Class 6 : Maths ( English ) – Lesson 7. Fractions

EXPLANATION AND ANALYSIS

🌿 Explanation & Analysis

🔵 1. Meaning of a Fraction
In everyday life, we often talk about parts of a whole—half an apple 🍎, one-quarter of a pizza 🍕, or three-fourths of a litre of milk 🥛. A fraction is a number that represents such a part of a whole.
A fraction is written in the form a/b, where a and b are whole numbers and b ≠ 0.
Here, a is called the numerator and b is called the denominator.

🧠 The denominator tells us how many equal parts the whole is divided into, while the numerator tells us how many of those parts are taken.

✏️ Note: The denominator can never be zero because a whole cannot be divided into zero parts.

💡 Concept: Fraction = (Number of equal parts taken) / (Total equal parts)

🔵 2. Fractions of a Whole
To understand fractions clearly, the whole must be divided into equal parts.
For example, if a chocolate bar 🍫 is divided into 4 equal pieces and you eat 1 piece, you have eaten 1/4 of the chocolate.

🟢 If the parts are not equal, the fraction has no meaning.
🟡 Equality of parts is the foundation of fractions.

➡️ This idea applies to shapes, quantities, and measurements alike.

🔵 3. Fractions of a Collection
Fractions are not limited to a single object; they can also describe a group of objects.
Suppose there are 12 pencils ✏️ in a box.

🔵 1/3 of 12 pencils = 4 pencils
🔵 1/2 of 12 pencils = 6 pencils

🧠 Here, the whole is the collection, and the fraction tells how many items are selected from it.

✏️ Note: To find a fraction of a collection, first divide the total equally, then count the required parts.

🔵 4. Proper, Improper, and Mixed Fractions

🟢 Proper Fractions
A fraction is called a proper fraction when the numerator is smaller than the denominator.
Examples: 1/2, 3/5, 7/9

✔️ These fractions represent values less than 1.

🟡 Improper Fractions
A fraction is called an improper fraction when the numerator is equal to or greater than the denominator.
Examples: 5/5, 7/4, 9/3

🧠 These fractions represent values equal to or greater than 1.

🔴 Mixed Fractions (Mixed Numbers)
A mixed fraction has two parts: a whole number and a proper fraction.
Examples: 1 3/4, 2 1/2

➡️ Mixed fractions help us understand quantities greater than one more clearly.

💡 Concept: Improper fractions and mixed fractions represent the same quantity in different forms.

🔵 5. Converting Improper Fractions to Mixed Fractions
To convert an improper fraction into a mixed fraction:

🔵 Divide the numerator by the denominator
🔵 The quotient becomes the whole number
🔵 The remainder becomes the numerator

Example idea:
7/3 = 2 1/3

✏️ Note: The denominator remains the same in the fractional part.

🔵 6. Converting Mixed Fractions to Improper Fractions
To convert a mixed fraction into an improper fraction:

🔵 Multiply the whole number by the denominator
🔵 Add the numerator
🔵 Write the result over the same denominator

Example idea:
2 1/4 = 9/4

✔️ This form is useful for calculations.

🔵 7. Equivalent Fractions
Fractions are called equivalent if they represent the same part of a whole.

Examples:
1/2 = 2/4 = 3/6

🧠 Equivalent fractions are formed by multiplying or dividing the numerator and denominator by the same number.

💡 Concept: The value of a fraction does not change if both numerator and denominator are multiplied or divided by the same non-zero number.

🔵 8. Simplest Form of a Fraction
A fraction is in simplest form when the numerator and denominator have no common factor other than 1.

Example idea:
4/8 = 1/2

🟡 Simplifying fractions makes them easier to compare and use.

🔵 9. Like and Unlike Fractions

🟢 Like Fractions
Fractions with the same denominator.
Examples: 2/7, 5/7, 6/7

🔴 Unlike Fractions
Fractions with different denominators.
Examples: 1/3, 2/5, 4/7

🔵 10. Comparing Fractions
Like fractions are compared using numerators.
Unlike fractions are first converted into like fractions, then compared.

💡 Concept: After equalizing denominators, the fraction with the larger numerator is greater.

🔵 11. Fractions on the Number Line
Fractions can be shown on a number line by dividing the distance between two whole numbers into equal parts.

🧠 This helps visualize size and order of fractions.

🔵 12. Real-Life Applications of Fractions
Fractions are used in:

🍳 Cooking
💰 Money
⏰ Time
📏 Measurements

✔️ Fractions help in daily decision-making and logical thinking.

Summary

Fractions represent parts of a whole or a collection and are written as a/b. Equal division is essential for meaningful fractions. Fractions may be proper, improper, or mixed, and improper fractions can be converted into mixed fractions and vice versa.

Equivalent fractions show the same value in different forms, while simplifying fractions makes them easier to understand. Fractions may be like or unlike based on denominators. Comparing fractions and representing them on number lines helps understand their relative sizes. Fractions play an important role in daily life, making them a fundamental concept in mathematics.

📝 Quick Recap

🔵 Fraction shows a part of a whole or collection
🟢 Numerator = parts taken, Denominator = total parts
🟡 Proper < 1, Improper ≥ 1, Mixed = whole + fraction
🔴 Equivalent fractions have the same value
✔️ Fractions are used in time, money, and measurements

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TEXTBOOK QUESTIONS

🌿 FIGURE IT OUT

🌿 FRACTIONALUNITS AND EQUAL SHARES

🔒 ❓ Question

1. Three guavas together weigh 1 kg. If they are roughly of the same size, each guava will roughly weigh ___ kg.

📌 ✅ Answer:
🔹 Total weight of 3 guavas is 1 kg
🔹 Weight of 1 guava = 1 ÷ 3 kg
🔸 This gives one equal share out of 3
🔹 Each guava weighs 1/3 kg

🔒 ❓ Question
2. A wholesale merchant packed 1 kg of rice in four packets of equal weight. The weight of each packet is ___ kg.

📌 ✅ Answer:
🔹 Total rice weight is 1 kg
🔹 Number of equal packets is 4
🔹 Weight of each packet = 1 ÷ 4 kg
🔸 One part out of four equal parts
🔹 Each packet weighs 1/4 kg

🔒 ❓ Question
3. Four friends ordered 3 glasses of sugarcane juice and shared it equally among themselves. Each one drank ___ glass of sugarcane juice.

📌 ✅ Answer:
🔹 Total juice ordered is 3 glasses
🔹 Number of friends sharing is 4
🔹 Juice per friend = 3 ÷ 4 glass
🔸 Each friend gets three parts out of four
🔹 Each one drank 3/4 glass

🔒 ❓ Question
4. The big fish weighs 1/2 kg. The small one weighs 1/4 kg. Together they weigh ___ kg.

📌 ✅ Answer:
🔹 Weight of big fish = 1/2 kg
🔹 Weight of small fish = 1/4 kg
🔹 Convert to like fractions
🔸 1/2 = 2/4
🔹 Add the weights
🔸 2/4 + 1/4 = 3/4
🔹 Together they weigh 3/4 kg

🔒 ❓ Question
5. Arrange these fraction words in order of size from the smallest to the biggest in the empty box below:
One and a half, three quarters, one and a quarter, half, quarter, two and a half.

