Question 1

Q1: A 210 gram packet of peanut chikki costs ₹70.5, while a 110 gram packet of potato chips costs ₹33.25. Which is cheaper?

Accepted Answer

Given: Peanut chikki: 210 g for ₹70.5 Potato chips: 110 g for ₹33.25 To Find: Which item is cheaper per gram. Solution: To compare, we need to find the cost per gram for each item. Cost per gram of peanut chikki: $$= \frac{	ext{Total cost}}{	ext{Total weight}} = \frac{70.5}{210} 	ext{ ₹/g}$$ $$=...

Question 2

Q10: Using the digits 2, 4, 5, 8, and 0 fill the boxes $\square . \square . \square 	imes \square . \square$ to get the: (a) maximum product (b) minimum p...

Accepted Answer

Note: The format of the multiplication is ambiguous. Based on typical problems and the targets given, we will assume the format is $\square\square.\square 	imes \square.\square$. The five digits 2, 4, 5, 8, and 0 must be used exactly once. (a) maximum product To maximize the product, we should plac...

Question 3

Q11: Sort the following expressions in increasing order: (a) $245.05 	imes 0.942368$ (b) $245.05 	imes 7.9682$ (c) $245.05 \div 7.9682$ (d) $245.05 \div...

Accepted Answer

Given expressions: Let $A = 245.05$, $B = 7.9682$, and $C = 0.942368$. (a) $A 	imes C$ (b) $A 	imes B$ (c) $A \div B$ (d) $A \div C$ (e) $A$ (f) $B$ Reasoning: 1.  Multiplying a positive number ($A$) by a number less than 1 ($C$) gives a product smaller than $A$. So, $A 	imes C  A$. 3.  Dividing...

Question 4

Q2: Write the decimal number at the arrow mark:

Accepted Answer

Description of the image: The question shows a number line segment from 0.7 to 0.8. This segment is divided into 10 equal smaller intervals. The arrow points to the 4th mark after 0.7. Solution: Each small interval represents one-tenth of the distance between 0.7 and 0.8. The total distance is $0.8...

Question 5

Q3: Shyamala bought 3 kg bananas at ₹30/- per kg. She counted 35 bananas in all. She sells each banana for ₹5/-. How much profit does she make selling all...

Accepted Answer

Given: Quantity of bananas bought = 3 kg Cost of bananas = ₹30 per kg Total number of bananas = 35 Selling price of each banana = ₹5 To Find: Total profit made. Solution: Step 1: Calculate the total cost price (CP). Total CP = Quantity in kg $	imes$ Price per kg $$= 3 	ext{ kg} 	imes 	ext{₹}30/\...

Question 6

Q4: A teacher placed textbooks that are 2.5 cm thick on a bookshelf. The teacher wanted to place 80 textbooks on the shelf. The bookshelf is 160 cm long....

Accepted Answer

Given: Thickness of one textbook = 2.5 cm Length of the bookshelf = 160 cm Number of books the teacher wanted to place = 80 To Find: 1. How many books could be placed on the shelf. 2. If there was any space left, and how much. Solution: Step 1: Calculate the number of books that can fit on the shelf...

Question 7

Q5: Fill in the following blanks appropriately: | $5.5 	ext{ km} = \_\_\_\_$ m | $35 	ext{ cm} = \_\_\_\_$ m | $14.5 	ext{ cm} = \_\_\_\_$ mm | |---|--...

Accepted Answer

Conversion Factors: $1 	ext{ km} = 1000 	ext{ m}$ $1 	ext{ m} = 100 	ext{ cm}$ $1 	ext{ cm} = 10 	ext{ mm}$ $1 	ext{ kg} = 1000 	ext{ g}$ $1 	ext{ m} = 1000 	ext{ mm}$ $1 	ext{ l} = 1000 	ext{ ml}$ Solutions:    $5.5 	ext{ km} = 5.5 	imes 1000 = 5500 	ext{ m}$    $35 	ext{ cm} = 35 \...

Question 8

Q6: The following problem was set by Sridharacharya in his book, Patiganita. "$6\frac{1}{4}$ is divided by $2\frac{1}{2}$, and $60\frac{1}{4}$ is divided...

