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Number - Understanding and comparing fractions (halves, quarters, thirds, eighths)

Grade 3IGCSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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A fraction represents a part of a whole that has been divided into equal pieces.

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The Denominator (bottom number) tells us the total number of equal parts the whole is divided into.

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The Numerator (top number) tells us how many of those equal parts we are talking about.

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Unit Fractions are fractions where the numerator is 1 (e.g., 1/2, 1/3, 1/4, 1/8).

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Comparing Unit Fractions: The larger the denominator, the smaller the actual piece (e.g., 1/8 is smaller than 1/2).

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Equivalence: Some fractions represent the same amount even if the numbers are different (e.g., 2/4 is the same as 1/2).

📐Formulae

Fraction=Parts Shaded/SelectedTotal Equal Parts\text{Fraction} = \frac{\text{Parts Shaded/Selected}}{\text{Total Equal Parts}}

12=24=48\frac{1}{2} = \frac{2}{4} = \frac{4}{8}

If b>a, then 1b<1a (for unit fractions)\text{If } b > a, \text{ then } \frac{1}{b} < \frac{1}{a} \text{ (for unit fractions)}

💡Examples

Problem 1:

Which fraction is larger: 1/31/3 or 1/41/4?

Solution:

1/31/3 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, 1/3>1/41/3 > 1/4.

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:

4/84/8 or 1/21/2.

Explanation:

The total number of pieces (denominator) is 8. Sarah ate 4 pieces (numerator), making the fraction 4/84/8. Since 4 is exactly half of 8, this is equivalent to 1/21/2.

Problem 3:

Order these fractions from smallest to largest: 1/8,1/2,1/41/8, 1/2, 1/4.

Solution:

1/8,1/4,1/21/8, 1/4, 1/2.

Explanation:

The denominator tells us how small the pieces are. 8 is the largest denominator, so 1/81/8 is the smallest piece. 2 is the smallest denominator, so 1/21/2 is the largest piece.