What is the volume, in cubic inches, of a rectangular prism with 3 2/3 2 1/6 in., a length of in., and a width of 1 1/2 in.? Answer in the simplest form of a fraction. (1 point)
The volume of the rectangular prism is:
(3 2/3) x (2 1/6) x (1 1/2) = (11/3) x (13/6) x (3/2)
Simplifying the fractions:
(11/3) x (13/6) x (3/2) = (11/1) x (13/2) x (1/2) = 429/4
Therefore, the volume of the rectangular prism is 429/4 cubic inches.
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To find the volume of a rectangular prism, you need to multiply the length, width, and height of the prism. Let's first convert the given dimensions into fractions.
The given dimensions are:
Length = 3 2/3 in.
Width = 2 1/6 in.
Height = 1 1/2 in.
To convert mixed numbers into improper fractions, you can use the following steps:
1. Multiply the whole number by the denominator.
2. Add the numerator to the result.
3. Write the sum as the new numerator over the original denominator.
Converting the dimensions to improper fractions, we get:
Length = (3 * 3 + 2) / 3 = 11/3 in.
Width = (2 * 6 + 1) / 6 = 13/6 in.
Height = (1 * 2 + 1) / 2 = 3/2 in.
Now that we have the dimensions in fraction form, we can calculate the volume.
Volume = Length * Width * Height
= (11/3) in. * (13/6) in. * (3/2) in.
To multiply fractions, you need to multiply the numerators together and the denominators together:
Volume = (11/3) * (13/6) * (3/2)
= (11 * 13 * 3) / (3 * 6 * 2)
= (429) / (36)
Therefore, the volume of the rectangular prism is 429/36 cubic inches.