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__________

c. 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______________

c. 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.

a. 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

8. You need a total of 23 different symbols or numerals

9. 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

a. 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