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CBSE · Class 5 · Math Mela

Chapter 2: Fractions

4 concepts · 32 practice questions with answers · Free to read

This lesson is also in: मराठी · हिंदी

Equivalent fractions

From daily life

Half a roti and 2 quarter pieces of the same roti are the same amount to eat. Different-looking fractions can show the same part of a whole.

Simple definition

Equivalent fractions are fractions that show the same part of a whole, like 1/2, 2/4 and 4/8. Multiply (or divide) the numerator and the denominator by the same number to get one.

Formula: a/b = (a × k)/(b × k) = (a ÷ k)/(b ÷ k).

1/2 = 2/4 = 4/81/22/44/8

In the figure: All three bars have the same length shaded, so 1/2 = 2/4 = 4/8.

Rule 1: Multiply to make equivalent fractions — Multiply the numerator and the denominator by the same number (2, 3, 4, …).

Live figure

Equivalent fractions

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  • Easy: 2/5 = (2 × 3)/(5 × 3) = 6/15.
  • Medium: 3/4 = (3 × 2)/(4 × 2) = 6/8 and also 9/12 (× 3).
  • Exam-type: 1/6 = 4/24, because 6 × 4 = 24 and 1 × 4 = 4.

Rule 2: Divide to simplify — Divide the numerator and the denominator by a number that divides both. Keep going until no common factor is left.

  • Easy: 8/12 = (8 ÷ 4)/(12 ÷ 4) = 2/3.
  • Medium: 15/20 = 3/4 (divide by 5).
  • Exam-type: 18/24 → ÷ 2 → 9/12 → ÷ 3 → 3/4; or in one step ÷ 6 → 3/4.
Remember

Always do the SAME thing to the top and the bottom. Then the value of the fraction does not change.

Common mistake

Adding the same number: 1/2 → (1 + 2)/(2 + 2) = 3/4. That is wrong! Multiply, do not add: 1/2 = 2/4.

Shortcut

To check two fractions a/b and c/d, see if a × d = b × c (cross-multiply). Memory clue: "Same on top, same on bottom" — a fraction wearing a different dress is still the same fraction.

Spot the difference

PointMultiplyAdd
2/3 becomes4/6 (× 2)4/5 (+ 2)
Same value?YesNo

Practice questions

Easy
  1. 1Write one fraction equivalent to 2/3.
  2. 2Fill in: 1/4 = ___/12
  3. 3Simplify 6/8.
Medium
  1. 4Fill in: 3/5 = 12/___
  2. 5Simplify 20/30 completely.
  3. 6Are 4/6 and 10/15 equivalent? Show why.
Challenging
  1. 7Write three fractions equivalent to 5/7 with denominators less than 30.
  2. 8A pizza is cut into 12 equal slices and Neha eats 9. Write her share in the simplest form.
Show answers (try them yourself first)
  1. 14/6 (or 6/9, 8/12)
  2. 23 (4 × 3 = 12, so 1 × 3 = 3)
  3. 33/4
  4. 420 (3 × 4 = 12, so 5 × 4 = 20)
  5. 52/3 (÷ 10)
  6. 6Yes: 4/6 = 2/3 and 10/15 = 2/3.
  7. 710/14, 15/21, 20/28
  8. 89/12 = 3/4

Comparing fractions with the same denominator or numerator

From daily life

Two friends share identical chocolate bars. One eats 3 of 8 equal pieces and the other eats 5 of 8. Who ate more? Same-sized pieces make it easy to decide.

Simple definition

Same denominator: the fraction with the bigger numerator is bigger. Same numerator: the fraction with the smaller denominator is bigger (fewer, larger pieces).

Formula: Same denominator: a/d > b/d if a > b. Same numerator: n/a > n/b if a < b.

Same denominator 8: 3/8 < 5/83/85/8

In the figure: Both bars have 8 equal parts; 5 shaded parts are more than 3 shaded parts, so 5/8 > 3/8.

Rule 1: Same denominator — The pieces are the same size, so just count the pieces: compare the numerators.

Live figure

Comparing fractions with the same denominator or numerator

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  • Easy: 4/9 < 7/9 because 4 < 7.
  • Medium: 11/13 > 6/13 because 11 > 6.
  • Exam-type: Ascending: 2/10, 5/10, 8/10, 9/10.

