Hello, fair sharer! In this chapter, we learn how equal sharing creates fractions. A whole can be a paper sheet, a ribbon, a garden bed, a set of counters, or a measuring strip. The big rule is simple: fractions are fair only when the parts are equal.
Caregiver: Use paper strips, folded napkins, string, or counters. Let the child fold, compare, and explain before writing fraction symbols.
This original guide follows the learning scope of Chapter 5, Sharing and Measuring, from NCERT’s Maths Mela for Class 4. The explanations, examples, activity, and questions are newly written for PrincipalSaab and do not copy textbook stories, exercises, or artwork.
Fractions become easier when measurement feels familiar, so you may first review Measuring Length, explore the Class 4 Mathematics learning path, or use Ask a Doubt when a fair-share step needs another example.
Words to Know
whole
the complete object or collection
one full strip
equal parts
parts of the same size
fair pieces
half
one of two equal parts
1/2
quarter
one of four equal parts
1/4
numerator
number of selected parts
top number
denominator
number of equal parts in the whole
bottom number
Take three same-sized paper strips. Fold one into halves, one into quarters, and one into eighths. Colour one part on each strip, place them side by side, and say which coloured part is largest and why. (15-20 min)
Your Learning Plan
- Start by identifying the whole.
- Check whether the parts are equal before naming a fraction.
- Read the denominator as the number of equal parts in the whole.
- Read the numerator as the number of parts selected.
- Use drawings, folding, and measuring to check your answer.
1. Understand Equal Parts
Sharing is mathematical only when the parts are equal. If a paper is torn into two pieces and one piece is much larger, we cannot call each piece a half. A half means one of two equal parts. Equal size is the promise inside every fraction.
The same idea works for objects and collections. A whole could be one rectangle, one metre of ribbon, one round plate, or 20 counters. First ask, “What is the whole?” Then ask, “How many equal parts has it been divided into?” Without these two questions, a fraction answer can become unclear.
Children often think that more pieces always means more food or more paper. Actually, if the whole stays the same, more equal pieces usually means each piece is smaller. This is why one eighth of the same strip is smaller than one fourth.
A quick fairness test is to place the parts on top of one another or fold along the dividing lines. If the parts match neatly, the sharing is equal. If one part sticks out or leaves a gap, the share may look tidy but it is not a true fraction share yet.
Situation: A rectangle is divided into four equal parts. Two parts are shaded.
- Each small equal part is one quarter, written as 1/4.
- Two shaded parts are 1/4 + 1/4.
- Two out of four equal parts means 2/4.
- If the same rectangle is split into two equal big parts, the shaded area covers one of those big parts.
Answer: 2/4 is the same amount as 1/2.
A fraction is fair only when the whole is divided into equal parts.
2. Use Fraction Language
A fraction has two numbers. The bottom number is called the denominator. It tells how many equal parts are in the whole. The top number is called the numerator. It tells how many of those equal parts we are talking about.
In 3/4, the denominator 4 says the whole has four equal parts. The numerator 3 says three parts are selected. Read this as three-fourths or three quarters. Saying the meaning aloud helps more than simply naming the numbers.
Unit fractions have numerator 1. Examples are 1/2, 1/3, 1/4, and 1/5. They are useful because many other fractions are built from them. For example, 3/5 means three one-fifth parts.
Situation: A paper strip is cut into 5 equal parts, and one part is coloured.
- The whole strip has 5 equal parts.
- Only 1 part is coloured.
- The fraction is coloured parts over equal parts in the whole.
- So the fraction is 1/5.
Answer: One coloured part is one-fifth of the strip.
3. Compare Unit Fractions
When the whole is the same size, unit fractions can be compared by thinking about cutting. If one strip is cut into 3 equal parts, each part is quite large. If the same-sized strip is cut into 6 equal parts, each part is smaller. Therefore 1/3 is larger than 1/6.
This feels surprising because 6 is greater than 3. But the denominator is not a count of selected parts; it is the number of equal cuts in the whole. More cuts mean smaller pieces when the whole does not change.
Always compare fractions from the same whole. One half of a tiny biscuit is not necessarily bigger than one fourth of a very large roti. In this chapter, our comparisons use the same-sized whole unless the question says otherwise.
Situation: Compare 1/3 and 1/6 using equal-sized rotis drawn on paper.
- Both fractions use the same-sized whole.
- One third means the whole is split into 3 equal pieces.
- One sixth means the whole is split into 6 equal pieces.
- When the same whole is split into more equal pieces, each piece is smaller.
Answer: 1/3 is greater than 1/6.
Do not say 1/9 is larger than 1/5 just because 9 is larger than 5. For the same whole, ninths are smaller pieces.
4. Join Same-Size Parts
Fractions with the same denominator use the same kind of equal parts. That makes them easy to join. If a strip is divided into fifths, then 1/5, 2/5, and 3/5 all talk about fifth-size pieces.
