Unit Test(Solutions): Fractions and Decimals | Mathematics (Maths) Class 7 (Old NCERT) PDF Download

Time: 1 hour

M.M.: 30

Attempt all questions.

Question numbers 1 to 5 carry 1 mark each.

Question numbers 6 to 8 carry 2 marks each.

Question numbers 9 to 11 carry 3 marks each.

Question numbers 12 & 13 carry 5 marks each.

Q1: Which of the drawings (a) to (d) show: (1 Mark)

(i) 2 × (1/5) (ii) 2 × ½ (iii) 3 × (2/3) (iv) 3 × ¼

Ans:

(i) 2 × (1/5) represents the addition of 2 figures, each represents 1 shaded part out of the given 5 equal parts.

∴ 2 × (1/5) is represented by fig (d).

(ii) 2 × ½ represents the addition of 2 figures, each represents 1 shaded part out of the given 2 equal parts.

∴ 2 × ½ is represented by fig (b).

(iii) 3 × (2/3) represents the addition of 3 figures, each represents 2 shaded parts out of the given 3 equal parts.

∴ 3 × (2/3) is represented by fig (a).

(iii) 3 × ¼ represents the addition of 3 figures, each represents 1 shaded part out of the given 4 equal parts.

∴ 3 × ¼ is represented by fig (c).

Q2: What is the product of 2/3 and 4/5? (1 Mark)
(i) 8/15
(ii) 8/5
(iii) 6/15
(iv) 12/15
Ans: (i) 8/15

$\frac{2}{3}\times \frac{4}{5}=\frac{2}{\times }=\frac{8}{15}\backslash frac\{2\}\{3\}\; \backslash times\; \backslash frac\{4\}\{5\}\; =\; \backslash frac\{2\; \backslash times\; 4\}\{3\; \backslash times\; 5\}\; =\; \backslash frac\{8\}\{15\}$

Q3: Multiply 3.4 by 0.05. (1 Mark)

Ans: 0.17

$3.4\times 0.05=0.173.4\; \backslash times\; 0.05\; =\; 0.17$

Q4: What is the reciprocal of 9/11? (1 Mark)
(i) 9
(ii) 11/9
(iii) 9/11
(iv) 1

Ans: (ii) 11/9
The reciprocal of a fraction is obtained by swapping the numerator and the denominator.

Q5: Multiply: $\frac{7}{9}\times 0.5\backslash frac\{7\}\{9\}\; \backslash times\; 0.5$ (1 Mark)

Ans: 0.5 = 1/2

$\frac{7}{9}\times \frac{1}{2}=\frac{7}{18}$

$\frac{\mathrm{<strong\; style="font-weight:\; 700;\; word-break:\; break-word;\; line-height:\; 1.8;\; font-family:\; Lato,\; sans-serif;\; font-size:\; 20px;\; letter-spacing:\; inherit;\; color:\; black;">Q6: </strong>}}{}$A rectangular field is 15.4 m long and 7.6 m wide. Find its area. (2 Marks)

Ans:

$Area\backslash text\{Area\}\; =\; \backslash text\{Length\}\; \backslash times\; \backslash text\{Breadth\}\; =\; 15.4\; \backslash times\; 7.6\; =\; 117.04\; \backslash ,\; \backslash text\{m\}^2$Area=Length×Breadth=15.4×7.6=117.04m²

Q7: Simplify: $1.23÷0.3$. (2 Marks)

Ans:

$\frac{1.23}{0.3}=\frac{123}{30}=$4.1

Q8:Find three different fractions between $\frac{1}{3}\backslash frac\{1\}\{3\}$ and $\frac{2}{3}\backslash frac\{2\}\{3\}$. (2 Marks)

Ans:
$\frac{\mathrm{1/3\; =\; 4/12,\; 2/3\; =\; 8/12}}{}\backslash frac\{2\}\{6\},\; \backslash frac\{3\}\{6\},\; \backslash frac\{4\}\{6\}$

Examples: $\frac{1}{2},\frac{5}{12},\frac{3}{5}$

$\frac{\mathrm{<strong\; style="font-weight:\; 700;\; word-break:\; break-word;\; line-height:\; 1.8;\; font-family:\; Lato,\; sans-serif;\; font-size:\; 20px;\; letter-spacing:\; inherit;\; color:\; black;">Q9: </strong>}}{}$Vidya and Pratap went for a picnic. Their mother gave them a water bottle that contained 5 litres of water. Vidya consumed $\frac{2}{5}\backslash frac\{2\}\{5\}$of the water, and Pratap consumed the remaining water.(3 Marks)

(i) How much water did Vidya drink?
(ii) What fraction of the total quantity of water did Pratap drink?

Ans: Total quantity of water in the bottle = 5 litres.

(i) How much water did Vidya drink?
Vidya drank $\frac{2}{5}\backslash frac\{2\}\{5\}$of the total water. Therefore, the amount of water Vidya drank is:

$\frac{2}{5}\times 5=\frac{10}{5}=$2litres.

So, Vidya drank 2 litres of water.

