A pizza is cut into 3 equal slices. An identical pizza is cut into 4 equal slices. You take one slice from each pizza. Which slice is bigger?
AThe slice from the pizza cut into 4 pieces, because 4 is a bigger number
BThe slice from the pizza cut into 3 pieces, because fewer equal parts means each part is larger
CBoth slices are the same size, because you took one slice from each
DYou cannot tell without knowing how big the pizza is
When a whole is divided into more equal parts, each part gets smaller. Dividing a pizza into 3 equal parts gives larger slices (1/3 each) than dividing the same-size pizza into 4 equal parts (1/4 each). The denominator tells you how many equal pieces the whole was split into — bigger denominator, smaller each piece.
Question 2 True / False
A square can primarily be cut into halves by slicing it straight down the middle (vertically or horizontally) — a diagonal cut does not produce halves.
TTrue
FFalse
Answer: False
A diagonal cut that produces two pieces of the same size is a valid way to make halves. The critical requirement is that the two pieces are equal in size, not that they look identical or are cut a particular way. An L-shaped piece and a different-shaped piece can both be halves of the same shape, as long as both pieces are the same area.
Question 3 Short Answer
A rectangle is cut into 4 pieces, but the pieces are not all the same size. Does each piece represent one-fourth of the rectangle? Why or why not?
Think about your answer, then reveal below.
Model answer: No. For each piece to be one-fourth, the rectangle must be divided into exactly 4 equal parts. If the pieces are different sizes, they are not fourths — the equal-parts rule is required.
The word 'fourth' means one of four equal parts. If the parts are unequal, no piece is a true fourth, even though there are four pieces. Fractions always require the whole to be divided into equal-sized pieces — equality is the defining condition.