CBSE Class 7 Mathematics Fractions And Decimals Worksheet Set 05

CBSE Class 7 Maths Worksheet - Fractions and Decimals (4)

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CLASS – VII
SUBJECT – MATHS
TOPIC – FRACTION (DIVISION)

Question. Which of the following is a reducible fraction?
a) (105/112)
b) (104/121)
C) (77/72)
d) (46/63)

Answer : A

Question. [(3/10)+(8/15)] = ?
a) (11/10)
b) (11/15)
c) (5/6)
d) none of these

Answer : C

Question. Which of the following is a vulgar fraction?
a) (3/10)
b) (13/10)
c) (10/3)
d) none of these

Answer : C

Question. Which of the following statement is true?
a) (9/16) = (13/24)
b) (9/16) < (13/4)
c) (9/16) > (13/24)
d) none of these

Answer : A

Question. Which of the following is an improper fraction?
a) (7/10)
b) (7/9)
c) (9/7)
d) none of these

Answer : C

Question. [3(1/4)] – [2(1/3)] =?
a) [1(1/12)]
b) (1/12)
c) [1 (1/11)]
d) (11/12)

Answer : D

Question. (2/3), (4/6), (6/9), (8/12) are
a) Like fractions
b) irreducible fraction
c) equivalent fraction
d) None of these

Answer : A

Question. Reciprocal of [1(3/4)]
a) [1(4/3)]
b) [4(1/3)]
c) [3(1/4)]
d) none of these

Answer : D

Write down the reciprocal of :

Question. 7
Answer : Reciprocal of 7 is (1/7) [∵ ((7/1) × (1/7)) = 1]

Question. (1/12)
Answer : Reciprocal of (1/12) is (12/1) [∵ ((1/12) × (12/1)) = 1]
= 12

Question. (5/8)
Answer : Reciprocal of (5/8) is (8/5) [∵ ((5/8) × (8/5)) = 1]

Question. [12(3/5)]
Answer : Convert mixed fraction into improper fraction,
= (63/5)
Reciprocal of (63/5) is (5/63) [∵ ((63/5) × (5/63)) = 1]

Simplify :

Question. (4/7) ÷ (9/14)
Answer : We have,
= (4/7) ÷ (9/14)
= (4/7) × (14/9)
(Because reciprocal of (9/14) is (14/9)
= (4 × 14) / (7 × 9)
= (4 × 2) / (1×9)
= (8/9)

Question. (7/10) ÷ (3/5)
Answer : We have,
= (7/10) ÷ (3/5)
= (7/10) × (5/3)
(Because reciprocal of (3/5) is (5/3)
= (7 × 5) / (10 × 3)
= (7 × 1) / (2 × 3)
= (7/6)
= [1(1/6)]

Divide:

Question. (11/24) by (7/8)
Answer : The above question can be written as,
= (11/24) ÷ (7/8)
We have,
= (11/24) × (8/7)
(Because reciprocal of (7/8) is (8/7)
= (11 × 8) / (24 × 7)
= (11 × 1) / (3 × 9)
= (11/21)

Question. [6(7/8)] by (11/16)
Answer : The above question can be written as,
= [6(7/8)] ÷ (11/16)
Convert mixed fraction into improper fraction,
= [6(7/8)] = (55/8)
We have,
= (55/8) × (16/11)
(Because reciprocal of (11/16) is (16/11)
= (55 × 16) / (8 × 11)
= (5 × 2) / (1 × 1)
= 10

Short Answer Type Questions :

Question. By selling oranges at the rate of ₹ [6(3/4)] per orange, a man gets ₹ 378. How many oranges does he sell?
Answer : From the question,
Cost for 1 orange = ₹ [6(3/4)] = (27/4)
Man gets = ₹ 378
Then we have,
= (378/1) ÷ (27/4)
= (378/1) × (4/27)
(Because reciprocal of (27/4) is (4/27)
= (378 × 4) / (1 × 27)
= (42×4) / (1×3)
= (14×4) / (1×1)
= 56
Hence, the man sold 56 orange.