📌 ✅ Answer:
🔹 Convert words into fractions
🔸 quarter = 1/4
🔸 half = 1/2
🔸 three quarters = 3/4
🔸 one and a quarter = 5/4
🔸 one and a half = 3/2
🔸 two and a half = 5/2

🔹 Arrange from smallest to biggest
🔸 1/4 < 1/2 < 3/4 < 5/4 < 3/2 < 5/2

🔹 Final order (in words):
🔸 quarter, half, three quarters, one and a quarter, one and a half, two and a half

🌿 FRACTIONA UNIT AS PARTS OF WHOLE

🔒 ❓ Question
The figures below show different fractional units of a whole chikki.
How much of a whole chikki is each piece?

🔒 ❓ Question (a)

📌 ✅ Answer:
🔹 In the given figure, the whole chikki is divided into 12 equal rectangular parts
🔹 The shown piece matches one such equal part
🔸 Fractional unit means one equal part of the whole
🔹 Therefore, the piece represents 1/12 of a chikki

🔒 ❓ Question (b)

📌 ✅ Answer:
🔹 The whole chikki is divided into 4 equal triangular parts
🔹 The given triangle is exactly one of those equal parts
🔸 Shape does not matter, equality of area matters
🔹 Therefore, the piece represents 1/4 of a chikki

🔒 ❓ Question (c)

📌 ✅ Answer:
🔹 Here, the whole chikki is divided into 8 equal triangular parts
🔹 The shown triangle matches one equal part
🔸 So it is one out of eight equal parts
🔹 Therefore, the piece represents 1/8 of a chikki

🔒 ❓ Question (d)

📌 ✅ Answer:
🔹 The whole chikki is divided into 6 equal vertical strips
🔹 The given strip is one such equal strip
🔸 Each equal strip represents the same fraction
🔹 Therefore, the piece represents 1/6 of a chikki

🔒 ❓ Question (e)

📌 ✅ Answer:
🔹 Even though the piece is L-shaped, the whole chikki is divided into 8 equal parts
🔹 This L-shaped piece covers exactly one of those equal areas
🔸 Fraction depends on area, not shape
🔹 Therefore, the piece represents 1/8 of a chikki

🔒 ❓ Question (f)

📌 ✅ Answer:
🔹 The whole chikki is divided into 6 equal triangular parts
🔹 The given triangle matches one equal triangular part
🔸 So it is one out of six equal parts
🔹 Therefore, the piece represents 1/6 of a chikki

🔒 ❓ Question (g)

📌 ✅ Answer:
🔹 The whole chikki is divided into 24 equal small squares
🔹 The given small square is one of these equal parts
🔸 So it is one out of twenty-four equal parts
🔹 Therefore, the piece represents 1/24 of a chikki

🔒 ❓ Question (h)

📌 ✅ Answer:
🔹 The whole chikki is divided into 24 equal triangular parts
🔹 The given small triangle is one such equal part
🔸 Different shape, same area
🔹 Therefore, the piece represents 1/24 of a chikki

📌 ✅ Teacher’s Classroom Summary
🔹 Fractional unit means one equal part of a whole
🔹 Equal area is important, not shape
🔹 A whole can be divided in many ways, but the fraction depends on the number of equal parts
🔹 This is why different shapes can represent the same fraction

🌿 MEASURING USING FRACTIONAL UNITS

🔒 ❓ Figure it Out – Question 1
Continue this table of 1/2 for 2 more steps.

📌 ✅ Answer:
🔹 The table in the image is already shown up to 5 times half.
🔹 So the next 2 steps are for 6 times half and 7 times half.

🔹 Step for 6 times half
🔸 6 times 1/2 = 6/2 = 3

🔹 Step for 7 times half
🔸 7 times 1/2 = 7/2 = 3 1/2

🔹 Final (two more steps)
🔸 6 times 1/2 = 3
🔸 7 times 1/2 = 7/2 (or 3 1/2)

🔒 ❓ Figure it Out – Question 2
Can you create a similar table for 1/4?

📌 ✅ Answer:
🔹 Here the fractional unit is 1/4.
🔹 We keep adding 1/4 each time.

🔹 Table (first four steps to reach a whole)
🔸 1 time 1/4 = 1/4
🔸 2 times 1/4 = 1/4 + 1/4 = 2/4
🔸 3 times 1/4 = 3/4
🔸 4 times 1/4 = 4/4 = 1

🔹 Teacher takeaway
🔸 4 times 1/4 makes 1 whole.

🔒 ❓ Figure it Out – Question 3
Make 1/3 using a paper strip. Can you use this to also make 1/6?

📌 ✅ Answer:
🔹 To make 1/3
🔸 Divide the strip into 3 equal parts.
🔸 One part is 1/3.

🔹 To make 1/6 using 1/3
🔸 Take one 1/3 part and divide it into 2 equal parts.
🔸 Each new part is 1/6.

🔹 Final
🔸 Yes, we can make 1/6 using the strip made for 1/3.

🔒 ❓ Figure it Out – Question 4(a)
Draw a picture and write an addition statement as above to show: 5 times 1/4 of a roti

📌 ✅ Answer:
🔹 Addition statement (collecting 1/4 five times)
🔸 1/4 + 1/4 + 1/4 + 1/4 + 1/4

🔹 Total
🔸 = 5/4

🔒 ❓ Figure it Out – Question 4(b)
Draw a picture and write an addition statement as above to show: 9 times 1/4 of a roti

📌 ✅ Answer:
🔹 Addition statement (collecting 1/4 nine times)
🔸 1/4 + 1/4 + 1/4 + 1/4 + 1/4 + 1/4 + 1/4 + 1/4 + 1/4

🔹 Total
🔸 = 9/4

🔒 ❓ Figure it Out – Question 5
Match each fractional unit with the correct picture: 1/3, 1/5, 1/8, 1/6

📌 ✅ Answer:
🔹 Match by counting how many equal parts the circle is divided into.
🔸 Circle divided into 3 equal parts, one part shaded = 1/3
🔸 Circle divided into 5 equal parts, one part shaded = 1/5
🔸 Circle divided into 8 equal parts, one part shaded = 1/8
🔸 Circle divided into 6 equal parts, one part shaded = 1/6

🌿 MARKING FRACTIONAL LENGTHS ON THE NUMBER LINE

🔒 ❓ Question 1
On a number line, draw lines of lengths 1/10, 3/10, and 4/5.

📌 ✅ Answer:
🔹 First, understand the unit
🔸 On a number line, the distance from 0 to 1 is taken as 1 whole unit

🔹 Marking 1/10
🔸 Divide the segment from 0 to 1 into 10 equal parts
🔸 One such small part represents 1/10

🔹 Marking 3/10
🔸 Take three equal parts of size 1/10 starting from 0
🔸 So, 3/10 lies after three small divisions

🔹 Marking 4/5
🔸 Divide the segment from 0 to 1 into 5 equal parts
🔸 Each part is 1/5
🔸 Take 4 such parts → this gives 4/5, which lies close to 1

🔹 Teacher note:
🔸 Bigger denominator → smaller pieces
🔸 4/5 is much longer than 3/10 because 4/5 is closer to 1

🔒 ❓ Question 2
Write five more fractions of your choice and mark them on the number line.

