Which of the following statements is true about the product of two fractions, where one fraction is between 0 and 1, and the other is greater than 1?

The product is less than the number greater than 1 and greater than the number between 0 and 1.

The product is always greater than both numbers.

The product is always less than both numbers.

The product is less than the number greater than 1 and greater than the number between 0 and 1.

Assertion (A): When multiplying two fractions, if both numbers are between 0 and 1, the product is less than both the numbers. Reason (R): Multiplying by a fraction less than 1 always decreases the value.

A and R both correct, R explains A

Assertion (A): When we divide 6 by 1/4, the quotient is 24. Reason (R): When dividing a whole number by a fraction less than 1, the quotient is greater than the dividend.

A and R both correct, R explains A

Is this Class 7 Maths Chapter 8 quiz free?

Yes, this quiz on 'Working with Fractions' for CBSE Class 7 Maths is completely free to use. No registration or payment is required.

How many questions are in the quiz?

The main 'Game' mode of this quiz contains 40 questions, covering various aspects of working with fractions. There are also 'Book Questions' and 'Monthly Test' sections.

Is this quiz aligned with the NCERT syllabus?

Absolutely! All questions are carefully crafted based on the CBSE NCERT Class 7 Maths Chapter 8: 'Working with Fractions' to ensure full syllabus coverage.

What topics does this quiz cover?

This quiz covers multiplication of fractions (by whole numbers and other fractions), division of fractions, the concept of reciprocals, and solving word problems involving fractional operations.

Can I re-attempt the quiz multiple times?

Yes, you can attempt the quiz as many times as you like to practice and improve your understanding of fractions.

Are there explanations for the answers?

Yes, detailed explanations are provided for every question to help you understand the correct reasoning and learn from your mistakes.

Home › CBSE › Class 7 › Maths › WORKING WITH FRACTIONS

CBSE · Class 7 · 🧮 Maths · Chapter 8

WORKING WITH FRACTIONS

Multiplication of FractionsDivision of FractionsReciprocal of a FractionProduct of FractionsSimplifying FractionsFraction Word Problems

Chapter 8, 'Working with Fractions', introduces students to the fundamental operations of multiplication and division involving fractions. You will learn how to multiply a whole number by a fraction, multiply two fractions, understand the concept of a reciprocal, and apply these operations to solve real-world problems. This chapter builds a strong foundation for more advanced topics in mathematics by clarifying how fractions behave under these essential operations.

Multiplying a Whole Number by a Fraction

Jab hum ek whole number ko fraction se multiply karte hain, toh basically hum us fraction ko utni baar repeat kar rahe hote hain.

Concept: Whole Number × Fraction ka matlab hai Fraction ko Whole Number times add karna.
Example: 3 × 1/4 ka matlab 1/4 + 1/4 + 1/4.
Method:

Whole number ko fraction ke numerator se multiply karo.
Denominator same rakho.

Formula: a × (b/c) = (a × b) / c
Visualisation:
Imagine karo ek cake hai, uske 4 equal parts hain. Agar tum 1/4th part 3 baar lete ho, toh total 3/4th part liya.
[IMAGE: multiplying_fractions_on_a_number_line_fig1] mein dekho, tortoise 1/4 km chalta hai 1 hour mein. 3 hours mein 3 × 1/4 = 3/4 km chalta hai.
Mixed Fractions ke saath:
Agar mixed fraction hai, toh pehle usko improper fraction mein convert karo.
Phir whole number se multiply karo.
Example: 2 × 1(1/2) = 2 × (3/2) = (2 × 3) / 2 = 6/2 = 3.

Simplification: Agar numerator aur denominator mein koi common factor ho, toh multiplication se pehle ya baad mein simplify kar sakte hain. Pehle simplify karna usually easier hota hai.

🧮Formula

Multiplication of Whole Number and Fraction: Whole Number × (Numerator / Denominator) = (Whole Number × Numerator) / Denominator Example: 5 × (2/7) = (5 × 2) / 7 = 10/7

⭐Remember

Of ka matlab maths mein multiplication hota hai. Jaise 1/2 of 10 ka matlab 1/2 × 10.