Question. A rope of length [13(1/2)] m has been divided into 9 pieces of the same length. What is the length of each piece?
Answer : From the question,
Rope length = [13(1/2)] m = (27/2)
Number of equal pieces divided into = 9
Then we have,
= (27/2) ÷ (9/1)
= (27/2) × (1/9)
(Because reciprocal of (9/1) is (1/9)
= (27 × 1) / (2 × 9)
= (3×1) / (2×1)
= (3 / 2)
= [1(1/2)] m
Hence, the length of 9 pieces of rope is [1(1/2)] m

Question. Vikas can cover a distance of [20(2/3)] km in [7(3/4)] hours on foot. How many km per hour does he walk?
Answer : From the question,
Distance covered by vikas in [7(3/4)] hours on foot = [20(2/3)] km = (62/3)
Distance covered by vikas in 1 hour = (62/3) ÷ (31/4)
Then we have,
= (62/3) × (4/31)
(Because reciprocal of (31/4) is (4/31)
= (62 × 4) / (3 × 31)
= (2×4) / (3×1)
= (8) / (3)
= [2(2/3) km
Hence, Distance covered by vikas in 1 hour is [2(2/3) km

Question. 18 boxes of nails weigh equally and their total weight is [49(1/2)] kg. How much does each box weigh?
Answer : From the question,
Total weight of boxes= [49(1/2)] kg = (99/2)
Number of boxes = 18
Then we have,
= (99/2) ÷ (18/1)
= (99/2) × (1/18)
(Because reciprocal of (18/1) is (1/18)
= (99 × 1) / (2 × 18)
= (11×1) / (2×2)
= (11 / 4)
= [2(3/4)] kg
Hence, the weight of each box is [2(3/4)] kg

Question. Mangos are sold at ₹ [43(1/2)] per kg. What is the weight of mangoes available for ₹ [326(1/4)]?
Answer : From the question,
Mangos are sold at = ₹ [43(1/2)]+ = (87/2)
The weight of mangos available for = ₹ [26(1/4)] = (1305/4)
Then we have,
= (1305/4) ÷ (87/2)
= (1305/4) × (2/87)
(Because reciprocal of (87/2) is (2/87)
= (1305 × 2) / (4 × 87)
= (435×1) / (2×29)
= [7(1/2)] kg
Hence, the weight of mangos available for (1305/4) is [7(1/2)] kg 

Please click the below link to access CBSE Class 7 Maths Worksheet - Fractions and Decimals (4)

Fill in the Blanks

Question 1. The product of two proper fractions is _______________ than each of the fractions.
Answer: less
In simple words: When you multiply two proper fractions, the result is always smaller than the starting fractions.

Exam Tip: Proper fractions have a value below one, so multiplying them always reduces the overall size.

Question 2. The product of two improper fractions is _______________ than each of the two fractions.
Answer: greater
In simple words: When you multiply two improper fractions, the result is always larger than the starting fractions.

Exam Tip: Improper fractions represent values equal to or larger than one, so multiplying them increases the size.

Question 3. \( \frac{4}{5} \times \frac{\square}{\square} = \frac{28}{30} \)
Answer: \( \frac{7}{6} \)
In simple words: Find the missing top and bottom numbers by dividing the final numbers by the first numbers.

Exam Tip: Since \( 4 \times 7 = 28 \) and \( 5 \times 6 = 30 \), the missing fraction is 7 over 6.

Question 4. \( \frac{2}{\square} \times \frac{4}{9} = \frac{8}{45} \)
Answer: 5
In simple words: Since 5 times 9 equals 45, the missing number under the line is 5.

Exam Tip: You can set up a simple multiplication equation for the denominators to solve for the missing blank.

Question 5. Reciprocal of \( \frac{2}{3} \) is \( \frac{\square}{\square} \)
Answer: \( \frac{3}{2} \)
In simple words: Flip the fraction upside down to find its reciprocal.