📌 ✅ Answer:
🔹 Goal: Choose any 5 fractions (between 0 and 1 is easiest) and show where they lie on the number line.
🔹 Best classroom method: Use one common denominator so all fractions fit on the same set of equal divisions.

🔹 Step 1: Choose 5 fractions (example set)
🔸 1/10, 2/10, 4/10, 6/10, 9/10

🔹 Step 2: Prepare the number line from 0 to 1
🔸 Mark 0 and 1.
🔸 Divide the segment from 0 to 1 into 10 equal parts (because denominator is 10).
🔸 Each small division represents 1/10.

🔹 Step 3: Mark each fraction by counting equal parts from 0
🔸 1/10 is at the 1st tick after 0.
🔸 2/10 is at the 2nd tick after 0.
🔸 4/10 is at the 4th tick after 0.
🔸 6/10 is at the 6th tick after 0.
🔸 9/10 is at the 9th tick after 0 (very close to 1).

🔹 Step 4: Teacher check (quick sense check)
🔸 Fractions with smaller numerator are closer to 0.
🔸 Fractions with numerator near the denominator are closer to 1.
🔸 So 9/10 must be near 1, and 1/10 must be near 0.

🔹 Extra teacher tip (if your chosen fractions have different denominators)
🔸 Convert them to a common denominator first.
🔸 Example: If you choose 1/2 and 3/5, you can use denominator 10.
🔸 1/2 = 5/10 and 3/5 = 6/10, then mark using 10 equal parts.

🔒 ❓ Question 3
How many fractions lie between 0 and 1?

📌 ✅ Answer:
🔹 There are infinitely many fractions between 0 and 1

🔹 Explanation
🔸 Between 0 and 1/2, we can write 1/4
🔸 Between 1/4 and 1/2, we can write 3/8
🔸 Between any two fractions, we can always find another fraction

🔹 Conclusion:
🔸 Fractions between 0 and 1 never end

🔒 ❓ Question 4
What is the length of the blue line and black line shown below?
📌 ✅ Answer:

🔹 Blue line
🔸 The distance from 0 to 1 is 1 unit
🔸 It is divided into 2 equal parts
🔸 Each part is 1/2
🔸 The blue line covers one such part

📌 ✅ Blue line length = 1/2 unit

🔹 Black line
🔹 The black line starts at 0 and ends halfway between 1 and 2.
🔸 Halfway between 1 and 2 is 3/2.
🔹 So the black line length is 3/2 units.

📌 ✅ Final:
🔹 Black line length = 3/2

🔒 ❓ Question 5
Write the fraction that gives the lengths of the black lines in the respective boxes.

📌 ✅ Answer:
(Using the given number line divided into fifths)

🔹 The scale shows:
🔸 0, 1/5, 2/5, 3/5, 4/5, 1, … , 2

🔹 Observing the black lines one by one:

🔹 First black line
🔸 Ends at 1 + 1/5
📌 ✅ Fraction = 6/5

🔹 Second black line
🔸 Ends at 1 + 2/5
📌 ✅ Fraction = 7/5

🔹 Third black line
🔸 Ends at 1 + 3/5
📌 ✅ Fraction = 8/5

🔹 Fourth black line
🔸 Ends at 1 + 4/5
📌 ✅ Fraction = 9/5

🔹 Teacher note:
🔸 Improper fractions show lengths greater than 1
🔸 Counting fractional units helps us measure long lengths easily

🌿 MIXED FRACTIONS

🌟 Figure it Out

🔒 ❓ Question 1
How many whole units are there in 7/2?

📌 ✅ Answer:
🔹 Step 1: Understand 7/2
🔸 It means 7 parts, each of size 1/2.

🔹 Step 2: Form whole units
🔸 2 halves make 1 whole.

🔹 Step 3: Divide
🔸 7 ÷ 2 = 3 wholes and 1 half left.

🔹 Step 4: Mixed form
🔸 7/2 = 3 + 1/2 = 3 1/2.

📌 ✅ Final:
🔹 Number of whole units = 3

🔒 ❓ Question 2
How many whole units are there in 4/3 and in 7/3?

📌 ✅ Answer:

🔹 For 4/3
🔸 Meaning: 4 parts of size 1/3.
🔸 3 parts of 1/3 make 1 whole.
🔸 4 ÷ 3 = 1 whole and 1/3 left.

📌 ✅ Final (4/3):
🔹 Whole units = 1

🔹 For 7/3
🔸 Meaning: 7 parts of size 1/3.
🔸 3 parts of 1/3 make 1 whole.
🔸 7 ÷ 3 = 2 wholes and 1/3 left.

📌 ✅ Final (7/3):
🔹 Whole units = 2

🌿 Figure it Out (Next Set)

🔒 ❓ Question 1
Figure out the number of whole units in each of the following fractions:
a) 8/3 b) 11/5 c) 9/4

📌 ✅ Answer:

🔹 (a) 8/3
🔸 3 thirds make 1 whole.
🔸 8 ÷ 3 = 2 wholes and 2/3 left.

📌 ✅ Final:
🔹 Whole units = 2

🔹 (b) 11/5
🔸 5 fifths make 1 whole.
🔸 11 ÷ 5 = 2 wholes and 1/5 left.

📌 ✅ Final:
🔹 Whole units = 2

🔹 (c) 9/4
🔸 4 quarters make 1 whole.
🔸 9 ÷ 4 = 2 wholes and 1/4 left.

📌 ✅ Final:
🔹 Whole units = 2

🔒 ❓ Question 2
Can all fractions greater than 1 be written as such mixed numbers?

📌 ✅ Answer:
🔹 Yes, every fraction greater than 1 can be written as a mixed number.
🔸 This is because the numerator contains one or more complete groups of the denominator.

📌 ✅ Final:
🔹 Yes, all fractions greater than 1 can be written as mixed numbers.