To add like fractions in Class 4, keep the denominator and add the selected parts. Two fifths and three fifths make five fifths. Five fifths make one whole because all five equal parts are included.
Use drawings for confidence. Shade the parts you are joining, then count the shaded equal parts. The drawing also helps you notice when the answer is one whole or more than half.
Situation: A garden plan has 3/5 of a row for marigold and 1/5 for jasmine.
- Both fractions have the same denominator, 5.
- That means the row is divided into the same kind of equal parts.
- Add only the numerators: 3 + 1 = 4.
- Keep the denominator 5 because the size of each part has not changed.
Answer: 3/5 + 1/5 = 4/5 of the row.
5. Find Fractions Of Collections
A fraction can describe a collection too. If 12 beads are split into 4 equal groups, each group is one fourth of the collection. We do not cut the beads; we arrange them fairly into equal groups.
For one fourth of 12, divide 12 by 4. For three fourths of 12, first find one fourth, then take three such groups. This method is clear and easy to check with counters.
Fractions of collections appear in class displays, packets, beads, stickers, and game cards. Keep the collection small at first. Once the method is clear, larger collections become less scary.
Situation: There are 12 paper stars. One fourth of them are blue.
- One fourth means 1 out of 4 equal groups.
- Split 12 stars into 4 equal groups.
- 12 divided by 4 is 3.
- One group has 3 stars.
Answer: 1/4 of 12 stars is 3 stars.
Situation: Four children share 16 counters equally.
- The whole collection has 16 counters.
- Four children means 4 equal shares.
- 16 divided by 4 is 4.
- Each child gets one fourth of the collection.
Answer: Each child gets 4 counters, which is 1/4 of the collection.
6. Measure With Halves And Quarters
Fractions are also useful in measurement. One metre is 100 centimetres. Half a metre is half of 100 cm, which is 50 cm. A quarter metre is one fourth of 100 cm, which is 25 cm.
When you fold a measuring strip into equal parts, you can see these lengths. Two quarter metres make 50 cm, the same as half a metre. Three quarter metres make 75 cm. Four quarter metres make the full 100 cm.
Measurement fractions help in craft, classroom displays, ribbons, borders, and simple maps. Always write the unit in the answer, because 1/4 metre and 1/4 litre are different kinds of measures.
For Class 4, it is enough to connect the fraction with an equal division of the measuring unit. Draw a 100 cm strip, mark 0 cm and 100 cm, then fold or divide it into 2 or 4 equal spaces. The marks at 25 cm, 50 cm, and 75 cm become easy to understand because they are positions on the same whole metre.
Situation: A ribbon is 1 metre long. A child uses three quarters of it.
- 1 metre is 100 centimetres.
- One quarter of 100 cm is 25 cm.
- Three quarters means 3 groups of 25 cm.
- 3 x 25 = 75.
Answer: Three quarters of a metre is 75 cm.
If your answer is a length, include cm or m. A correct number without a unit is still incomplete.
Practise With Answers
Try these original questions. Open the answer only after you have drawn, folded, or reasoned it out.
Practice 1. A square is divided into 4 equal parts. Three parts are shaded. Write the fraction.
Answer: 3/4 is shaded.
Practice 2. Which is larger: 1/4 or 1/8 of the same whole?
Answer: 1/4 is larger because the whole is cut into fewer equal parts.
Practice 3. Complete: 1/4 + 1/4 = __.
Answer: 1/4 + 1/4 = 2/4, which is the same as 1/2.
Practice 4. How many fifths make one whole?
Answer: 5 fifths make one whole.
Practice 5. Add 1/5 + 3/5.
Answer: 1/5 + 3/5 = 4/5.
Practice 6. There are 16 beads. What is 3/4 of the beads?
Answer: 1/4 of 16 is 4, so 3/4 is 12 beads.
Practice 7. What is half of 1 metre in centimetres?
Answer: Half of 100 cm is 50 cm.
Practice 8. What is one quarter of 1 metre in centimetres?
Answer: One quarter of 100 cm is 25 cm.
Practice 9. A strip is split into 6 equal parts. Two parts are coloured. Write the fraction.
Answer: 2/6 is coloured, which is the same amount as 1/3.
Practice 10. A child says 1/9 is bigger than 1/5 because 9 is bigger than 5. Is this correct?
Answer: No. For the same whole, 1/9 is smaller because the whole is divided into more pieces.
Quick Self-Check
Self-check 1. What must be true before parts can be called halves, thirds, or quarters?
Answer: The parts must be equal.
Self-check 2. What does the denominator tell us?
Answer: It tells how many equal parts the whole is divided into.
Self-check 3. What does the numerator tell us?
Answer: It tells how many of those equal parts are being talked about.
Self-check 4. Which is greater for the same whole: 1/2 or 1/4?
Answer: 1/2 is greater.
Self-check 5. How many quarters make one whole?
Answer: Four quarters make one whole.
Kaizen line: One fair fold today can make every fraction easier to see tomorrow.