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Fractions - Fraction of a Collection

Grade 3ICSE

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

🔑Concepts

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A collection is a group of separate objects, such as a set of 12 pencils, 8 marbles, or 10 flowers, rather than a single whole object like a pizza.

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Finding a fraction of a collection means dividing the total number of items into equal-sized groups. If you have 10 balls and want to find half, imagine drawing two large boxes and placing an equal number of balls in each.

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The denominator (the bottom number in a fraction) represents the total number of equal groups the collection is divided into. For example, in 14\frac{1}{4} of 8, the denominator 44 tells us to make 4 equal groups.

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The numerator (the top number in a fraction) represents how many of those equal groups we are interested in. For 34\frac{3}{4}, we would count the items in 3 out of the 4 groups.

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A Unit Fraction of a collection (where the numerator is 1) is found by simply dividing the total number of items by the denominator. To find 12\frac{1}{2} of 6, you calculate 6÷2=36 \div 2 = 3.

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When the numerator is greater than 1, you find the value of one group first and then multiply it by the numerator. To find 23\frac{2}{3} of 9, you first find one-third (9÷3=39 \div 3 = 3) and then take two such groups (3×2=63 \times 2 = 6).

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In word problems, the word 'of' acts like a multiplication sign between the fraction and the total collection size. For example, 'Find 15\frac{1}{5} of 25' means 15×25\frac{1}{5} \times 25.

📐Formulae

Value of one part=Total Number of Objects÷Denominator\text{Value of one part} = \text{Total Number of Objects} \div \text{Denominator}

Fraction of a collection=(Total÷Denominator)×Numerator\text{Fraction of a collection} = (\text{Total} \div \text{Denominator}) \times \text{Numerator}

1d of X=X÷d\frac{1}{d} \text{ of } X = X \div d

nd of X=(X÷d)×n\frac{n}{d} \text{ of } X = (X \div d) \times n

💡Examples

Problem 1:

Rohan has a collection of 15 chocolates. He gives 13\frac{1}{3} of them to his sister. How many chocolates does his sister get?

Solution:

Step 1: Identify the total number of chocolates, which is 1515. Step 2: Identify the fraction, which is 13\frac{1}{3}. The denominator is 33. Step 3: Divide the total number by the denominator: 15÷3=515 \div 3 = 5. Step 4: Since the numerator is 11, the answer is 55.

Explanation:

To find a unit fraction (13\frac{1}{3}) of a collection, we divide the total number of items by the denominator to see how many items are in one equal group.

Problem 2:

There are 20 stars in a sky. Color 34\frac{3}{4} of them yellow. How many stars should be colored yellow?

Solution:

Step 1: Total stars = 2020. Fraction = 34\frac{3}{4}. Step 2: Divide the total by the denominator to find the value of one group: 20÷4=520 \div 4 = 5 stars. Step 3: Multiply the value of one group by the numerator: 5×3=155 \times 3 = 15. Final Answer: 1515 stars should be colored yellow.

Explanation:

When the numerator is more than 1, we first find the size of one equal part (by dividing) and then multiply that size by the number of parts we need (the numerator).