🔒 ❓ Question 3
Write the following fractions as mixed fractions:
a) 9/2 b) 9/5 c) 21/19 d) 47/9 e) 12/11 f) 19/6

📌 ✅ Answer:

🔹 (a) 9/2
🔸 9 ÷ 2 = 4 remainder 1
📌 ✅ Final: 4 1/2

🔹 (b) 9/5
🔸 9 ÷ 5 = 1 remainder 4
📌 ✅ Final: 1 4/5

🔹 (c) 21/19
🔸 21 ÷ 19 = 1 remainder 2
📌 ✅ Final: 1 2/19

🔹 (d) 47/9
🔸 47 ÷ 9 = 5 remainder 2
📌 ✅ Final: 5 2/9

🔹 (e) 12/11
🔸 12 ÷ 11 = 1 remainder 1
📌 ✅ Final: 1 1/11

🔹 (f) 19/6
🔸 19 ÷ 6 = 3 remainder 1
📌 ✅ Final: 3 1/6

🌟 Figure it Out

🔒 ❓ Question
Write the following mixed numbers as fractions:

a) 3 1/4
b) 7 2/3
c) 9 4/9
d) 3 1/6
e) 2 3/11
f) 3 9/10

📌 ✅ Answer (Teacher-style explanation)

🔹 Rule to remember:
🔸 To convert a mixed number into an improper fraction:
🔸 (Whole number × Denominator + Numerator) / Denominator

🔒 ❓ (a) 3 1/4

📌 ✅ Answer:
🔹 Step 1: Multiply the whole number by the denominator
🔸 3 × 4 = 12

🔹 Step 2: Add the numerator
🔸 12 + 1 = 13

🔹 Step 3: Keep the same denominator
🔸 Fraction = 13/4

📌 ✅ Final:
🔹 3 1/4 = 13/4

🔒 ❓ (b) 7 2/3

📌 ✅ Answer:
🔹 Step 1: 7 × 3 = 21
🔹 Step 2: 21 + 2 = 23
🔹 Step 3: Write over the same denominator

📌 ✅ Final:
🔹 7 2/3 = 23/3

🔒 ❓ (c) 9 4/9

📌 ✅ Answer:
🔹 Step 1: 9 × 9 = 81
🔹 Step 2: 81 + 4 = 85
🔹 Step 3: Write over 9

📌 ✅ Final:
🔹 9 4/9 = 85/9

🔒 ❓ (d) 3 1/6

📌 ✅ Answer:
🔹 Step 1: 3 × 6 = 18
🔹 Step 2: 18 + 1 = 19
🔹 Step 3: Write over 6

📌 ✅ Final:
🔹 3 1/6 = 19/6

🔒 ❓ (e) 2 3/11

📌 ✅ Answer:
🔹 Step 1: 2 × 11 = 22
🔹 Step 2: 22 + 3 = 25
🔹 Step 3: Write over 11

📌 ✅ Final:
🔹 2 3/11 = 25/11

🔒 ❓ (f) 3 9/10

📌 ✅ Answer:
🔹 Step 1: 3 × 10 = 30
🔹 Step 2: 30 + 9 = 39
🔹 Step 3: Write over 10

📌 ✅ Final:
🔹 3 9/10 = 39/10

🌿 EQUIVALENT FRACTIONS

🔒 ❓ Question 1. Are 3/6, 4/8, 5/10 equivalent fractions? Why?

📌 ✅ Answer:
🔹 Equivalent fractions mean they represent the same value (same part of a whole).
🔹 Step 1: Simplify 3/6
🔸 3/6 = (3 ÷ 3)/(6 ÷ 3)
🔸 3/6 = 1/2
🔹 Step 2: Simplify 4/8
🔸 4/8 = (4 ÷ 4)/(8 ÷ 4)
🔸 4/8 = 1/2
🔹 Step 3: Simplify 5/10
🔸 5/10 = (5 ÷ 5)/(10 ÷ 5)
🔸 5/10 = 1/2
📌 ✅ Final:
🔹 Yes, 3/6, 4/8, 5/10 are equivalent because all simplify to 1/2.

🔒 ❓ Question 2. Write two equivalent fractions for 2/6.

📌 ✅ Answer:
🔹 Step 1: Simplify 2/6
🔸 2/6 = (2 ÷ 2)/(6 ÷ 2)
🔸 2/6 = 1/3
🔹 Step 2: Make another equivalent fraction by multiplying numerator and denominator by the same number
🔸 1/3 = (1 × 2)/(3 × 2)
🔸 1/3 = 2/6
🔹 Step 3: One more equivalent fraction
🔸 1/3 = (1 × 4)/(3 × 4)
🔸 1/3 = 4/12
📌 ✅ Final:
🔹 Two equivalent fractions for 2/6 are 1/3 and 4/12.

🔒 ❓ Question 3. 4/6 = / = / = / = ………. (Write as many as you can)

📌 ✅ Answer:
🔹 Step 1: Simplify 4/6
🔸 4/6 = (4 ÷ 2)/(6 ÷ 2)
🔸 4/6 = 2/3
🔹 Step 2: Write equivalent fractions by multiplying numerator and denominator by the same number
🔸 2/3 = (2 × 2)/(3 × 2) = 4/6
🔸 2/3 = (2 × 3)/(3 × 3) = 6/9
🔸 2/3 = (2 × 4)/(3 × 4) = 8/12
🔸 2/3 = (2 × 5)/(3 × 5) = 10/15
🔸 2/3 = (2 × 6)/(3 × 6) = 12/18
📌 ✅ Final:
🔹 4/6 = 2/3 = 6/9 = 8/12 = 10/15 = 12/18 = ……….

🔒 ❓ Figure it Out

1. Three rotis are shared equally by four children. Show the division in the picture and write a fraction for how much each child gets. Also, write the corresponding division facts, addition facts, and, multiplication facts.
   Fraction of roti each child gets is ____.
   Division fact:
   Addition fact:
   Multiplication fact:
   Compare your picture and answers with your classmates!

📌 ✅ Answer:
🔹 Step 1: Total rotis = 3
🔹 Step 2: Total children = 4
🔹 Step 3: Share per child = Total rotis ÷ Total children
🔸 Share per child = 3 ÷ 4
🔸 Share per child = 3/4
📌 ✅ Fraction of roti each child gets is:
🔹 3/4
📌 ✅ Division fact:
🔹 3 ÷ 4 = 3/4
📌 ✅ Addition fact:
🔹 3/4 = 1/4 + 1/4 + 1/4
📌 ✅ Multiplication fact:
🔹 3 = 4 × 3/4

🔒 ❓ 2. Draw a picture to show how much each child gets when 2 rotis are shared equally by 4 children. Also, write the corresponding division facts, addition facts, and multiplication facts.

📌 ✅ Answer:
🔹 Step 1: Total rotis = 2
🔹 Step 2: Total children = 4
🔹 Step 3: Share per child = 2 ÷ 4
🔸 2 ÷ 4 = 2/4
🔸 2/4 = 1/2
📌 ✅ Fraction each child gets:
🔹 1/2
📌 ✅ Division fact:
🔹 2 ÷ 4 = 1/2
📌 ✅ Addition fact:
🔹 1/2 = 1/4 + 1/4
📌 ✅ Multiplication fact:
🔹 2 = 4 × 1/2

🔒 ❓ 3. Anil was in a group where 2 cakes were divided equally among 5 children. How much cake would Anil get?

📌 ✅ Answer:
🔹 Step 1: Total cakes = 2
🔹 Step 2: Total children = 5
🔹 Step 3: Share per child = 2 ÷ 5
🔸 2 ÷ 5 = 2/5
📌 ✅ Final:
🔹 Anil would get 2/5 cake.

🔒 ❓ Follow-up (Thinking Question)
If there are 10 children, how many cakes are needed so that they get the same amount of cake as Anil?