Multiplying Two Fractions

Do fractions ko multiply karna matlab ek fraction ka part nikalna.

Concept: 1/2 of 1/4 ka matlab 1/2 × 1/4.
Imagine karo ek square hai, uske 1/4th part ko shade kiya. Ab us shaded part ka 1/2 nikalna hai. Toh woh original square ka 1/8 part hoga.
[IMAGE: visualizing_fraction_multiplication_fig5] aur [IMAGE: visualizing_fraction_multiplication_fig83] mein isko visually samjhaya gaya hai.
Method:

Numerators ko multiply karo.
Denominators ko multiply karo.

Formula: (a/b) × (c/d) = (a × c) / (b × d)
Historical Context: Ye formula Brahmagupta ne 628 CE mein apne 'Brāhmasphuṭasiddhānta' mein diya tha.
Simplification:
Multiplication se pehle cross-cancellation kar sakte hain. Numerator aur opposite denominator mein common factor ho toh unhe divide kar do.
Example: (2/3) × (3/4) = (2/4) = 1/2 (yahan 3 se 3 cancel ho gaya, aur 2/4 simplify ho gaya).
Area of Rectangle: Fractional sides wale rectangle ka area nikalne ke liye sides ko multiply karte hain. Area = Length × Breadth.
Example: Length = 1/2 unit, Breadth = 1/4 unit. Area = (1/2) × (1/4) = 1/8 square units.
Order of Multiplication (Commutative Property): Fractions ke multiplication mein order matter nahi karta. (a/b) × (c/d) = (c/d) × (a/b).
[IMAGE: order_of_multiplication_of_fractions_figorderofmultiplication] is property ko dikhata hai.

🧮Formula

Multiplication of Two Fractions (Brahmagupta's Formula): (a/b) × (c/d) = (a × c) / (b × d) Example: (3/5) × (1/2) = (3 × 1) / (5 × 2) = 3/10

💡Tip

Multiplication se pehle cross-cancellation karne se calculations easy ho jaati hain aur mistakes kam hoti hain. Always check for common factors diagonally.

Product of Fractions and its Relation to Numbers Multiplied

Fraction multiplication ke results ko original numbers se compare karna important hai.

Case 1: Dono numbers > 1
Agar dono fractions 1 se bade hain (ya mixed numbers hain), toh product dono numbers se bada hoga.
Example: 2 × 3 = 6 (6 > 2, 6 > 3)
Example: 1(1/2) × 2(1/3) = (3/2) × (7/3) = 7/2 = 3(1/2) (3.5 > 1.5, 3.5 > 2.33)
Case 2: Dono numbers 0 aur 1 ke beech mein
Agar dono fractions 0 aur 1 ke beech mein hain (proper fractions), toh product dono numbers se chhota hoga.
Example: (1/2) × (1/4) = 1/8 (1/8 < 1/2, 1/8 < 1/4)
Ye 'of' concept se samjha ja sakta hai: 1/2 of 1/4 matlab 1/4 ka bhi aadha, toh aur chhota ho gaya.
Case 3: Ek number 0 aur 1 ke beech, aur doosra > 1
Product 1 se bade number se chhota hoga, aur 0 se 1 ke beech wale number se bada hoga.
Example: 2 × (1/2) = 1 (1 < 2, 1 > 1/2)
Example: 5 × (1/4) = 5/4 = 1(1/4) (1.25 < 5, 1.25 > 0.25)

Ye observations estimation aur checking answers ke liye useful hain.

❗Important

Product ki Comparison:

Fraction > 1 aur Fraction > 1 $\implies$ Product > dono fractions
Fraction < 1 aur Fraction < 1 $\implies$ Product < dono fractions
Fraction < 1 aur Fraction > 1 $\implies$ Product < Fraction > 1 aur Product > Fraction < 1

Reciprocal of a Fraction

Reciprocal ka concept division of fractions mein bahut important hai.

