MTHT 450 F98

Homework 3

1. Which of these two numbers is bigger, 100000001/1000000002 or

200000001/2000000002? Explain your answer for a fourth grader.

(Hint: Work out $1-10000001/10000002$ and $1 - 20000001/20000002$.)

2. Arrange each of the following sets of three numbers in order of size with the smallest first. If the answer is ambiguous, explain the possibilities.

1/2, 1/4, 1/2+1/4

1/5 + 1/10, 1/5, 1/10

a/b, c/d, a/b + c/d where a, b, c, d are all positive.

3. Draw a baseline AB 20 centimeters long. Draw a perpendicular 19 centimeters long up from B and complete a right triangle ABC. Now mark a point D 10 centimeters from the left on the base. Draw a perpendicular up from that point. Make two triangles, ADE and ADFwith height 9 cm and 10 cm. Compare the sizes of the fractions DE/AD, DF/AD, BC/AB.

4. Arrange in proper order: a/b, c/d, (a+b)/(c+d) where a, b, c, d are all positive. If the answer isambiguous, explain the possibilities.

5. Which is bigger? 12345/54321 or 12346/54322. Can you explain this result in terms of question 3 or 4? Can you give an algebraic explanation? List as many ways as you can to solve this problem. Which methods best help students learn ideas they need in future mathematics.

6. Solve the following: SEND + MORE = MONEY.