There are 5 parts to this question. a. b. c. d. and e. Please be sure to label and answer all 5 parts in the space below please :)

a.
4 x [tex] \frac{1}{2} [/tex]
When multiplying a whole number by a fraction, simply multiply the whole number by the numerator (number on the top of the fraction bar). The denominator (number on the bottom of the reaction bar) will stay the same.

For 4 x [tex] \frac{1}{2} [/tex], you would multiply 4 x 1 = 4 as the numerator and keep 2 as the denominator. Your answer would be [tex] \frac{4}{2} [/tex]. This is an improper fraction because the numerator is larger than the denominator. To change this, divide the numerator by the denominator (4 ÷ 2 = 2). This answer becomes your whole number. 
4 x [tex] \frac{1}{2} [/tex] = 2

[tex] \frac{1}{2} [/tex] x [tex] \frac{3}{4} [/tex]
When multiplying a fraction by another fraction, multiply both numerators of the fractions to get the new numerator. Then, multiply the denominators of the fractions to get the new denominator. Simplify if needed.
[tex] \frac{1}{2} [/tex] x [tex] \frac{3}{4} [/tex] = [tex] \frac{1 x 3}{2 x 4} [/tex] = 
[tex] \frac{3}{8} [/tex]. There is no simplifying to do here, so your answer of [tex] \frac{1}{2} [/tex] x [tex] \frac{3}{4} [/tex] is [tex] \frac{3}{8} [/tex].


[tex] \frac{3}{4} [/tex] x [tex] \frac{1}{3} [/tex]
Same steps as we did for the last one. Multiply the numerators together to get the new numerator and denominators together to get the new denominator. 

[tex] \frac{3}{4} [/tex] x [tex] \frac{1}{3} [/tex] = [tex] \frac{3 x 1}{4 x 3} [/tex] = 
[tex] \frac{3}{12} [/tex]. Reduce this fraction by dividing the numerator and denominator by 3 to get an answer for [tex] \frac{3}{4} [/tex] x [tex] \frac{1}{3} [/tex] of [tex] \frac{1}{4} [/tex].

b. When you multiply any number by a fraction that's smaller than one, the product will be less than the original number (as you can see for the first problem in question A). 

c. To divide a fraction by another one, change the problem to multiplication and multiply the two fractions.

d. 4 ÷[tex] \frac{1}{2} [/tex]
Dividing a whole number by a fraction is the same as dividing two fractions. First, let's flip (invert) the fraction, then multiply. Whole numbers can be written as fractions by making its denominator a 1. For your problem, we'll change the whole number 4 to a fraction: [tex] \frac{4}{1} [/tex], then flip (invert) the second fraction so we can multiply it. Now we have:

[tex] \frac{4}{1} [/tex] x [tex] \frac{2}{1} [/tex]. Same as above, multiply the numerators to get the new numerator and denominators to get a new denominator.

[tex] \frac{4 x 2}{1 x 1} [/tex] = [tex] \frac{8}{1} [/tex]. 4 ÷[tex] \frac{1}{2} [/tex] = 8

[tex] \frac{1}{2} [/tex] ÷ [tex] \frac{3}{4} [/tex] 
To divide a fraction by a fraction, start by flipping the second fraction (the one you want to divide by). Then multiply as you did in the previous questions and simplify if needed.

Flip second fraction: [tex] \frac{1}{2} [/tex] x [tex] \frac{4}{3} [/tex]
Multiply numerators together and denominators together: [tex] \frac{1 x 4}{2 x 3} [/tex]
Now we have [tex] \frac{4}{6} [/tex]. Simplify by dividing the numerator and denominator by 2. [tex] \frac{1}{2} [/tex] ÷ [tex] \frac{3}{4} [/tex] equals [tex] \frac{2}{3} [/tex].

[tex] \frac{3}{4} [/tex] ÷ [tex] \frac{1}{3} [/tex]
Same as we did with the last problem!

Flip the second fraction: [tex] \frac{3}{4} [/tex] x [tex] \frac{3}{1} [/tex]
Multiply the numerators and denominators: [tex] \frac{3 x 3}{4 x 1} [/tex]
Now we have [tex] \frac{9}{4} [/tex], which we can't leave as an improper fraction so let's change it to a mixed number like we did in part A. Divide the denominator by the numerator (9 ÷ 4 = 2r1). 2 becomes our whole number, the remainder 1 becomes the new numerator and the denominator stays the same to become the answer 2. [tex] \frac{3}{4} [/tex] ÷ [tex] \frac{1}{3} [/tex] equals 2[tex] \frac{1}{4} [/tex]. 

e. When dividing a number by a fraction, the quotient will be greater than the original number.