Question

Helppp Please I kind of get it but not really

Answer 1

D) 46 1/5

Explanation:

3 x 4 2/5 x 3 1/2

Separate into parts that you can handle

3 x 4 2/5 then multiply that some by 3 1/2

Change 3 to a fraction = 3/1

Change 4 2/5 to a improper fraction = 22/5

22/5 x 3/1 = 66/5

Second part

Change 3 1/2 to a improper fraction = 7/2

66/5 x 7/2= 462/ 10

Now simply

462/10 = 46 2/10 = 46 1/5

D is the correct choice

Answer 2

The last option,
`46(1)/(5)` cubic units

Explanation:

The volume of a rectangular prism can be found by multiplying the length (l), the width (w), and the height (h) of the structure together, represented by the following formula:

V = l(w)(h), or V = lwh

To begin, convert the mixed fractions to improper fractions by multiply the denominator by the whole number to the left of the fraction and adding the numerator. You then place this new integer in the numerator and keep the original denominator.


`3(1)/(2) = (3(2) + 1)/(2) = (6 + 1)/(2) = (7)/(2) \\\\4(2)/(5) = (4(5) + 2)/(5) = (20 + 2)/(5) = (22)/(5)`

Let length (l) = 22/5
Let width (w) = 3
Let height (h) = 7/2

Now we multiply together:


`V = ((22)/(5))(3)((7)/(2))\\\\V = ((22)/(5))((3)/(1))((7)/(2)) \\\\V = (22(3)(7))/(5(1)(2)) \\\\V = (66(7))/(5(2)) \\\\V = (462)/(10)`

Next, turn this improper fraction back into a mixed fraction by dividing the numerator by the denominator. The dividend goes to the left of fraction as a whole number and the remainder goes back to the numerator. The original denominator remains. If further simplifying is possible, we divide both numerator and denominator by their greatest common factor (GCF).


`(462)/(10) = 46(2)/(10)`

The greatest common factor for 2 and 10 is 2, so we divide both top and bottom of the fraction by 2.

2 / 2 = 1 10 / 2 = 5

Therefore, the volume is
`46(1)/(5)` units³ or
`46(1)/(5)` cubic units.