Exam Tip: To find a reciprocal, simply swap the position of the top number and the bottom number.

Question 6. 1.2 x 100 = _________
Answer: 120
In simple words: Shift the dot two places to the right to multiply by 100.

Exam Tip: Count the number of zeros in 100 to know how many places to move the decimal point.

Question 7. 2.5 x 1000 = _________
Answer: 2500
In simple words: Move the dot three places to the right to multiply by 1000.

Exam Tip: Use zeros as placeholders when you need to shift the dot past the existing digits.

Question 8. 2.97 x 10 = _________
Answer: 29.7
In simple words: Shift the dot one place to the right to multiply by 10.

Exam Tip: Multiplying a decimal by 10 simply shifts the decimal point one place to the right.

Answer the Following

Question 1. Solve
i) \( 4 - \frac{1}{5} \)
ii) \( 2\frac{3}{7} + 3\frac{1}{2} \)
iii) \( \frac{2}{3} + \frac{1}{6} + \frac{7}{12} \)
Answer:
i) Convert 4 to a fraction with a denominator of 5:
\( 4 - \frac{1}{5} = \frac{20}{5} - \frac{1}{5} = \frac{19}{5} = 3\frac{4}{5} \)

ii) Convert mixed numbers to improper fractions:
\( 2\frac{3}{7} = \frac{17}{7} \), \( 3\frac{1}{2} = \frac{7}{2} \)
Find a common denominator of 14:
\( \frac{17 \times 2}{14} + \frac{7 \times 7}{14} = \frac{34}{14} + \frac{49}{14} = \frac{83}{14} = 5\frac{13}{14} \)

iii) Find a common denominator of 12:
\( \frac{2 \times 4}{12} + \frac{1 \times 2}{12} + \frac{7}{12} = \frac{8}{12} + \frac{2}{12} + \frac{7}{12} = \frac{17}{12} = 1\frac{5}{12} \)
In simple words: Make the bottom numbers of the fractions match before adding or subtracting them.

Exam Tip: Change any mixed numbers into improper fractions before you start working out the sum.

Question 2. Arrange the numbers in descending order and ascending order
a. \( \frac{4}{5}, \frac{2}{7}, \frac{5}{3} \)
b. \( \frac{5}{2}, \frac{3}{5}, \frac{7}{6} \)
Answer:
a. Convert fractions to decimal values to compare easily:
\( \frac{4}{5} = 0.8 \), \( \frac{2}{7} \approx 0.29 \), \( \frac{5}{3} \approx 1.67 \)
Descending order: \( \frac{5}{3}, \frac{4}{5}, \frac{2}{7} \)
Ascending order: \( \frac{2}{7}, \frac{4}{5}, \frac{5}{3} \)

b. Convert fractions to decimal values to compare easily:
\( \frac{5}{2} = 2.5 \), \( \frac{3}{5} = 0.6 \), \( \frac{7}{6} \approx 1.17 \)
Descending order: \( \frac{5}{2}, \frac{7}{6}, \frac{3}{5} \)
Ascending order: \( \frac{3}{5}, \frac{7}{6}, \frac{5}{2} \)
In simple words: Turn the fractions into standard decimal numbers to see which is largest and which is smallest.

Exam Tip: Changing fractions into decimals is often the fastest way to arrange them in order.

Question 3. Raju finished his work in \( \frac{5}{6} \) hrs. Vrinda finished her work in \( \frac{3}{4} \) hrs. Who worked longer ? By what fraction was it longer?
Answer:
Find a common denominator of 12 to compare the times:
Raju: \( \frac{5 \times 2}{12} = \frac{10}{12} \) hours
Vrinda: \( \frac{3 \times 3}{12} = \frac{9}{12} \) hours
Comparing the two, Raju worked longer because \( \frac{10}{12} > \frac{9}{12} \).
Difference: \( \frac{10}{12} - \frac{9}{12} = \frac{1}{12} \) hours.
Raju worked longer by \( \frac{1}{12} \) of an hour.
In simple words: Raju spent more time working, and he worked longer by 1 over 12 of an hour.

