Parts and Wholes Class 5 NCERT: Fractions Made Simple

Key Fraction Words

Whole

The complete object or complete group we are talking about, such as one full pizza or a set of 12 pencils.

Equal parts

Parts that have the same size or the same number of objects. Fractions are correct only when the parts are equal.

Numerator

The top number in a fraction. It tells how many equal parts are taken or shaded.

Denominator

The bottom number in a fraction. It tells how many equal parts the whole is divided into.

Equivalent fractions

Different fractions that show the same amount, such as 1/2 and 2/4.

Understanding Parts and Wholes

A fraction always needs a clear whole. Suppose one square is divided into 4 equal smaller squares and 3 are shaded. The whole is the large square, the denominator is 4 because there are 4 equal parts, and the numerator is 3 because 3 parts are shaded. So the shaded part is 3/4. But if a shape is cut into unequal pieces, we should not call one piece 1/4 just because there are 4 pieces. In Class 5, the most important habit is to ask: What is the whole? Are the parts equal? How many equal parts are selected? This habit prevents most fraction mistakes.

How to Find a Fraction of a Collection

1. Step 1: Find the whole group — Count the total number of objects. For example, if there are 15 flowers, the whole is 15 flowers.
2. Step 2: Read the denominator — The denominator tells how many equal groups to make. For 2/5 of 15, divide 15 flowers into 5 equal groups.
3. Step 3: Find one part — 15 divided by 5 is 3, so 1/5 of 15 is 3 flowers.
4. Step 4: Read the numerator — The numerator tells how many such parts to take. For 2/5, take 2 groups of 3 flowers, which is 6 flowers.

Worked Examples

• Example 1: A ribbon is divided into 8 equal parts. 5 parts are coloured red. What fraction is red? Step 1: The whole ribbon has 8 equal parts, so the denominator is 8. Step 2: The coloured red parts are 5, so the numerator is 5. Step 3: Write coloured parts over total equal parts. Final answer: 5/8 of the ribbon is red.
• Example 2: Find 3/4 of 20 mangoes. Step 1: The whole group is 20 mangoes. Step 2: Denominator 4 means divide 20 into 4 equal groups: 20 ÷ 4 = 5. Step 3: Numerator 3 means take 3 such groups: 3 × 5 = 15. Final answer: 3/4 of 20 mangoes is 15 mangoes.
• Example 3: Are 2/4 and 1/2 the same amount? Step 1: Imagine one rectangle divided into 4 equal parts. Shading 2 parts gives 2/4. Step 2: The same rectangle can be divided into 2 equal halves. Shading 1 half gives 1/2. Step 3: 2 out of 4 equal parts covers the same area as 1 out of 2 equal parts. Final answer: Yes, 2/4 and 1/2 are equivalent fractions.

Common Mistakes to Avoid

• Do not write a fraction until you know the whole. Half of a small chocolate and half of a large chocolate are not the same amount.
• Do not count unequal pieces as equal fraction parts. Four unequal pieces do not automatically mean each piece is 1/4.
• In a fraction, the denominator is total equal parts, not the unshaded parts. If 3 out of 5 parts are shaded, the fraction shaded is 3/5, not 3/2.
• When finding a fraction of a collection, divide first by the denominator, then multiply by the numerator. This keeps the meaning clear.
• For comparison, same denominators are easy: 3/8 is greater than 2/8 because both wholes are cut into 8 equal parts and 3 parts is more than 2 parts.

Exam Tip for NCERT Questions

In Class 5 maths parts and wholes questions, draw a quick sketch whenever possible. If the question says 3/5 of 25, draw or imagine 5 equal boxes and place 5 objects in each box because 25 ÷ 5 = 5. Then choose 3 boxes. A small diagram helps you avoid reversing numerator and denominator, especially in word problems.

Practice Questions with Solutions

• Q: A circle is divided into 6 equal parts. 4 parts are shaded. What fraction is shaded? A: Step 1: Count the total equal parts in the whole circle: 6. Step 2: Count the shaded parts: 4. Step 3: Write shaded parts over total equal parts: 4/6. Final answer: 4/6 of the circle is shaded.
• Q: Find 2/3 of 18 apples. A: Step 1: The whole group is 18 apples. Step 2: Denominator 3 means make 3 equal groups: 18 ÷ 3 = 6. Step 3: Numerator 2 means take 2 groups: 2 × 6 = 12. Final answer: 2/3 of 18 apples is 12 apples.
• Q: Rani ate 1/4 of a chocolate and Aman ate 2/4 of an equal chocolate. Who ate more? A: Step 1: Both chocolates are equal wholes, so we can compare the fractions. Step 2: The denominators are the same: 4 and 4. Step 3: Compare numerators: 2 is greater than 1. Final answer: Aman ate more because 2/4 is greater than 1/4.
• Q: A rectangle has 10 equal squares. 5 squares are blue. Write the blue part as a fraction and name an equivalent fraction. A: Step 1: The whole rectangle has 10 equal squares, so the denominator is 10. Step 2: Blue squares are 5, so the fraction is 5/10. Step 3: 5 out of 10 is the same as half of the rectangle. Final answer: The blue part is 5/10, which is equivalent to 1/2.

Frequently Asked Questions