Accepted Answer

Problem 1: $6\frac{1}{4}$ divided by $2\frac{1}{2}$ Solution: First, convert the mixed fractions to decimals. $$6\frac{1}{4} = 6 + 0.25 = 6.25$$ $$2\frac{1}{2} = 2 + 0.5 = 2.5$$ Now, perform the division. $$6.25 \div 2.5 = \frac{6.25}{2.5} = \frac{62.5}{25} = 2.5$$ Final Answer for Problem 1: The qu...

Question 9

Q7: Fill the boxes in at least 2 different ways: (a) □ × □ $= 2.4$ (b) □ × □ $= 14.5$

Accepted Answer

(a) □ × □ $= 2.4$ Solution: Here are two possible ways: 1.  $2 	imes 1.2 = 2.4$ 2.  $4 	imes 0.6 = 2.4$ (Other examples: $3 	imes 0.8 = 2.4$, $6 	imes 0.4 = 2.4$) Final Answer: Way 1: $2 	imes 1.2 = 2.4$ Way 2: $4 	imes 0.6 = 2.4$ (b) □ × □ $= 14.5$ Solution: Here are two possible ways: 1.  $2...

Question 10

Q8: Find the following quotients given that $756 \div 36 = 21$: (a) $75.6 \div 3.6$ (b) $7.56 \div 0.36$ (c) $756 \div 0.36$ (d) $75.6 \div 360$ (e) $7560...

Accepted Answer

Given: $756 \div 36 = 21$ (a) $75.6 \div 3.6$ Solution: $$75.6 \div 3.6 = \frac{75.6}{3.6} = \frac{756}{36} = 21$$ Final Answer: 21 (b) $7.56 \div 0.36$ Solution: $$7.56 \div 0.36 = \frac{7.56}{0.36} = \frac{756}{36} = 21$$ Final Answer: 21 (c) $756 \div 0.36$ Solution: $$756 \div 0.36 = \frac{756}{...

Question 11

Q9: Find the missing cells if each cell represents $a \div b$: | b$\downarrow$ a$\rightarrow$ | 1517 | 151.7 | 15.17 | 1.517 | 15170 | |---|---|---|---|--...

Accepted Answer

Base Information: From the table, we are given: 1. $1517 \div 37 = 41$ 2. $15.17 \div 3.7 = 4.1$ 3. $151.7 \div 0.037 = 4100$ All these are consistent with the base fact $1517 \div 37 = 41$. For example, $15.17 \div 3.7 = \frac{15.17}{3.7} = \frac{151.7}{37} = 4.1$. Solution: We will fill the table...

Question 12

Q1: Find the quotient by converting the denominator into 1, 10, 100 or 1000 and verify the solution by the long division method (division by place value)....

Accepted Answer

(a) $\frac{18}{5}$ Method 1: Converting the denominator To make the denominator 10, we multiply the numerator and denominator by 2. $$\frac{18}{5} = \frac{18 	imes 2}{5 	imes 2} = \frac{36}{10} = 3.6$$ Method 2: Long Division (Verification)    3.6   _____ 5 | 18.0    -15    ---      3 0     -3 0...

Question 13

Q2: Choose the correct answer: (a) $\frac{1526}{4}=$ (i) 38.15 (ii) 380.15 (iii) 381.5 (iv) 381.05 (b) $\frac{3567}{8}=$ (i) 4458.75 (ii) 44.5875 (iii) 44...

Accepted Answer

(a) $\frac{1526}{4}$ Solution: We perform the long division of 1526 by 4.    381.5   _______ 4 | 1526.0    -12    ---     32    -32    ---      06      -4      --       2 0      -2 0      ----         0 The quotient is 381.5. Answer: (iii) 381.5 (b) $\frac{3567}{8}$ Solution: We perform the long div...

Question 14

Q3: What is the quotient? (a) $132 \div 4=$ (b) $13.2 \div 4=$ (c) $1.32 \div 4=$ (d) $0.132 \div 4=$

Accepted Answer

(a) $132 \div 4$ Solution: $$132 \div 4 = 33$$ Final Answer: 33 (b) $13.2 \div 4$ Solution: Since $132 \div 4 = 33$, and the dividend 13.2 has one decimal place, the quotient will also have one decimal place. $$13.2 \div 4 = 3.3$$ Final Answer: 3.3 (c) $1.32 \div 4$ Solution: Since $132 \div 4 = 33$...

