## Archive for April, 2014

## 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 × b^{3 }+ 0 × b^{2} + 4 × b^{1} + 5 × b^{0}

## 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 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 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