   of the repeating pattern of digits to the right of the decimal point. (It’s 923076.) If you
   don’t have such a calculator, you can perform old-fashioned, manual long division to
   discover the pattern.


7. This problem can be solved in two steps. First, we use a calculator or long division to
   determine the decimal equivalent of 1/17. We get this endless repeating decimal:

0.05882352941176470588235294117647...

The repeating sequence of digits is 0588235294117647. The initial cipher is important

here! Next, we count up the number of digits in this sequence, including the cipher at the

beginning. There are 16 digits in the repeating string. We construct a fraction with the

Chapter 7 609