## Problem 308

Problem 308

Use the definition of division to justify that 120 ÷ 40 = 3.

Solution

120 ÷ 40 = 3 because 3 x 40 = 120

## Problem 307

Problem  307

Use addition to justify that 123 > 85.

Solution

123 > 85

since 123 = 85+38

so 123 > 85 is true

## Problem 306

Problem 306

Use expanded notation to describe the value of 1,045.

Solution

(1045) b=1 × b3 + 0 × b2 + 4 × b1 + 5 × b0

## Problem 305

Problem 305

For each of the following action, write a word problem that can be solved with the equation 85 – 62 = n:

a. Taking away one length from another

b. Taking away a subset from a set

c. Separating a length into two set

d. Separating a set into two subsets

e. Comparing two lengths

f. Comparing two sets

Solution

a. Difference of two sides are 62, one side is 85 what will be the length of other side?

b.  Length of two sets are 85 and 62 , what will be the difference between them?

c.  Total length of a side is 85, and length of one part is 62, what will the length of other part?

d.  Length of one set is 62, what should the length of the other set to get a set of 85?

e.  One of the Side of a rectangle is 62 more than the other, sum of both side is 85 , what are the lengths of both side?

f.  Length of one is more than 62 to other and total length of resultant set is 85 so what will be the lengths of the sets?

## Problem 304

Problem 304

For sets U = (0, 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12)

A = {2, 3, 5, 6}, B = {3, 4}, and

C = {2, 6, 7, 8}, find

a. A  B

b.

c. A B C

d. (A C)  B

e. A

f. A C

Solution

a. {2,3,4,5,6}

b. {0,1,3,4,5,9,10,11,12}

c. {}

d. {2,3,4,6}

e. {3,5}

f. {2,6}

## Problem 303

Problem 303

Express the quantity 184 as the equivalent numeral in each base given.

a. Base five

b. Base two

Solution

a. (1214)5

b. (10111000)2

## Problem 302

Problem  302

Translate Hindu-Arabic numerals 100,66,247, and 180 into the equivalent  Egyptian, Babylonian, Roman, and Mayan numerals.(Hint: Make a table and record your answers in it.)

Solution

## Problem 301

Problem 301

Find the representation  of the number 256 in the following bases:

a. Base six

b. Base twelve

c. Base two

Solution

a. (1104)6

b. (194)12

c. (100000000)2

## Problem 300

Problem 300

Write the number of objects as a

a. Base-ten numeral.

b. Base –two numeral.

c. Base-five numeral.

Solution

a. 14

b. (1110)2

c. (24)5

## Problem 299

Problem 299

The product 12 x 16 can be found by thinking, (10 +2) x 6 = (10 x 6 ) + (2 x 6) = 60 + 12 = 72.

a. What properties of multiplication are being used?

b. Use these properties to verify the product 12 x 64.

Solution

a.      the distributive property of multiplication over addition and closure property.

b.      12 x 64 = (10 + 2) x 64 = 10 x 64 + 2 x 64 = 640 + 128 = 768