Rule 2: Same numerator — The bigger the denominator, the smaller each piece. So the bigger denominator gives the smaller fraction.

  • Easy: 3/4 > 3/6 because fourths are bigger than sixths.
  • Medium: 5/8 < 5/7 because 8 > 7.
  • Exam-type: Descending: 2/3, 2/5, 2/7, 2/11.
Remember

Same denominator → compare the tops. Same numerator → compare the bottoms, but the order flips.

Common mistake

Thinking 1/8 is bigger than 1/5 because 8 > 5. Remember: a bigger denominator means smaller pieces, so 1/8 < 1/5.

Shortcut

Picture the pieces: more people sharing a cake means a smaller slice each. Memory clue: "Same bottom → big top wins; same top → small bottom wins."

Spot the difference

Point3/8 and 5/83/4 and 3/6
What is same?DenominatorNumerator
Compare3 and 54 and 6
Greater5/83/4

Practice questions

Easy
  1. 1Which is greater: 6/11 or 9/11?
  2. 2Which is smaller: 5/6 or 5/9?
  3. 3Put the right sign: 7/10 ___ 3/10
Medium
  1. 4Arrange in ascending order: 5/12, 11/12, 2/12, 7/12.
  2. 5Arrange in descending order: 4/5, 4/9, 4/3, 4/7.
  3. 6Which sign: 2/7 ___ 2/5?
Challenging
  1. 7Ria drank 3/5 litre of juice and Tara drank 3/8 litre. Who drank more? How do you know?
  2. 8Write a fraction with numerator 5 that is smaller than 5/9 but bigger than 5/12.
Show answers (try them yourself first)
  1. 19/11
  2. 25/9
  3. 3>
  4. 42/12, 5/12, 7/12, 11/12
  5. 54/3, 4/5, 4/7, 4/9
  6. 6< (sevenths are smaller than fifths)
  7. 7Ria — same numerator 3, and fifths are bigger than eighths.
  8. 85/10 or 5/11

Fractions greater than 1: improper and mixed

From daily life

Maa cuts each paratha into 4 equal pieces. Dadaji eats 7 pieces. He has eaten more than one paratha: 7/4 = 1 whole paratha and 3 more pieces.

Simple definition

An improper fraction has a numerator that is greater than or equal to its denominator (7/4). A mixed number has a whole part and a fraction part (1 3/4). They show the same amount.

Formula: n/d = (n ÷ d) quotient and remainder: quotient r/d. w r/d = (w × d + r)/d.

7/4 = 1 3/413/4

In the figure: One full bar (4/4) plus 3 more quarter pieces: 7/4 = 1 3/4.

Rule 1: Improper → mixed — Divide the numerator by the denominator. The quotient is the whole part and the remainder is the new numerator.

Live figure

Fractions greater than 1: improper and mixed

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  • Easy: 9/2: 9 ÷ 2 = 4 r 1, so 9/2 = 4 1/2.
  • Medium: 13/5: 13 ÷ 5 = 2 r 3, so 13/5 = 2 3/5.
  • Exam-type: 20/6: 20 ÷ 6 = 3 r 2, so 20/6 = 3 2/6 = 3 1/3.

Rule 2: Mixed → improper — Multiply the whole part by the denominator, add the numerator, and keep the same denominator.

  • Easy: 2 3/4 = (2 × 4 + 3)/4 = 11/4.
  • Medium: 5 1/3 = (5 × 3 + 1)/3 = 16/3.
  • Exam-type: 3 2/7 = (3 × 7 + 2)/7 = 23/7.

Rule 3: On the number line — Between 0 and 1 draw d equal parts. Keep counting the same-sized parts past 1: n/d is the n-th mark.

  • Easy: 7/3 is the 7th mark with thirds: it lies between 2 and 3.
  • Medium: 5/5 is the 5th mark: it is exactly 1.
  • Exam-type: 11/4 = 2 3/4 lies between 2 and 3.
Remember

The denominator stays the same in both forms. 1 whole = d/d, so 3 wholes = 3d/d.

Common mistake

Writing 7/4 as 3 1/4 (swapping quotient and remainder). Quotient 1 is the whole part: 7/4 = 1 3/4.

Shortcut

Check by converting back: 1 3/4 → 1 × 4 + 3 = 7 → 7/4 ✓. Memory clue: "Divide to get a mixed number; multiply-and-add to get an improper one."