Definition: Ek fraction ka reciprocal woh fraction hota hai jisko original fraction se multiply karne par product 1 aata hai.
Simply, numerator aur denominator ko interchange kar do.
Example: 2/3 ka reciprocal 3/2 hai, kyunki (2/3) × (3/2) = 6/6 = 1.
Whole Numbers ka Reciprocal:
Kisi whole number a ko a/1 likh sakte hain.
Toh a ka reciprocal 1/a hoga.
Example: 5 ka reciprocal 1/5.
Mixed Fractions ka Reciprocal:
Pehle mixed fraction ko improper fraction mein convert karo.
Phir improper fraction ka reciprocal nikaalo.
Example: 1(2/3) = 5/3. Iska reciprocal 3/5.
Important Points:
0 ka koi reciprocal nahi hota, kyunki 1/0 undefined hai.
1 ka reciprocal 1 hai.
-1 ka reciprocal -1 hai.

Reciprocal ko multiplicative inverse bhi kehte hain.

📖Definition

Reciprocal (Multiplicative Inverse): Ek fraction a/b ka reciprocal b/a hota hai. Jab a/b ko b/a se multiply karte hain, toh result 1 aata hai. Example: 7/9 ka reciprocal 9/7.

🚧Misconception

Students aksar mixed fraction ka reciprocal seedha ulta kar dete hain, jaise 1(2/3) ka 1(3/2) bol dete hain. Ye galat hai! Pehle improper fraction mein convert karna zaroori hai.

Division of Fractions

Fractions ko divide karna matlab reciprocal se multiply karna.

Concept: Division ko multiplication mein convert kiya ja sakta hai.
12 ÷ 4 ka matlab hai 4 × ? = 12. Answer 3.
1 ÷ (2/3) ka matlab hai (2/3) × ? = 1. Yahan ? reciprocal 3/2 hoga.
Method (Keep, Change, Flip - KCF):

Keep the first fraction (dividend) as it is.
Change the division sign ÷ to multiplication sign ×.
Flip the second fraction (divisor) to its reciprocal.

Formula: (a/b) ÷ (c/d) = (a/b) × (d/c) = (a × d) / (b × c)
Historical Context: Ye method bhi Brahmagupta ne hi apne 'Brāhmasphuṭasiddhānta' mein explain kiya tha.
Division of a Whole Number by a Fraction:
Whole number ko a/1 ki form mein likho.
Phir KCF method apply karo.
Example: 5 ÷ (1/2) = (5/1) × (2/1) = 10/1 = 10.
Division of a Fraction by a Whole Number:
Whole number ko a/1 ki form mein likho.
Phir KCF method apply karo.
Example: (3/4) ÷ 2 = (3/4) ÷ (2/1) = (3/4) × (1/2) = 3/8.
[IMAGE: dividing_a_fraction_by_a_whole_number_fig81] aur [IMAGE: visualizing_32_divided_by_4_fig82] mein isko visually samjhaya gaya hai.
Quotient ki Comparison:
Whole numbers mein Dividend ÷ Divisor mein quotient aksar dividend se chhota hota hai (e.g., 6 ÷ 3 = 2).
Fractions mein aisa hamesha nahi hota. Agar divisor 1 se chhota hai, toh quotient dividend se bada ho sakta hai.
Example: 6 ÷ (1/2) = 12 (12 > 6).
Example: (1/2) ÷ (1/4) = 2 (2 > 1/2).
Agar divisor 1 se bada hai, toh quotient dividend se chhota ho sakta hai.
Example: (1/2) ÷ 2 = 1/4 (1/4 < 1/2).

🧮Formula

Division of Fractions (KCF Method): (a/b) ÷ (c/d) = (a/b) × (d/c) Example: (3/4) ÷ (1/5) = (3/4) × (5/1) = 15/4

💡Tip

Word problems mein 'how many times' ya 'how many parts' jaise phrases aksar division indicate karte hain. Dhyan se padho ki kaunsa fraction dividend hai aur kaunsa divisor.