📌 ✅ Answer:
🔹 Anil’s share = 2/5 cake per child
🔹 For 10 children:
🔸 Required cakes = 10 × 2/5 = 20/5 = 4

📌 ✅ Final:
🔹 4 cakes are needed.

📘 Figure it Out

🔒 ❓ a. 5 glasses of juice shared equally among 4 friends is the same as ___ glasses of juice shared equally among 8 friends.
So, 5/4 = ⬜ / 8.

📌 ✅ Answer:

🔹 Step 1: Sharing 5 glasses among 4 friends means each friend gets
🔸 5 ÷ 4 = 5/4 glass

🔹 Step 2: Number of friends increases from 4 to 8
🔸 This is multiplying by 2

🔹 Step 3: To keep each friend’s share the same, multiply the number of glasses by the same number

🔹 Step 4:
🔸 5 × 2 = 10 glasses
🔸 4 × 2 = 8 friends

🔹 Step 5:
🔸 5/4 = 10/8

📌 Filled blank:
🔸 10

📌 Final:
🔹 So, 5/4 = 10/8

🔒 ❓ b. 4 kg of potatoes divided equally in 3 bags is the same as 12 kg of potatoes divided equally in ___ bags.
So, 4/3 = 12/⬜.

📌 ✅ Answer:

🔹 Step 1: 4 kg divided into 3 bags means each bag gets
🔸 4/3 kg

🔹 Step 2: Potatoes increase from 4 kg to 12 kg
🔸 4 × 3 = 12

🔹 Step 3: To keep the amount in each bag the same, multiply the number of bags by 3

🔹 Step 4:
🔸 3 × 3 = 9 bags

🔹 Step 5:
🔸 4/3 = 12/9

📌 Filled blank:
🔸 9

📌 Final:
🔹 So, 4/3 = 12/9

🔒 ❓ c. 7 rotis divided among 5 children is the same as ___ rotis divided among ___ children.
So, 7/5 = ⬜ / ⬜.

📌 ✅ Answer:

🔹 Step 1: 7 rotis divided among 5 children means each child gets
🔸 7/5 roti

🔹 Step 2: Multiply both rotis and children by the same number to get an equivalent fraction

🔹 Step 3: Multiply by 2

🔹 Step 4:
🔸 7 × 2 = 14 rotis
🔸 5 × 2 = 10 children

🔹 Step 5:
🔸 7/5 = 14/10

📌 Filled blanks:
🔸 14 rotis, 10 children

📌 Final:
🔹 So, 7/5 = 14/10

🌿 EXPRESSING A FRACTION IN TOWEST TERMS OR IN ITS SIMPLEST FORM

🔒 ❓ Figure it Out
Question: Express the following fractions in lowest terms:

a. 17/51
b. 64/144
c. 126/147
d. 525/112

📌 ✅ Answer

🔒 ❓ (a) 17/51

📌 ✅ Answer:
🔹 Step 1: Find the common factor of 17 and 51
🔹 Step 2: 51 = 17 × 3
🔹 Step 3: Divide numerator and denominator by 17

17 ÷ 17 = 1
51 ÷ 17 = 3

🔹 Lowest form = 1/3

🔒 ❓ (b) 64/144

📌 ✅ Answer:
🔹 Step 1: Find the greatest common factor (GCF) of 64 and 144
🔹 Step 2:
64 = 2 × 2 × 2 × 2 × 2 × 2
144 = 2 × 2 × 2 × 2 × 3 × 3

🔹 Common factor = 2 × 2 × 2 × 2 = 16

🔹 Step 3: Divide numerator and denominator by 16

64 ÷ 16 = 4
144 ÷ 16 = 9

🔹 Lowest form = 4/9

🔒 ❓ (c) 126/147

📌 ✅ Answer:
🔹 Step 1: Find common factors
126 = 2 × 3 × 3 × 7
147 = 3 × 7 × 7

🔹 Common factor = 3 × 7 = 21

🔹 Step 2: Divide numerator and denominator by 21

126 ÷ 21 = 6
147 ÷ 21 = 7

🔹 Lowest form = 6/7

🔒 ❓ (d) 525/112

📌 ✅ Answer:
🔹 Step 1: Prime factorisation
525 = 3 × 5 × 5 × 7
112 = 2 × 2 × 2 × 2 × 7

🔹 Common factor = 7

🔹 Step 2: Divide numerator and denominator by 7

525 ÷ 7 = 75
112 ÷ 7 = 16

🔹 Lowest form = 75/16

🌿 COMPARING FRACTIONS

🔒 ❓ 1. Compare the following fractions and justify your answers:

🔒 ❓ (a) 8/3 , 5/2

📌 ✅ Answer:
🔹 We compare the two fractions using cross-multiplication
🔸 8 × 2 = 16
🔸 5 × 3 = 15
🔹 Since 16 > 15
🔹 Therefore, 8/3 > 5/2

🔒 ❓ (b) 4/9 , 3/7

📌 ✅ Answer:
🔹 Use cross-multiplication
🔸 4 × 7 = 28
🔸 3 × 9 = 27
🔹 Since 28 > 27
🔹 Therefore, 4/9 > 3/7

🔒 ❓ (c) 7/10 , 9/14

📌 ✅ Answer:
🔹 Cross-multiply both fractions
🔸 7 × 14 = 98
🔸 9 × 10 = 90
🔹 Since 98 > 90
🔹 Therefore, 7/10 > 9/14

🔒 ❓ (d) 12/5 , 8/5

📌 ✅ Answer:
🔹 Both fractions have the same denominator
🔸 Compare numerators: 12 and 8
🔹 Since 12 > 8
🔹 Therefore, 12/5 > 8/5

🔒 ❓ (e) 9/4 , 5/2

📌 ✅ Answer:
🔹 Convert to the same denominator
🔸 5/2 = 10/4
🔹 Compare 9/4 and 10/4
🔹 Since 10/4 > 9/4
🔹 Therefore, 5/2 > 9/4

🔒 ❓ 2. Write the following fractions in ascending order.

🔒 ❓ (a) 7/10 , 11/15 , 2/5

📌 ✅ Answer:
🔹 Find LCM of 10, 15 and 5
🔸 LCM = 30
🔸 7/10 = 21/30
🔸 11/15 = 22/30
🔸 2/5 = 12/30
🔹 Arrange from smallest to greatest
🔹 2/5 < 7/10 < 11/15

🔒 ❓ (b) 19/24 , 5/6 , 7/12

📌 ✅ Answer:
🔹 LCM of 24, 6 and 12 is 24
🔸 19/24 = 19/24
🔸 5/6 = 20/24
🔸 7/12 = 14/24
🔹 Arrange in ascending order
🔹 7/12 < 19/24 < 5/6

🔒 ❓ 3. Write the following fractions in descending order.

