1Book Back Questions28 questions
Q.1Fill in the blanks: (i) 7\(\frac{3}{4}\) + 6\(\frac{1}{2}\) ……….. (ii) The sum of a whole number and a proper fraction is called ………. (iii) 5\(\frac{1}{3}\) – 3\(\frac{1}{2}\) ……….. (iv) 8 ÷ \(\frac{1}{2}\) ……….. (v) The number which has its own reciprocal is ……….v
Answer:(ii) Mixed Fraction
(iii) 5\(\frac{1}{3}\) – 3\(\frac{1}{2}\)
= \(\frac{16}{3}\) – \(\frac{7}{2}\) = \(\frac{32-21}{6}\) = \(\frac{11}{6}\)
= 1\(\frac{5}{6}\)
(iv) 8 ÷ \(\frac{1}{2}\)
= 8 × \(\frac{2}{1}\)
= 16
(v) 1The first step would be to write the mix number 223 as an improper fraction.
Q.2Say True or False (i) 3\(\frac{1}{2}\) can be written as 3 + \(\frac{1}{2}\). (ii) The sum of any two proper fractions is always an improper fraction. (iii) The mixed fraction of \(\frac{13}{4}\) is 3\(\frac{1}{4}\). (iv) The reciprocal of an improper fraction is always a proper fraction. (v) 3\(\frac{1}{4}\) × 3\(\frac{1}{4}\) = 9\(\frac{1}{16}\)v
Answer:(i) True
(ii) False
(iii) True
(iv) True
(v) False
Q.3Answer the following: (i) Find the sum of \(\frac{1}{7}\) and \(\frac{3}{9}\). (ii) What is the total of 3\(\frac{1}{3}\) and 4\(\frac{1}{6}\)? (iii) Simplify: 1\(\frac{3}{5}\)+5\(\frac{4}{7}\). (iv) Find the difference between \(\frac{8}{9}\) and \(\frac{2}{7}\) (v) Subtract: 1\(\frac{3}{5}\) from 2\(\frac{1}{3}\). (vi) Simplify: 7\(\frac{2}{7}\) – 3\(\frac{4}{21}\)v
Answer:(i) \(\frac{1}{7}\) + \(\frac{3}{9}\)
= \(\frac{9+21}{63}\) = \(\frac{30}{63}\) = \(\frac{10}{21}\)
Q.4Convert mixed fractions into improper fractions and vice versa: (i) 3\(\frac{7}{18}\) (ii) \(\frac{99}{7}\) (iii) \(\frac{47}{6}\) (iv) 12\(\frac{1}{9}\)v
Answer:(i) 3\(\frac{7}{18}\) = \(\frac{61}{18}\)
(ii) \(\frac{99}{7}\) = 14\(\frac{1}{7}\)
(iii) \(\frac{47}{6}\) = 7\(\frac{5}{6}\)
(iv) 12\(\frac{1}{9}\) = \(\frac{109}{9}\)
Q.5Multiply the following: (i) \(\frac{2}{3}\) × 6 (ii) 8\(\frac{1}{3}\) × 5 (iii) \(\frac{3}{8}\) × \(\frac{4}{5}\) (iv) 3\(\frac{5}{7}\) × 1\(\frac{1}{13}\)v
Answer:(i) \(\frac{2}{3}\) × 6 = 4
(ii) 8\(\frac{1}{3}\) × 5
= \(\frac{25}{3}\) × 5
= \(\frac{125}{3}\)
= 41\(\frac{2}{3}\)
(iii) \(\frac{3}{8}\) × \(\frac{4}{5}\)
= \(\frac{12}{40}\) = \(\frac{3}{10}\)
(iv) 3\(\frac{5}{7}\) × 1\(\frac{1}{13}\)
= \(\frac{26}{7}\) × \(\frac{14}{13}\)
= \(\frac{4}{1}\)
= 4
Q.6Divide the following (i) \(\frac{3}{7}\) ÷ 4 (ii) \(\frac{4}{3}\) ÷ \(\frac{5}{9}\) (iii) 4\(\frac{1}{5}\) ÷ 3\(\frac{3}{4}\) (iv) 9\(\frac{2}{3}\) ÷ 1\(\frac{2}{3}\)v
Answer:(i) \(\frac{3}{7}\) ÷ 4
= \(\frac{3}{7}\) × \(\frac{1}{4}\) = \(\frac{3}{28}\)
(ii) \(\frac{4}{3}\) ÷ \(\frac{5}{9}\)
= \(\frac{4}{3}\) × \(\frac{9}{5}\)
= \(\frac{12}{5}\)
= 2\(\frac{2}{5}\)
