Number - Understanding and comparing fractions (halves, quarters, thirds, eighths)
Review the key concepts, formulae, and examples before starting your quiz.
🔑Concepts
A fraction represents a part of a whole that has been divided into equal pieces.
The Denominator (bottom number) tells us the total number of equal parts the whole is divided into.
The Numerator (top number) tells us how many of those equal parts we are talking about.
Unit Fractions are fractions where the numerator is 1 (e.g., 1/2, 1/3, 1/4, 1/8).
Comparing Unit Fractions: The larger the denominator, the smaller the actual piece (e.g., 1/8 is smaller than 1/2).
Equivalence: Some fractions represent the same amount even if the numbers are different (e.g., 2/4 is the same as 1/2).
📐Formulae
💡Examples
Problem 1:
Which fraction is larger: or ?
Solution:
is larger.
Explanation:
Imagine a pizza. If you cut it into 3 equal slices, the pieces will be bigger than if you cut the same pizza into 4 equal slices. Therefore, .
Problem 2:
A chocolate bar is divided into 8 equal pieces. Sarah eats 4 pieces. What fraction of the bar did she eat? Simplify if possible.
Solution:
or .
Explanation:
The total number of pieces (denominator) is 8. Sarah ate 4 pieces (numerator), making the fraction . Since 4 is exactly half of 8, this is equivalent to .
Problem 3:
Order these fractions from smallest to largest: .
Solution:
.
Explanation:
The denominator tells us how small the pieces are. 8 is the largest denominator, so is the smallest piece. 2 is the smallest denominator, so is the largest piece.