🔒 ❓ (a) 25/16 , 7/8 , 13/4 , 17/32

📌 ✅ Answer:
🔹 Convert all fractions to denominator 32
🔸 25/16 = 50/32
🔸 7/8 = 28/32
🔸 13/4 = 104/32
🔸 17/32 = 17/32
🔹 Arrange from greatest to smallest
🔹 13/4 > 25/16 > 7/8 > 17/32

🔒 ❓ (b) 3/4 , 12/5 , 7/12 , 5/4

📌 ✅ Answer:
🔹 Convert to decimals for easy comparison
🔸 12/5 = 2.4
🔸 5/4 = 1.25
🔸 3/4 = 0.75
🔸 7/12 ≈ 0.58
🔹 Arrange from greatest to smallest
🔹 12/5 > 5/4 > 3/4 > 7/12

🌿 ADDITION AND SUBTRACTION OF FRACTIONS

🔒 ❓ Figure it Out

🔒 ❓ 1. Add the following fractions using Brahmagupta’s method:

🔒 ❓ a. 2/7 + 5/7 + 6/7
📌 ✅ Answer:
🔹 Step 1: Same denominator, so add numerators
🔹 Step 2: (2 + 5 + 6)/7
🔹 Step 3: 13/7
🔹 Final: 13/7 (= 1 6/7)

🔒 ❓ b. 3/4 + 1/3
📌 ✅ Answer:
🔹 Step 1: Use Brahmagupta’s rule: a/b + c/d = (ad + bc)/(bd)
🔹 Step 2: 3/4 + 1/3 = (33 + 41)/(43)
🔹 Step 3: (9 + 4)/12
🔹 Step 4: 13/12
🔹 Final: 13/12 (= 1 1/12)

🔒 ❓ c. 2/3 + 5/6
📌 ✅ Answer:
🔹 Step 1: 2/3 + 5/6 = (26 + 35)/(3*6)
🔹 Step 2: (12 + 15)/18
🔹 Step 3: 27/18
🔹 Step 4: 27/18 = 3/2
🔹 Final: 3/2 (= 1 1/2)

🔒 ❓ d. 2/3 + 2/7
📌 ✅ Answer:
🔹 Step 1: 2/3 + 2/7 = (27 + 32)/(3*7)
🔹 Step 2: (14 + 6)/21
🔹 Step 3: 20/21
🔹 Final: 20/21

🔒 ❓ e. 3/4 + 1/3 + 1/5
📌 ✅ Answer:
🔹 Step 1: First add 3/4 + 1/3
🔹 Step 2: 3/4 + 1/3 = (33 + 41)/(43) = (9 + 4)/12 = 13/12
🔹 Step 3: Now add 13/12 + 1/5
🔹 Step 4: 13/12 + 1/5 = (135 + 121)/(125)
🔹 Step 5: (65 + 12)/60
🔹 Step 6: 77/60
🔹 Final: 77/60 (= 1 17/60)

🔒 ❓ f. 2/3 + 4/5
📌 ✅ Answer:
🔹 Step 1: 2/3 + 4/5 = (25 + 34)/(3*5)
🔹 Step 2: (10 + 12)/15
🔹 Step 3: 22/15
🔹 Final: 22/15 (= 1 7/15)

🔒 ❓ g. 4/5 + 2/3
📌 ✅ Answer:
🔹 Step 1: 4/5 + 2/3 = (43 + 52)/(5*3)
🔹 Step 2: (12 + 10)/15
🔹 Step 3: 22/15
🔹 Final: 22/15 (= 1 7/15)

🔒 ❓ h. 3/5 + 5/8
📌 ✅ Answer:
🔹 Step 1: 3/5 + 5/8 = (38 + 55)/(5*8)
🔹 Step 2: (24 + 25)/40
🔹 Step 3: 49/40
🔹 Final: 49/40 (= 1 9/40)

🔒 ❓ i. 9/2 + 5/4
📌 ✅ Answer:
🔹 Step 1: 9/2 + 5/4 = (94 + 25)/(2*4)
🔹 Step 2: (36 + 10)/8
🔹 Step 3: 46/8
🔹 Step 4: 46/8 = 23/4
🔹 Final: 23/4 (= 5 3/4)

🔒 ❓ j. 8/3 + 2/7
📌 ✅ Answer:
🔹 Step 1: 8/3 + 2/7 = (87 + 32)/(3*7)
🔹 Step 2: (56 + 6)/21
🔹 Step 3: 62/21
🔹 Final: 62/21 (= 2 20/21)

🔒 ❓ k. 3/4 + 1/3 + 1/5
📌 ✅ Answer:
🔹 Step 1: This is the same as part (e)
🔹 Step 2: 3/4 + 1/3 + 1/5 = 77/60
🔹 Final: 77/60 (= 1 17/60)

🔒 ❓ l. 2/3 + 4/5 + 3/7
📌 ✅ Answer:
🔹 Step 1: First add 2/3 + 4/5
🔹 Step 2: 2/3 + 4/5 = (25 + 34)/(35) = (10 + 12)/15 = 22/15
🔹 Step 3: Now add 22/15 + 3/7
🔹 Step 4: 22/15 + 3/7 = (227 + 153)/(157)
🔹 Step 5: (154 + 45)/105
🔹 Step 6: 199/105
🔹 Final: 199/105 (= 1 94/105)

🔒 ❓ m. 9/2 + 5/4 + 7/6
📌 ✅ Answer:
🔹 Step 1: First add 9/2 + 5/4
🔹 Step 2: 9/2 + 5/4 = (94 + 25)/(24) = (36 + 10)/8 = 23/4
🔹 Step 3: Now add 23/4 + 7/6
🔹 Step 4: 23/4 + 7/6 = (236 + 47)/(46)
🔹 Step 5: (138 + 28)/24
🔹 Step 6: 166/24
🔹 Step 7: 166/24 = 83/12
🔹 Final: 83/12 (= 6 11/12)

🔒 ❓ 2. Rahim mixes 2/3 litres of yellow paint with 3/4 litres of blue paint to make green paint. What is the volume of green paint he has made?
📌 ✅ Answer:
🔹 Step 1: Total volume = 2/3 + 3/4 litres
🔹 Step 2: 2/3 + 3/4 = (24 + 33)/(3*4)
🔹 Step 3: (8 + 9)/12
🔹 Step 4: 17/12 litres
🔹 Final: 17/12 litres (= 1 5/12 litres)

🔒 ❓ 3. Geeta bought 2/5 meter of lace and Shamim bought 3/4 meter of the same lace to put a complete border on a table cloth whose perimeter is 1 meter long. Find the total length of the lace they both have bought. Will the lace be sufficient to cover the whole border?
📌 ✅ Answer:
🔹 Step 1: Total lace = 2/5 m + 3/4 m
🔹 Step 2: 2/5 + 3/4 = (24 + 53)/(5*4)
🔹 Step 3: (8 + 15)/20
🔹 Step 4: 23/20 m
🔹 Step 5: Compare with perimeter 1 m
🔹 Step 6: 1 m = 20/20 m
🔹 Step 7: 23/20 m > 20/20 m, so it is sufficient
🔹 Step 8: Extra lace = 23/20 m – 20/20 m
🔹 Step 9: Extra lace = 3/20 m
🔹 Final: Total lace = 23/20 m (= 1 3/20 m), Yes sufficient, extra = 3/20 m

🔒 ❓ Figure it Out

🔒 ❓ 1. 5/8 − 3/8

📌 ✅ Answer:
🔹 Both fractions have the same denominator, which is 8.
🔸 When denominators are the same, subtract only the numerators.