Q.7Gowri purchased 3\(\frac{1}{2}\) kg of tomatoes, \(\frac{3}{4}\) kg of brinjal and 1\(\frac{1}{4}\) kg of onion. What is the total weight of the vegetables she bought?v
Answer:Total weight of vegetables bought
Q.8An oil tin contains 3\(\frac{3}{4}\) litres of oil of which 2\(\frac{1}{2}\) litres of oil is used. How much oil is left over?v
Q.9Nilavan can walk 4\(\frac{1}{2}\) km in an hour. How much distance will he cover in 3\(\frac{1}{2}\) hours?v
Answer:Distance walked in an hour = 4\(\frac{1}{2}\) km
Distance covered in 3\(\frac{1}{2}\)
Hours
Q.10Ravi bought a curtain of length 15\(\frac{3}{4}\) m. If he cut the curtain into small pieces each of length 2\(\frac{1}{4}\) m, then how many small curtains will he get?v
Answer:Total length = 15\(\frac{3}{4}\)
Length of the small pieces = 2\(\frac{1}{4}\)
Small curtains obtained= 7Objective Type Questions
Q.11Which of the following statement is incorrect?v
- A. \(\frac{1}{2}\) > \(\frac{1}{3}\)
- B. \(\frac{7}{8}\) > \(\frac{6}{7}\)
- C. \(\frac{8}{9}\) < \(\frac{9}{10}\)
- D. \(\frac{10}{11}\) > \(\frac{9}{10}\)
Answer:(d) \(\frac{10}{11}\) > \(\frac{9}{10}\)
Q.12The difference between \(\frac{3}{7}\) and \(\frac{2}{9}\) isv
- A. \(\frac{13}{63}\)
- B. \(\frac{1}{9}\)
- C. \(\frac{1}{7}\)
- D. \(\frac{9}{16}\)
Answer:(a) \(\frac{13}{63}\)
Q.13The reciprocal of \(\frac{53}{17}\) isv
- A. \(\frac{53}{17}\)
- B. 5\(\frac{3}{17}\)
- C. \(\frac{17}{53}\)
- D. 3\(\frac{5}{17}\)
Answer:(c) \(\frac{17}{53}\)
Q.14If \(\frac{6}{7}=\frac{\mathbf{A}}{49}\), then the value of A isv
- A. 42
- B. 36
- C. 25
- D. 48
Answer:(a) 42
Hint: \(\frac{6 \times 49}{7}=42\)
Q.15Pugazh has been given four choices for his pocket money by his father. Which of the choices should he take in order to get the maximum money?v
- A. \(\frac{2}{3}\) of Rs 150
- B. \(\frac{3}{5}\) of Rs 150
- C. \(\frac{4}{5}\) of Rs 150
- D. \(\frac{1}{5}\) of Rs 150
Answer:(c) \(\frac{4}{5}\) of Rs 150
Q.1Sankari purchased 2\(\frac{1}{2}\) m cloth to stich a long skirt and 1\(\frac{3}{4}\) m cloth to stitch blouse. If the cost is Rs. 120 per metre then find the cost of cloth purchased by her.v
Answer:Total cloth purchasedcost of 1 metre = Rs. 120
Total cost of cloth purchased
= Rs. 120 × \(\frac{17}{4}\)
= Rs. 510
Q.2From his office, a person wants to reach his house on foot which is at a distance of 5\(\frac{3}{4}\) km. If he had walked 2\(\frac{1}{2}\) km, how much distance still he has to walk to reach his house?v
Q.3Which is smaller? The difference between 2\(\frac{1}{2}\) and 3\(\frac{2}{3}\) or the sum of 1\(\frac{1}{2}\) and 2\(\frac{1}{4}\).v
Answer:∴ The difference of 2\(\frac{1}{2}\) and 3\(\frac{2}{3}\) is smaller
