T-101  Worksheet       Chapter 2 section 3 and 4 and Chapter 3          Names____________

                                                                                                                        ____________

Listen for oral directions.  Show all work on a separate sheet of paper.

1. Change to Roman numerals.

a.  76 __________         b.  1741__________            c.  192 ____________

2. Change to Hindu Arabic.

a.  CMLXXVI_______  b.  MCMXCI _________     c.  MMMCCXLV_____

3. What bases make these equations true?

a.  32 = 44_{______}               b.  57_eight= 10_{_______}               c.  31_four=11_{_______}

4.  What base four numeral follows 303_four?____________

5. In base six, write out the next four numbers after 254_six?_____________________

6. Convert each base ten numeral into a numeral in the base requested.

a.  395 in base eight___________                    b.  748 in base four__________

3.  54 in base two__________

7. Convert each of the following base ten numeral into base five numerals.

a.  74___________     b.  128___________               c.  2438___________

8. How many different symbols would be necessary for a base 23 system?_________

9. Add, subtract, multiply or divide each of the following as indicated.

a.  13_seven + 5_seven__________              b.  6_seven x 3_seven _____________

c.  21_seven – 4_seven__________              d.  24_seven + 16_seven_____________

e.  41_six + 33_six____________             f.  555_seven+ 66_seven____________

g.  3030_four + 322_four_______                h.  3030_four – 102_four____________

i.  534_seven 4_seven _________              j.  13002_four 33_four____________

k.  11011_two x 1101_two_______            l.  43_twelve x 23_{twelve ___________________}

m.  66_seven X 66_seven_________ n.  61245_seven 354_{seven ______________}

10. Calculate 43_five x 123_five using the following methods. 

a.  Lattice multiplication   b.  Instructional Algorithm   c.  Traditional algorithm

11. Find the quotient and remainder for 1443_five  34_five using the following methods.

a.  Scaffold method                   b.  Long division algorithm

12. Solve each of the following.

a.  333_four + 3333_four_________                        b.  TE_twelve + EE_{twelve______________}

c.  1102_four – 333_four__________                      d.  2134_six  14_six_____________

e.  213_five x 42_five ____________                      f.  47_eight x 25_eight _____________

13.  Calculate the following mentally using properties and/ or compatible numbers.

a.  (4 x 13) x 25_________                 b.  1710  9______________

86 x 15 ___________

14.  Rewrite each of the following using a single exponent.

a.  2²⁴ x 2¹⁵________               b.  4²⁶  4¹¹ _____________

15.  Identify the property of whole numbers being illustrated.

a.  4 ^. 5 = 5 ^. 4 ____________             b.  6(3 + 2) = (3 + 2)6___________

c.  5(2 + 9) = 5^.2 + 5^.9 _________      d.  1(x + y) = x + y _____________

e.  6(7^.2) = (6^.7)2 _____________      f.  (4 + 7) ^.0 = 0 ______________

16. Find 3_five x 43_five using repeated addition.________________

17. How many possible remainders including zero are there when dividing by the

following numbers?

            a.  2 _____                              b.  6_______               c.  23_______

18. Addition can be simplified using the associative property of addition.  For example,   26 + 57 = 26 + ( 4 + 53) = (26 + 4) + 53 = 30 + 53 = 83

Complete the following.

39 + 68 = 40 + _____= _____      b.  25 + 56 = 30 + _____= _____

ANSWERS

1.a.  LXXVI                 b. MDCCXLI             c.  CXCII

2a.  976           b.  1991           c.  3245

3a.  seven                     b.  forty-seven              c.  twelve

4.  310_four         5.   255_six, 300_six, 301_six, 302_six

6a.  613_eight b.  23230_four     c.  110110_two

7.a.  244_five       b. 1003_five        c.  34223_five

You need a total of 23 different symbols or numerals

a.  21_seven    b.  24_seven          c.  14_seven          d.  43_seven          e.  114_six

f.  654_seven   g.  10012_four      h. 2322_four        i.  (124 r 2)_seven j.  132_four

k.  101011111_two               l.  969_twelve        m. 6501_seven     n.  143_seven

10.  11444_five

11.  (23r1)_five
12. a.  10332_four      b.  1TT_twelve        c.  103_four         d.  121_six    e.  20101_five       f.  1463_eight
13. a.  13 x (4 x25) = 13 x 100 = 1300      b.  1710 9 = (1800-90)  9 = 200-10= 190

1.  86 x 15 = (80 + 6 x 15 = 80 x 15 + 6 x 15 = 1200 + 90 = 1290

14.  a.  2³⁹        b.  4¹⁵

15.  a.  Comm  b.  Comm       c. Dist     d. Identity      e.  Assoc       

 f.  Zero mulitiplication

     16..  43_five + 43_five + 43_five= 234_five

      17.  a.  2                b.  6                 c.  23

      18.  a.  39 + 68 =(39 + 1) + ( 68 – 1) = 40 + 67 = 107

              b.  25 + 56 = ( 25 + 5) + ( 56 – 5) = 30 + 51 = 81