(ii) What fraction of the total quantity of water did Pratap drink?
Pratap drank the remaining water after Vidya consumed her share. The fraction of water Pratap drank is the remaining fraction:

$1-\frac{2}{5}=\frac{5}{5}-\frac{2}{5}=\frac{3}{5}.$

So, Pratap drank $\frac{3}{5}\backslash frac\{3\}\{5\}$ of the total water.

Q10: A vehicle covers a distance of 72.8 km in 3.2 litres of petrol. How much distance will it cover in 1 litre of petrol? (3 Marks)

Ans:

To find how much distance the vehicle covers in 1 litre of petrol, we divide the total distance by the amount of petrol used:

$Distance per litreDistance\; per\; litre=\frac{72.8}{3.2}=22.75\hspace{0.17em}km/litre\backslash text\{Distance\; per\; litre\}\; =\; \backslash frac\{72.8\; \backslash ,\; \backslash text\{km\}\}\{3.2\; \backslash ,\; \backslash text\{litres\}\}\; =\; 22.75\; \backslash ,\; \backslash text\{km/litre\}$km/litre

So, the vehicle will cover 22.75 km in 1 litre of petrol.

Q11: Riya plants 5 saplings in a row in her garden. The distance between two adjacent saplings is $\frac{2}{3}\hspace{0.17em}m\backslash frac\{2\}\{3\}\; \backslash ,\; \backslash text\{m\}$m. Find the distance between the first and the last sapling. (3 Marks)

Ans: To find the distance between the first and the last sapling, we calculate the number of gaps between the saplings.

For 5 saplings, the number of gaps between them = 5 - 1 = 4 gaps.

Each gap has a distance of $\frac{2}{3}\hspace{0.17em}m\backslash frac\{2\}\{3\}\; \backslash ,\; \backslash text\{m\}$32m.

Therefore, the total distance between the first and the last sapling is:

$Total distance=4\times \frac{2}{3}=\frac{8}{3}\hspace{0.17em}m=2\frac{2}{3}\hspace{0.17em}m$m.

Thus, the distance between the first and the last sapling is 2 $\frac{2}{3}\backslash frac\{2\}\{3\}$ meters.

Q12: In a class of 50 students: (5 Marks)

$\frac{2}{5}\backslash frac\{2\}\{5\}$ of the total number of students like to study English,

$\frac{3}{10}$of the total number like to study Mathematics,

The remaining students like to study Science.

Answer the following questions:

(i) How many students like to study English?
(ii) How many students like to study Mathematics?
(iii) What fraction of the total number of students like to study Science?
(iv) How many students like to study Science?

Ans:
(i) We are given that $\frac{2}{5}\backslash frac\{2\}\{5\}$ of the students like to study English.

The number of students who like to study English =

$\frac{2}{5}\times 50=\frac{100}{5}$=20students.

(ii) We are given that $\frac{3}{10}\backslash frac\{3\}\{10\}$ of the students like to study Mathematics.

The number of students who like to study Mathematics =

$\frac{3}{10}\times 50=\frac{150}{10}=$15students.

(iii) The fraction of students who like to study Science can be found by subtracting the fractions of students who like English and Mathematics from the total class.

Fraction of students who like English and Mathematics =

$\frac{2}{5}+\frac{3}{10}=\frac{4}{10}+\frac{3}{10}=\frac{7}{10}$

Thus, the fraction of students who like to study Science =

$1-\frac{7}{10}=\frac{3}{10}$

(iv) The number of students who like to study Science =

$\frac{3}{10}\times 50=\frac{150}{10}=$15students.

Q13: Solve the following problems(5 Marks)

(i) Rani ate 2/7 part of a cake while her brother Ravi ate 4/5 of the remaining. Part of the cake left is

Ans:

Now, let us assume total part of cake be 1.

Then, from the question, given that Rani ate 2/7 part of a cake = 1 – (2/7)

= (7 – 2)/7

= 5/7

So, Ravi ate 4/5 of the remaining cake = (4/5) × (5/7)

= 4/7

Therefore, the part of the cake left = (5/7) – (4/7)

= 1/7

Rani ate 2/7 part of a cake while her brother Ravi ate 4/5 of the remaining. Part of the cake left is 1/7.

(ii) Provide the number in the box, such that:

Ans: To find the missing number, divide 

$\frac{18}{50}$ by $\frac{3}{5}$:

$=\frac{18}{50}÷\frac{3}{5}=\frac{18}{50}\times \frac{5}{3}=\frac{90}{150}=\frac{3}{5}$ 

So, the number in the box is $\frac{3}{5}$.

(iii) The simplest form of the number obtained in (ii) is ______.

Ans: The simplest form of $\frac{18}{50}\backslash frac\{18\}\{50\}$ is:

$\frac{18}{50}=\frac{9}{25}$

$\backslash frac\{1\}\{2\},\; \backslash frac\{5\}\{12\},\; \backslash frac\{3\}\{5\}$

$\backslash frac\{7\}\{9\}\; \backslash times\; \backslash frac\{1\}\{2\}\; =\; \backslash frac\{7\}\{18\}$