Exam Tip: Use a common denominator to compare and subtract fractions that have different bottom numbers.

Question 4. Multiply and reduce to lowest form and convert into a mixed fraction.
i) \( 40 \times \frac{6}{12} \)
ii) \( 22 \times \frac{3}{11} \)
iii) \( \frac{2}{5} \times 25 \)
iv) \( 2\frac{1}{7} \times 14 \)
v) \( 3\frac{5}{6} \times 18 \)
Answer:
i) Simplify \( \frac{6}{12} \) to \( \frac{1}{2} \):
\( 40 \times \frac{1}{2} = 20 \)

ii) Divide 22 by 11 first:
\( 2 \times 3 = 6 \)

iii) Divide 25 by 5 first:
\( 2 \times 5 = 10 \)

iv) Change \( 2\frac{1}{7} \) to the fraction \( \frac{15}{7} \):
\( \frac{15}{7} \times 14 = 15 \times 2 = 30 \)

v) Change \( 3\frac{5}{6} \) to the fraction \( \frac{23}{6} \):
\( \frac{23}{6} \times 18 = 23 \times 3 = 69 \)
In simple words: Simplify the values before multiplying to make the math much simpler.

Exam Tip: Canceling common factors before multiplying keeps your numbers small and prevents calculation errors.

Question 5. Multiply and reduce to lowest form
a. \( \frac{4}{15} \times \frac{20}{8} \)
b. \( 3\frac{4}{7} \times \frac{21}{10} \)
c. \( \frac{6}{13} \times \frac{26}{36} \)
Answer:
a. Simplify terms diagonally:
\( \frac{4}{8} \times \frac{20}{15} = \frac{1}{2} \times \frac{4}{3} = \frac{4}{6} = \frac{2}{3} \)

b. Change the mixed number to \( \frac{25}{7} \):
\( \frac{25}{7} \times \frac{21}{10} = \frac{25}{10} \times \frac{21}{7} = \frac{5}{2} \times 3 = \frac{15}{2} = 7\frac{1}{2} \)

c. Simplify terms diagonally:
\( \frac{6}{36} \times \frac{26}{13} = \frac{1}{6} \times 2 = \frac{2}{6} = \frac{1}{3} \)
In simple words: Reduce the fractions diagonally before multiplying to find the simplest answer.

Exam Tip: Always look to cross-cancel matching factors across the diagonal before performing fraction multiplication.

Question 6. Which is greater
a. \( \frac{1}{3} \) of \( \frac{4}{5} \) or \( \frac{2}{3} \) of \( \frac{3}{10} \)
Answer:
Find the value of both options:
First: \( \frac{1}{3} \times \frac{4}{5} = \frac{4}{15} \approx 0.27 \)
Second: \( \frac{2}{3} \times \frac{3}{10} = \frac{2}{10} = \frac{1}{5} = \frac{3}{15} = 0.2 \)
Comparing \( \frac{4}{15} \) and \( \frac{3}{15} \), the first one is larger.
Therefore, \( \frac{1}{3} \) of \( \frac{4}{5} \) is greater.
In simple words: The first set multiplies to a larger value than the second set.

Exam Tip: "Of" means multiplication in fraction problems. Convert both final answers to a common denominator to compare them.

