Step-by-step explanation:
A
the answers are already right in picture. we only need to count.
maybe the problem is understanding a cube ? when it says here "the edge of each cube is 1 1/2 in long", then it means that every side length of a cube is the same (length, width, height). it is the principle of a 2-dimensional square in 3 dimensions.
and "prism" is simply another word for "box".
so, we see that there are 5 cubes fitting along the length of the prism.
so, the length of the prism is
5× 1 1/2 in = 5× 3/2 = 15/2 = 7 1/2 in.
3 cubes are the width of the prism.
so, the width of the prism is
3× 1 1/2 in = 3× 3/2 = 9/2 = 4 1/2 in.
B
we know the height of the prism is 3/4 ft.
1 ft = 12 in
3/4 ft = 3/4 × 12 = (3×12)/4 = 36/4 = 9 in
how many layers of cubes fit into 9 in ?
well, that is what we use division for :
9 ÷ 1 1/2
this is the same as
9 / 3/2 = (9/1) / (3/2)
to divide by a fraction is the same as to multiply with the upside-down fraction. therefore :
(9/1) × (2/3) = (9×2) / (1×3) = 18/3 = 6
so, 6 layers of the cubes fit into the prism.