Spot the difference

PointImproper fractionMixed number
Example11/42 3/4
Numerator vs denominatorNumerator ≥ denominatorWhole part + proper fraction
Value2.75 wholes2.75 wholes

Practice questions

Easy
  1. 1Write 8/3 as a mixed number.
  2. 2Write 3 1/2 as an improper fraction.
  3. 3How many 1/5 pieces make 3 wholes?
Medium
  1. 4Write 17/6 as a mixed number.
  2. 5Write 4 2/5 as an improper fraction.
  3. 6Between which two whole numbers does 19/4 lie?
Challenging
  1. 7A ribbon is cut into pieces of 1/3 metre each. There are 11 pieces. How many metres of ribbon is that? Write it as a mixed number.
  2. 8Which is bigger: 13/4 or 3 1/2?
Show answers (try them yourself first)
  1. 12 2/3
  2. 27/2
  3. 315
  4. 42 5/6
  5. 522/5
  6. 64 and 5 (19/4 = 4 3/4)
  7. 711/3 = 3 2/3 metres
  8. 813/4 = 3 1/4 and 3 1/2 is bigger, so 3 1/2.

Comparing fractions with 1 as reference

From daily life

Asha has walked 5/6 of the way to school and Ravi has walked 9/8 of that distance on a longer path. One has not yet finished a whole trip, the other has gone beyond it. Comparing with 1 tells us quickly.

Simple definition

Compare each fraction with 1. If numerator < denominator the fraction is less than 1; if equal it is 1; if greater it is more than 1. Any number more than 1 beats any number less than 1.

Formula: n < d → less than 1; n = d → 1; n > d → more than 1.

0125/69/85/6 < 1 < 9/8

In the figure: 5/6 sits before 1 and 9/8 sits after 1 on the number line, so 5/6 < 1 < 9/8.

Rule 1: Use 1 as the milestone — Decide which fractions are less than 1 and which are more than 1. The "more than 1" group is bigger.

Live figure

Comparing fractions with 1 as reference

In the app you can move this figure with your finger.

Open in the app
  • Easy: 7/8 < 1 and 9/8 > 1, so 9/8 > 7/8.
  • Medium: 5/3 is greater than 4/5 (5/3 is more than 1; 4/5 is less than 1).
  • Exam-type: Greatest of 2/3, 6/5, 3/4: only 6/5 is above 1.

Rule 2: Mixed numbers: whole part first — Compare the whole parts first. If they are equal, compare the fraction parts.

  • Easy: 3 1/2 > 2 5/6 because 3 > 2.
  • Medium: 4 2/5 > 4 1/5: wholes are equal and 2/5 > 1/5.
  • Exam-type: 1 3/4 vs 7/4: 7/4 = 1 3/4, so they are equal.
Remember

1 is the line between "not yet a whole" (less than 1) and "a whole or more".

Common mistake

Thinking a big numerator always means a big fraction. 9/10 has a big numerator but is still less than 1, while 5/4 is more than 1.

Shortcut

If one fraction is below 1 and the other above 1, the answer is ready — no calculation needed. Memory clue: "Below the mark, above the mark — the one above wins."

Spot the difference

Point5/69/8
Numerator vs denominator5 < 69 > 8
Compared with 1Less than 1More than 1
Greater—9/8

Practice questions

Easy
  1. 1Is 6/7 less than, equal to, or more than 1?
  2. 2Which is greater: 4/5 or 5/4?
  3. 3Write 1 as a fraction with denominator 9.
Medium
  1. 4Which is greatest: 3/4, 7/6, 5/8, 1/2?
  2. 5Which is bigger: 2 3/5 or 2 4/5?
  3. 6Compare 5/3 and 1 2/3.
Challenging
  1. 7Arrange in ascending order: 5/4, 2/3, 1, 7/8.
  2. 8Mona ran 7/5 km and Rohan ran 9/10 km. Who ran farther? By how much more than 1 km did Mona run?
Show answers (try them yourself first)
  1. 1Less than 1
  2. 25/4
  3. 39/9
  4. 47/6
  5. 52 4/5
  6. 65/3 = 1 2/3, so they are equal.
  7. 72/3, 7/8, 1, 5/4
  8. 8Mona (more than 1 km); 7/5 = 1 2/5, so 2/5 km more than 1 km.