Question 7. Find
a. \( 6 \div 5\frac{1}{3} \)
b. \( 7 \div 2\frac{4}{7} \)
c. \( 7 \div \frac{2}{5} \)
d. \( 6 \div \frac{4}{7} \)
e. \( 2 \div \frac{8}{9} \)
f. \( \frac{3}{5} \div \frac{1}{2} \)
g. \( \frac{1}{2} \div \frac{3}{5} \)
h. \( 2\frac{1}{2} \div \frac{3}{5} \)
i. \( 5\frac{1}{6} \div \frac{9}{2} \)
Answer:
a. \( 6 \div \frac{16}{3} = 6 \times \frac{3}{16} = \frac{18}{16} = \frac{9}{8} = 1\frac{1}{8} \)
b. \( 7 \div \frac{18}{7} = 7 \times \frac{7}{18} = \frac{49}{18} = 2\frac{13}{18} \)
c. \( 7 \times \frac{5}{2} = \frac{35}{2} = 17\frac{1}{2} \)
d. \( 6 \times \frac{7}{4} = \frac{42}{4} = \frac{21}{2} = 10\frac{1}{2} \)
e. \( 2 \times \frac{9}{8} = \frac{18}{8} = \frac{9}{4} = 2\frac{1}{4} \)
f. \( \frac{3}{5} \times \frac{2}{1} = \frac{6}{5} = 1\frac{1}{5} \)
g. \( \frac{1}{2} \times \frac{5}{3} = \frac{5}{6} \)
h. \( \frac{5}{2} \div \frac{3}{5} = \frac{5}{2} \times \frac{5}{3} = \frac{25}{6} = 4\frac{1}{6} \)
i. \( \frac{31}{6} \div \frac{9}{2} = \frac{31}{6} \times \frac{2}{9} = \frac{31 \times 1}{3 \times 9} = \frac{31}{27} = 1\frac{4}{27} \)
In simple words: To divide by a fraction, turn the second fraction upside down and multiply instead.

Exam Tip: Remember the rule: Keep the first value, Change division to multiplication, and Flip the second fraction.

Question 8. Express as rupees using decimals
a. 479 paise
b. 2 rupees 30 paise
c. 25 rupees 85 paise
d. 75 paise
Answer:
a. Divide 479 by 100: Rs. 4.79
b. Convert paise: 2 + 0.30 = Rs. 2.30
c. Convert paise: 25 + 0.85 = Rs. 25.85
d. Divide 75 by 100: Rs. 0.75
In simple words: Since 100 paise makes 1 rupee, divide the paise by 100 using a decimal point.

Exam Tip: Always make sure to write the unit symbol "Rs." and place the decimal point correctly.

Question 9. Express 45 mm in cm, m and km
Answer:
Convert to centimeters (divide by 10):
\( 45 \text{ mm} = 4.5 \text{ cm} \)

Convert to meters (divide by 1000):
\( 45 \text{ mm} = 0.045 \text{ m} \)

Convert to kilometers (divide by 1,000,000):
\( 45 \text{ mm} = 0.000045 \text{ km} \)
In simple words: 45 millimeters is equal to 4.5 centimeters, 0.045 meters, or 0.000045 kilometers.

Exam Tip: Divide step-by-step: mm to cm is divide by 10, cm to m is divide by 100, and m to km is divide by 1000.

Question 10. Ajmal bought 21 kg 360 g Wheat and 37 kg 350g Rice. Roshan bought 32 kg 500g Wheat and 28 kg 150 g Rice. Who bought more cereals.
Answer:
Calculate total weight of Ajmal's purchase:
\( 21.360 \text{ kg} + 37.350 \text{ kg} = 58.710 \text{ kg} \)

Calculate total weight of Roshan's purchase:
\( 32.500 \text{ kg} + 28.150 \text{ kg} = 60.650 \text{ kg} \)

Compare the totals:
Since \( 60.650 \text{ kg} > 58.710 \text{ kg} \), Roshan bought more cereals.
In simple words: Roshan bought a total of 60.65 kg, which is more than Ajmal's total of 58.71 kg.

Exam Tip: Change grams into decimals of kilograms first to make adding and comparing the weights straightforward.