Q.4Mangai bought 6\(\frac{3}{4}\) kg of apples. If Kalai 1 bought 1\(\frac{1}{2}\) times a Mangai bought, then how many kilograms of apples did Kalai buy?v
Answer:Apples bought by Mangai = 6\(\frac{3}{4}\) kg
Apples bought by Kalai
Q.5The length of the staircase is 5\(\frac{1}{2}\) m. If one step is set at \(\frac{1}{4}\) m, then how many steps will be there in the staircase? v
Answer:Total length of the staircase = 5\(\frac{1}{2}\) m
length of each step = \(\frac{1}{4}\) m
No of steps in the stair case= 22 stepsChallenge Problems
Q.6By using the following clues, find who am I? (i) Each of my numerator and denominator is a single-digit number. (ii) The sum of my numerator and denominator is a multiple of 3. (iii) The product of my numerator and denominator is a multiple of 4.v
Answer:The numerator may be any one of!, 2, 3,4, 5, 6, 7, 8, 9 and the denominator may be any one of 1, 2,3,4, 5,6, 7,8,9. Sum of numerator and denominator is a multiple of 3.
∴ Possible proper fractions are \(\frac{1}{2}, \frac{1}{5}, \frac{1}{8}, \frac{2}{4}, \frac{2}{7}, \frac{3}{6}, \frac{3}{9}, \frac{4}{5}, \frac{4}{8}, \frac{5}{7}, \frac{6}{9}\)
Also given the product of numerator and denominator is a multiple of 4.
∴ Possible fractions are \(\frac{1}{8}, \frac{2}{4}, \frac{4}{5}, \frac{4}{8}\)
Q.7Add the difference between 1\(\frac{1}{3}\) and 3\(\frac{1}{6}\) and the difference between 4\(\frac{1}{6}\) and 2\(\frac{1}{3}\)v
Q.8What fraction is to be subtracted from 9\(\frac{3}{7}\) to get 3\(\frac{1}{5}\)?v
Answer:Let the fraction be x
According to the problemThe fraction to be subtracted is 6\(\frac{8}{35}\)
Q.9The sum of two fractions is 5\(\frac{3}{9}\). If one of the fractions is 2\(\frac{3}{4}\), find the other fraction.v
Answer:Let the other fraction be x
According to the problem,∴ The other fraction is 2\(\frac{7}{12}\)
Q.10By what number should 3\(\frac{1}{16}\) be multiplied to get 9\(\frac{3}{16}\)?v
Answer:Let the number be x
According to the problem,x = 3
The number is 3
Q.11Complete the fifth row in the Leibnitz triangle which is based on subtraction. v
Q.12A painter painted \(\frac{3}{8}\) of the wall of which one third is painted in yellow colour. What fraction is the yellow colour of the entire wall? v
Answer:yellow colour of the entire wall
= \(\frac{3}{8}\) × \(\frac{1}{3}\)
= \(\frac{1}{8}\)
Q.13A rabbit has to cover 26\(\frac{1}{4}\) m to fetch its food. If it covers 1\(\frac{3}{4}\) m in one jump, then how many jumps will it take to fetch its food? v
Answer:Total distance = 26\(\frac{1}{4}\) m
Distance covered in one jump = 1\(\frac{3}{4}\) m
Number of jumps required to fetch the food= 15