🔹 Step 1:
5/8 − 3/8 = (5 − 3)/8

🔹 Step 2:
= 2/8

🔹 Step 3 (simplify):
2/8 = 1/4

📌 ✅ Final Answer: 1/4

🔒 ❓ 2. 7/9 − 5/9

📌 ✅ Answer:
🔹 Both fractions have the same denominator, 9.
🔸 Subtract the numerators and keep the denominator unchanged.

🔹 Step 1:
7/9 − 5/9 = (7 − 5)/9

🔹 Step 2:
= 2/9

📌 ✅ Final Answer: 2/9

🔒 ❓ 3. 10/27 − 1/27

📌 ✅ Answer:
🔹 Denominators are the same, 27.
🔸 Subtract the numerators and keep the denominator the same.

🔹 Step 1:
10/27 − 1/27 = (10 − 1)/27

🔹 Step 2:
= 9/27

🔹 Step 3 (simplify):
9/27 = 1/3

📌 ✅ Final Answer: 1/3

🔒 ❓ Figure it Out

🔒 ❓ 1. Carry out the following subtractions using Brahmagupta’s method:

🔒 ❓ a) 8/15 − 3/15

📌 ✅ Answer:
🔹 Denominators are same
🔹 Subtract numerators: 8 − 3 = 5
🔹 Result = 5/15
🔸 Simplify by dividing numerator and denominator by 5
🔹 Final Answer = 1/3

🔒 ❓ b) 2/5 − 4/15

📌 ✅ Answer:
🔹 Denominators are different
🔹 LCM of 5 and 15 = 15
🔹 Convert 2/5 = 6/15
🔹 Subtract: 6/15 − 4/15
🔹 Numerator difference = 2
🔹 Final Answer = 2/15

🔒 ❓ c) 5/6 − 4/9

📌 ✅ Answer:
🔹 LCM of 6 and 9 = 18
🔹 Convert 5/6 = 15/18
🔹 Convert 4/9 = 8/18
🔹 Subtract: 15/18 − 8/18
🔹 Numerator difference = 7
🔹 Final Answer = 7/18

🔒 ❓ d) 2/3 − 1/2

📌 ✅ Answer:
🔹 LCM of 3 and 2 = 6
🔹 Convert 2/3 = 4/6
🔹 Convert 1/2 = 3/6
🔹 Subtract: 4/6 − 3/6
🔹 Final Answer = 1/6

🔒 ❓ 2. Subtract as indicated:

🔒 ❓ a) Subtract 13/4 from 10/3

📌 ✅ Answer:
🔹 This means 10/3 − 13/4
🔹 LCM of 3 and 4 = 12
🔹 Convert 10/3 = 40/12
🔹 Convert 13/4 = 39/12
🔹 Subtract: 40/12 − 39/12
🔹 Final Answer = 1/12

🔒 ❓ b) Subtract 18/5 from 23/3

📌 ✅ Answer:
🔹 Expression = 23/3 − 18/5
🔹 LCM of 3 and 5 = 15
🔹 Convert 23/3 = 115/15
🔹 Convert 18/5 = 54/15
🔹 Subtract: 115/15 − 54/15
🔹 Final Answer = 61/15

🔒 ❓ c) Subtract 29/7 from 45/7

📌 ✅ Answer:
🔹 Denominators are same
🔹 Subtract numerators: 45 − 29 = 16
🔹 Final Answer = 16/7

🔒 ❓ 3. Solve the following problems:

🔒 ❓ a) Jaya’s school is 7/10 km from her home. She takes an auto for 1/2 km and walks the remaining distance. How much does she walk daily?

📌 ✅ Answer:
🔹 Total distance = 7/10 km
🔹 Distance by auto = 1/2 = 5/10 km
🔹 Distance walked = 7/10 − 5/10
🔹 Subtract: 2/10
🔸 Simplify by dividing by 2
🔹 Final Answer = 1/5 km

🔒 ❓ b) Jeevika takes 10/3 minutes to complete a round of the park. Namit takes 13/4 minutes. Who takes less time and by how much?

📌 ✅ Answer:
🔹 LCM of 3 and 4 = 12
🔹 Convert 10/3 = 40/12
🔹 Convert 13/4 = 39/12
🔹 Compare: 39 < 40
🔹 Namit takes less time
🔹 Difference = 40/12 − 39/12 = 1/12
🔹 Final Answer: Namit takes 1/12 minute less than Jeevika

——————————————————————————————————————————————————————————————————————————–

OTHER IMPORTANT QUESTIONS

(CBSE MODEL QUESTION PAPER)

ESPECIALLY MADE FROM THIS CHAPTER ONLY

🔵 Section A — Very Short Answer

(Q1–Q6 | 1 × 6 = 6 marks)

🔵 Question
Q1. What is a fraction?

🟢 Answer
✔️ A fraction is a number that represents a part of a whole or a part of a collection.

🔵 Question
Q2. In the fraction 5/9, which number is the denominator?

🟢 Answer
✔️ The denominator is 9.

🔵 Question
Q3. Write one example of a proper fraction.

🟢 Answer
✔️ An example of a proper fraction is 3/7.

🔵 Question
Q4. Can the denominator of a fraction be zero? Write Yes or No.

🟢 Answer
✔️ No, the denominator of a fraction can never be zero.

🔵 Question
Q5. Which fraction is greater: 1/4 or 1/2?

🟢 Answer
✔️ 1/2 is greater than 1/4.

🔵 Question
Q6. Write the fraction that represents one half.

🟢 Answer
✔️ The fraction representing one half is 1/2.

🟢 Section B — Short Answer–I

(Q7–Q12 | 2 × 6 = 12 marks)

🟢 Question
Q7. Define numerator and denominator of a fraction.

🟢 Answer
🔵 The numerator is the number that shows how many equal parts are taken.
🔵 The denominator is the number that shows into how many equal parts the whole is divided.

🟢 Question
Q8. Write two equivalent fractions of 2/3.

🟢 Answer
🔵 Step 1: Multiply numerator and denominator by 2
2/3 = 4/6

🔵 Step 2: Multiply numerator and denominator by 3
2/3 = 6/9

✔️ Two equivalent fractions are 4/6 and 6/9.

🟢 Question
Q9. Convert the improper fraction 7/4 into a mixed fraction.

🟢 Answer
🔵 Step 1: Divide numerator by denominator
7 ÷ 4 = 1 remainder 3

✔️ Mixed fraction = 1 3/4

🟢 Question
Q10. Convert the mixed fraction 2 1/5 into an improper fraction.

🟢 Answer
🔵 Step 1: Multiply the whole number by the denominator
2 × 5 = 10

🔵 Step 2: Add the numerator
10 + 1 = 11

✔️ Improper fraction = 11/5

🟢 Question
Q11. What are like fractions? Give one example.