Question 11. Find
a. 7.2 x 4
b. 8.1 x 2.1
c. 3.2 x 5.34
d. 7.1 x 5.2
e. 2.4 x 4.2
f. 1.2 x 2.53
g. 3.25 x 10
h. 21.365 x 10
i. 6.17 x 10
j. 6.17 x 100
k. 3.25 x 100
l. 21.365 x 100
m. 21.365 x 1000
n. 6.17 x 1000
o. 3.25 x 1000
p. 0.5 x 10
q. 6.3 x 100
r. 65.3 x 1000
Answer:
a. \( 7.2 \times 4 = 28.8 \)
b. \( 8.1 \times 2.1 = 17.01 \)
c. \( 3.2 \times 5.34 = 17.088 \)
d. \( 7.1 \times 5.2 = 36.92 \)
e. \( 2.4 \times 4.2 = 10.08 \)
f. \( 1.2 \times 2.53 = 3.036 \)
g. \( 3.25 \times 10 = 32.5 \)
h. \( 21.365 \times 10 = 213.65 \)
i. \( 6.17 \times 10 = 61.7 \)
j. \( 6.17 \times 100 = 617 \)
k. \( 3.25 \times 100 = 325 \)
l. \( 21.365 \times 100 = 2136.5 \)
m. \( 21.365 \times 1000 = 21365 \)
n. \( 6.17 \times 1000 = 6170 \)
o. \( 3.25 \times 1000 = 3250 \)
p. \( 0.5 \times 10 = 5 \)
q. \( 6.3 \times 100 = 630 \)
r. \( 65.3 \times 1000 = 65300 \)
In simple words: Multiply as normal and then place the dot in the correct position. For powers of ten, just shift the dot.

Exam Tip: When multiplying decimals, count the total decimal places in both numbers and make sure your answer has the same number of decimal places.

Question 12. Find
a. 53.7 ÷ 3
b. 25.6 ÷ 8
c. 82.44 ÷ 6
d. 15.5 ÷ 5
e. 126.35 ÷ 7
f. 0.60 ÷ 5
g. 7.75 ÷ 0.25
h. 42.8 ÷ 0.02
i. 5.6 ÷ 1.4
j. 32.75 ÷ 0.25
k. 354.2 ÷ 10
l. 354.2 ÷ 100
m. 354.2 ÷ 1000
n. 2.38 ÷ 10
o. 2.38 ÷ 100
p. 2.38 ÷ 1000
q. 13.5 ÷ 10
r. 13.5 ÷ 100
s. 13.5 ÷ 1000
t. 29.63 ÷10
u. 29.63 ÷ 100
v. 29.63 ÷ 1000
Answer:
a. \( 53.7 \div 3 = 17.9 \)
b. \( 25.6 \div 8 = 3.2 \)
c. \( 82.44 \div 6 = 13.74 \)
d. \( 15.5 \div 5 = 3.1 \)
e. \( 126.35 \div 7 = 18.05 \)
f. \( 0.60 \div 5 = 0.12 \)
g. \( 7.75 \div 0.25 = 775 \div 25 = 31 \)
h. \( 42.8 \div 0.02 = 4280 \div 2 = 2140 \)
i. \( 5.6 \div 1.4 = 56 \div 14 = 4 \)
j. \( 32.75 \div 0.25 = 3275 \div 25 = 131 \)
k. \( 354.2 \div 10 = 35.42 \)
l. \( 354.2 \div 100 = 3.542 \)
m. \( 354.2 \div 1000 = 0.3542 \)
n. \( 2.38 \div 10 = 0.238 \)
o. \( 2.38 \div 100 = 0.0238 \)
p. \( 2.38 \div 1000 = 0.00238 \)
q. \( 13.5 \div 10 = 1.35 \)
r. \( 13.5 \div 100 = 0.135 \)
s. \( 13.5 \div 1000 = 0.0135 \)
t. \( 29.63 \div 10 = 2.963 \)
u. \( 29.63 \div 100 = 0.2963 \)
v. \( 29.63 \div 1000 = 0.02963 \)
In simple words: When dividing by 10, 100, or 1000, shift the dot to the left. If dividing by a decimal, clear the decimals first.

Exam Tip: When dividing by a decimal, multiply both numbers by 10, 100, or 1000 to turn the divisor into a whole number before you begin.