What does 3/4 actually mean?
3/4 means the whole is cut into 4 equal parts and you have 3 of them. The bottom number says how many equal parts make the whole; the top number says how many you have.
Why tho? Three levels deeper
Why must the parts be equal?
Because a fraction is a size. If the slices were different sizes, '3 of 4 slices' could be almost nothing or almost everything, and the number would mean nothing.
Why is 3/4 the same as 6/8?
Cut every quarter in half. Now there are 8 equal parts instead of 4, and your 3 quarters became 6 eighths. Same amount of pizza, more cuts.
What is 3/4 as a decimal?
Divide 3 by 4: 0.75. As a percentage that's 75%, three quarters of a hundred.
Two numbers, two jobs
The denominator (bottom) names the size of the pieces: quarters, eighths, thirds. The numerator (top) counts how many pieces you have.
Pictures that help
A pizza shows parts of a round whole. A bar or a number line shows where 3/4 sits between 0 and 1. Switching between pictures is one of the fastest ways to really get fractions.
Bigger bottom, smaller pieces
1/8 is smaller than 1/4: cutting the same pizza into more pieces makes each piece smaller.
Check yourself
Which is bigger, 2/3 or 3/4?
Answer
3/4. Written with twelfths, 2/3 = 8/12 and 3/4 = 9/12.