Question 15

Q4: What is the quotient? (a) $126 \div 8=$ (b) $12.6 \div 8=$ (c) $1.26 \div 8=$ (d) $0.126 \div 8=$ (e) $0.0126 \div 8=$

Accepted Answer

(a) $126 \div 8$ Solution: $$126 \div 8 = 15.75$$ Final Answer: 15.75 (b) $12.6 \div 8$ Solution: Since $126 \div 8 = 15.75$, and the dividend 12.6 has one decimal place, we shift the decimal in the quotient 15.75 one place to the left. $$12.6 \div 8 = 1.575$$ Final Answer: 1.575 (c) $1.26 \div 8$ S...

Question 16

Q1: Express the following fractions in decimal form: (a) $\frac{2}{5}$ (b) $\frac{13}{4}$ (c) $\frac{4}{50}$ (d) $\frac{5}{8}$

Accepted Answer

(a) $\frac{2}{5}$ Solution: To convert to a decimal, make the denominator a power of 10. $$\frac{2}{5} = \frac{2 	imes 2}{5 	imes 2} = \frac{4}{10} = 0.4$$ Final Answer: 0.4 (b) $\frac{13}{4}$ Solution: $$\frac{13}{4} = \frac{13 	imes 25}{4 	imes 25} = \frac{325}{100} = 3.25$$ Alternatively, $13...

Question 17

Q10: 13.5 kg of flour (aata) was distributed equally among 15 students. How much flour did each student receive?

Accepted Answer

Given: Total amount of flour = 13.5 kg Number of students = 15 To Find: Amount of flour each student received. Solution: Flour per student = Total flour $\div$ Number of students $$= 13.5 	ext{ kg} \div 15$$ $$= \frac{13.5}{15} = \frac{135}{150} = \frac{9}{10} = 0.9 	ext{ kg}$$ Final Answer: Each...

Question 18

Q2: Find the quotients: (a) $24.86 \div 1.2$ (b) $5.728 \div 1.52$

Accepted Answer

(a) $24.86 \div 1.2$ Solution: To make the divisor a whole number, multiply both dividend and divisor by 10. $$24.86 \div 1.2 = (24.86 	imes 10) \div (1.2 	imes 10) = 248.6 \div 12$$ Now, we perform long division:    20.7166...   __________ 12 | 248.6000     -24     ---      08      - 0      ---...

Question 19

Q3: Evaluate the following using the information $156 	imes 12 = 1872$. (a) $15.6 	imes 1.2 = \_\_\_\_$ (b) $187.2 \div 1.2 = \_\_\_\_$ (c) $18.72 \div...

Accepted Answer

Given: $156 	imes 12 = 1872$ (a) $15.6 	imes 1.2$ Solution: The numbers are the same as the given information, but with decimal points. Total decimal places = 1 + 1 = 2. So, $15.6 	imes 1.2 = 18.72$. Final Answer: 18.72 (b) $187.2 \div 1.2$ Solution: From the given information, we know $1872 \div...

Question 20

Q4: Evaluate the following: (a) $25 \div \_\_\_\_ = 0.025$ (b) $25 \div \_\_\_\_ = 250$ (c) $25 \div \_\_\_\_ = 2.5$ (d) $25 \div 10 = 25 	imes \_\_\_\_$...

Accepted Answer

(a) $25 \div x = 0.025$ Solution: $$x = 25 \div 0.025 = 25 \div \frac{25}{1000} = 25 	imes \frac{1000}{25} = 1000$$ Final Answer: 1000 (b) $25 \div x = 250$ Solution: $$x = 25 \div 250 = \frac{25}{250} = \frac{1}{10} = 0.1$$ Final Answer: 0.1 (c) $25 \div x = 2.5$ Solution: $$x = 25 \div 2.5 = 250...

	$\times 10$	$\times 100$	$\times 1000$
5.7
23.02
0.92
0.306
24.67

NCERT Solutions