Easy (15)

What is the product of 5 and 3/4?
- 15/4 (correct)
- 8/4
- 5/12
- 15/20
Why: To multiply a whole number by a fraction, multiply the whole number by the numerator and keep the denominator.
The reciprocal of 2/3 is 3/2.
Why: The reciprocal of a fraction is obtained by interchanging its numerator and denominator.
When multiplying two fractions, you multiply the numerators and the __________.
Why: The rule for multiplying fractions is to multiply numerators and denominators separately.
What is 1/2 × 1/4?
- 1/8 (correct)
- 2/4
- 1/6
- 2/8
Why: Multiply the numerators and multiply the denominators.
The product of a fraction and its reciprocal is always 1.
Why: Multiplying a fraction by its reciprocal cancels out the terms, resulting in 1.
To divide by a fraction, you multiply by its __________.
Why: Division by a fraction is equivalent to multiplication by its reciprocal.
Which of the following is the correct formula for multiplying two fractions a/b and c/d?
- (a+c)/(b+d)
- (a×c)/(b×d) (correct)
- (a/d) × (c/b)
- (a-c)/(b-d)
Why: Brahmagupta's formula states to multiply numerators and denominators.
When one of the numbers being multiplied is between 0 and 1, the product is always greater than the other number.
Why: If one factor is between 0 and 1, the product is less than the other factor.
What is 1/3 of 12?
- 3
- 4 (correct)
- 6
- 9
Why: To find 'of' a number, you multiply.
The order of multiplication of fractions does not matter.
Why: Multiplication is commutative, meaning the order does not change the product.
The result of dividing 1 by a fraction is the __________ of that fraction.
Why: Dividing 1 by a fraction is the same as multiplying 1 by its reciprocal.
What is 2/5 ÷ 3?
- 6/5
- 2/15 (correct)
- 5/6
- 2/3
Why: Divide a fraction by a whole number by multiplying the denominator by the whole number.
When multiplying fractions, we can cancel common factors between a numerator and a denominator.
Why: Simplifying before multiplying makes calculations easier and avoids larger numbers.
The area of a rectangle with fractional sides is found by __________ its sides.
Why: Area of a rectangle is always length times breadth, even with fractions.
What is 1/2 ÷ 1/2?
- 1/4
- 1 (correct)
- 0
- 2
Why: Any number divided by itself (except zero) is 1.

Medium (15)

A recipe calls for 3/4 cup of flour. If you want to make half of the recipe, how much flour do you need?
- 1/4 cup
- 3/8 cup (correct)
- 3/2 cup
- 1/2 cup
Why: To make half the recipe, multiply the flour amount by 1/2.
Match the fraction with its reciprocal.
Why: The reciprocal is found by flipping the numerator and denominator.
What is the term for the number being divided in a division problem?
Why: The dividend is the number that gets divided.
Arrange the steps for dividing two fractions in the correct order:
Why: The process is: identify, find reciprocal, multiply, simplify.
Observe the diagram. What multiplication operation does it represent?
- 1/2 + 1/4
- 1/2 × 1/4 (correct)
- 1/2 ÷ 1/4
- 1/2 - 1/4
Why: The shaded area formed by overlapping regions represents multiplication of fractions.
A car travels 60 km in 1 hour. How far will it travel in 2/3 of an hour?
- 20 km
- 30 km
- 40 km (correct)
- 60 km
Why: Multiply the total distance by the fraction of the hour.
Match the operation with its result when applied to 1/2 and 1/4.
Why: Perform the multiplication and division operations carefully.
What is the term for the number by which the dividend is divided?
Why: The divisor is the number that performs the division.
Which of the following statements is true about the product of two fractions, where one fraction is between 0 and 1, and the other is greater than 1?
- The product is always greater than both numbers.
- The product is always less than both numbers.
- The product is less than the number greater than 1 and greater than the number between 0 and 1. (correct)
- The product is always 1.
Why: The product will be 'in between' the two original numbers.
A water tank is filled from a tap. If the tap is open for 1 hour, 7/10 of the tank gets filled. How much of the tank is filled if the tap is open for 1/3 hour?
- 7/30 (correct)
- 10/21
- 1/30
- 7/10
Why: Multiply the fraction of the tank filled per hour by the fraction of the hour the tap is open.
Match the division problem with its equivalent multiplication problem.
Why: Division by a fraction is multiplication by its reciprocal.
Order the following fractions from smallest to largest: 1/2, 1/4, 3/8, 5/16.
Why: Convert all fractions to a common denominator (16) to compare them.
What is the result of the division in the diagram?
- 2/5
- 1/5
- 1/10 (correct)
- 2/20
Why: The diagram shows 2/5 divided into 4 equal parts, resulting in 1/10.
If 3/4 kg of sugar is used to make 6 cakes, how much sugar is used for one cake?
- 1/8 kg (correct)
- 1/4 kg
- 3/24 kg
- 1/2 kg
Why: Divide the total sugar by the number of cakes.
The diagram shows a unit square representing 3/2. If this is divided by 4, what does each shaded part represent?
- 3/8 (correct)
- 3/2
- 3/4
- 1/2
Why: The diagram shows 3/2 (which is 1.5 units) divided into 4 parts. Each part is 3/8.