🟢 Answer
🔵 Fractions having the same denominator are called like fractions.

✔️ Example: 3/7 and 5/7

🟢 Question
Q12. Find 1/3 of 12.

🟢 Answer
🔵 Step 1: Divide the number by the denominator
12 ÷ 3 = 4

✔️ 1/3 of 12 = 4

🟡 Section C — Short Answer–II

(Q13–Q22 | 3 × 10 = 30 marks)

🟡 Question
Q13. Convert the improper fraction 11/3 into a mixed fraction.

🟢 Answer
🔵 Step 1: Divide the numerator by the denominator
11 ÷ 3 = 3 remainder 2

✔️ Mixed fraction = 3 2/3

🟡 Question
Q14. Convert the mixed fraction 4 2/5 into an improper fraction.

🟢 Answer
🔵 Step 1: Multiply the whole number by the denominator
4 × 5 = 20

🔵 Step 2: Add the numerator
20 + 2 = 22

✔️ Improper fraction = 22/5

🟡 Question
Q15. Write any three equivalent fractions of 3/4.

🟢 Answer
🔵 Step 1: Multiply numerator and denominator by the same number

🔵 3/4 × 2/2 = 6/8
🔵 3/4 × 3/3 = 9/12
🔵 3/4 × 4/4 = 12/16

✔️ Three equivalent fractions are 6/8, 9/12, 12/16

🟡 Question
Q16. Simplify the fraction 18/24.

🟢 Answer
🔵 Step 1: Find a common factor of 18 and 24
Common factor = 6

🔵 Step 2: Divide numerator and denominator by 6
18 ÷ 6 = 3
24 ÷ 6 = 4

✔️ Simplest form = 3/4

🟡 Question
Q17. Compare 5/6 and 3/6.

🟢 Answer
🔵 Both fractions have the same denominator

🔵 Step 1: Compare the numerators
5 > 3

✔️ Therefore, 5/6 > 3/6

🟡 Question
Q18. Compare 2/3 and 3/4.

🟢 Answer
🔵 Step 1: Find the LCM of 3 and 4
LCM = 12

🔵 Step 2: Convert into like fractions
2/3 = 8/12
3/4 = 9/12

🔵 Step 3: Compare the numerators
8 < 9

✔️ Therefore, 3/4 > 2/3

🟡 Question
Q19. Find 2/5 of 20.

🟢 Answer
🔵 Step 1: Divide the number by the denominator
20 ÷ 5 = 4

🔵 Step 2: Multiply by the numerator
4 × 2 = 8

✔️ 2/5 of 20 = 8

🟡 Question
Q20. Write two like fractions and two unlike fractions.

🟢 Answer
🔵 Like fractions have the same denominator
✔️ Examples: 3/7, 5/7

🔵 Unlike fractions have different denominators
✔️ Examples: 2/3, 4/5

🟡 Question
Q21. Represent the fraction 3/4 on a number line.

🟢 Answer
🔵 Step 1: Draw a number line from 0 to 1
🔵 Step 2: Divide the segment between 0 and 1 into 4 equal parts
🔵 Step 3: Count three equal parts from 0 and mark the point

✔️ The marked point represents 3/4 on the number line.

🟡 Question
Q22. Explain why 6/8 and 3/4 are equivalent fractions.

🟢 Answer
🔵 Step 1: Simplify the fraction 6/8 by dividing numerator and denominator by the same number
6 ÷ 2 = 3
8 ÷ 2 = 4

🔵 Step 2: After simplification, the fraction becomes 3/4

✔️ Therefore, 6/8 and 3/4 represent the same part of a whole, so they are equivalent fractions.

🔴 Section D — Long Answer

(Q23–Q30 | 4 × 8 = 32 marks)

🔴 Question
Q23. Convert the mixed fraction 5 3/4 into an improper fraction. Explain each step clearly.

🟢 Answer
🔵 Step 1: Multiply the whole number by the denominator
5 × 4 = 20

🔵 Step 2: Add the numerator
20 + 3 = 23

🔵 Step 3: Write the result over the same denominator

✔️ Improper fraction = 23/4

🔴 Question
Q24. Convert the improper fraction 19/5 into a mixed fraction.

🟢 Answer
🔵 Step 1: Divide the numerator by the denominator
19 ÷ 5 = 3 remainder 4

🔵 Step 2: Write the quotient as the whole number and remainder as numerator

✔️ Mixed fraction = 3 4/5

🔴 Question
Q25. Simplify the fraction 36/48. Explain why the result is in simplest form.

🟢 Answer
🔵 Step 1: Find the greatest common factor of 36 and 48
Greatest common factor = 12

🔵 Step 2: Divide numerator and denominator by 12
36 ÷ 12 = 3
48 ÷ 12 = 4

🔵 Step 3: Check common factors of 3 and 4
They have no common factor other than 1

✔️ Simplest form = 3/4

🔴 Question
Q26. Compare the fractions 4/5 and 7/10 using the LCM method.

🟢 Answer
🔵 Step 1: Find the LCM of denominators 5 and 10
LCM = 10

🔵 Step 2: Convert both fractions into like fractions
4/5 = 8/10
7/10 = 7/10

🔵 Step 3: Compare numerators
8 > 7

✔️ Therefore, 4/5 > 7/10

🔴 Question
Q27. Find 3/8 of 40. Show all steps.

🟢 Answer
🔵 Step 1: Divide the number by the denominator
40 ÷ 8 = 5

🔵 Step 2: Multiply the result by the numerator
5 × 3 = 15

✔️ 3/8 of 40 = 15

🔴 Question
Q28. Represent the fraction 5/6 on a number line. Explain the steps.

🟢 Answer
🔵 Step 1: Draw a number line from 0 to 1
🔵 Step 2: Divide the segment between 0 and 1 into 6 equal parts
🔵 Step 3: Count five equal parts from 0 and mark the point

✔️ The marked point shows 5/6 on the number line.

🔴 Question
Q29. Write four equivalent fractions of 2/3. Explain the method used.

🟢 Answer
🔵 Step 1: Multiply numerator and denominator by the same whole number

🔵 2/3 × 2/2 = 4/6
🔵 2/3 × 3/3 = 6/9
🔵 2/3 × 4/4 = 8/12
🔵 2/3 × 5/5 = 10/15

✔️ Four equivalent fractions are 4/6, 6/9, 8/12, 10/15

🔴 Question
Q30. A ribbon is 12 metres long. Riya uses 3/4 of it for decoration. How much ribbon is left?

🟢 Answer

🔵 Step 1: Find the fraction of ribbon used
3/4 of 12 = (12 ÷ 4) × 3

🔵 Step 2: Perform the division
12 ÷ 4 = 3

🔵 Step 3: Multiply by the numerator
3 × 3 = 9

🔵 Step 4: Find the remaining ribbon
Remaining ribbon = Total ribbon − Used ribbon
12 − 9 = 3

✔️ Final Answer: 3 metres of ribbon is left.

✏️ Note:
To find the remaining part, always subtract the used part from the total quantity.

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