Hard (10)

Evaluate: 3 2/3 ÷ 1 3/8. Express your answer as a mixed number.
Why: Convert to improper fractions, multiply by reciprocal, then convert back to mixed number.
Assertion (A): When multiplying two fractions, if both numbers are between 0 and 1, the product is less than both the numbers. Reason (R): Multiplying by a fraction less than 1 always decreases the value.
Why: Both statements are true, and the reason correctly explains why the product is smaller.
A baker needs 1/6 kg of flour to make one loaf of bread. He has 5 kg of flour. How many loaves of bread can he make?
- 5/6 loaves
- 30 loaves (correct)
- 1/30 loaves
- 6 loaves
Why: Divide the total flour by the flour needed per loaf: 5 ÷ (1/6) = 30.
Find the area of a rectangle of sides 3 3/4 ft and 9 3/5 ft.
Why: Convert to improper fractions: 15/4 and 48/5. Multiply: (15/4) × (48/5) = 3 × 12 = 36.
Assertion (A): When we divide 6 by 1/4, the quotient is 24. Reason (R): When dividing a whole number by a fraction less than 1, the quotient is greater than the dividend.
Why: Both statements are true, and the reason correctly explains why the quotient is larger.
Tsewang plants four saplings in a row in his garden. The distance between two saplings is 3/4 m. Find the distance between the first and last sapling.
- 3/4 m
- 9/4 m (correct)
- 12/4 m
- 4 m
Why: There are 3 gaps between 4 saplings. Total distance = 3 × (3/4) = 9/4 m.
What is 14/4 ÷ 2?
Why: 14/4 ÷ 2 = 14/4 × 1/2 = 14/8 = 7/4.
Which is heavier: 12/15 of 500 grams or 3/20 of 4 kg?
- 12/15 of 500 grams
- 3/20 of 4 kg (correct)
- Both are equal
- Cannot be determined
Why: 12/15 of 500g = 400g. 3/20 of 4kg = 3/20 of 4000g = 600g. So, 3/20 of 4 kg is heavier.
Evaluate: 1/6 ÷ 11/12. Express your answer as a simplified fraction.
Why: 1/6 ÷ 11/12 = 1/6 × 12/11 = 12/66 = 2/11.
The government has taken 1/6 of Somu's land to build a road. What part of the land remains with Somu now? She gives half of the remaining part of the land to her daughter Krishna and 1/3 of it to her son Bora. After giving them their shares, she keeps the remaining land for herself. What part of the original land did Somu keep for herself?
- 5/36 (correct)
- 1/6
- 5/12
- 1/4
Why: Remaining land after road = 1 - 1/6 = 5/6. Krishna gets 1/2 of 5/6 = 5/12. Bora gets 1/3 of 5/6 = 5/18. Somu keeps 5/6 - 5/12 - 5/18 = 30/36 - 15/36 - 10/36 = 5/36.