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6 questions · self-marked practice — reveal the answer and mark yourself.

Question 15 Marks
Carry out the following Divisions:
i. $\frac{2}{3} \div \frac{1}{4}$
ii. $\frac{5}{9} \div \frac{3}{2}$
iii. $\frac{3}{7} \div \frac{5}{11}$
iv. $\frac{11}{12} \div \frac{4}{7}$
Answer
i. $\frac{2}{3} \div \frac{1}{4}$
$\frac{2}{3} \div \frac{1}{4}=\frac{2}{3} \times \frac{4}{1}=\frac{2 \times 4}{3 \times 1}=\frac{8}{3}$

$\begin{aligned} & \text { ii. } \frac{5}{9} \div \frac{3}{2} \\ & \frac{5}{9} \div \frac{3}{2}=\frac{5}{9} \times \frac{2}{3}=\frac{5 \times 2}{9 \times 3}=\frac{10}{27}\end{aligned}$

$\begin{aligned} & \text { iii. } \frac{3}{7} \div \frac{5}{11} \\ & \frac{3}{7} \div \frac{5}{11}=\frac{3}{7} \times \frac{11}{5}=\frac{3 \times 11}{7 \times 5}=\frac{33}{35}\end{aligned}$

$\begin{aligned} & \text { iv. } \frac{11}{12} \div \frac{4}{7} \\ & \frac{11}{12} \div \frac{4}{7}=\frac{11}{12} \times \frac{7}{4}=\frac{11 \times 7}{12 \times 4}=\frac{77}{48}\end{aligned}$

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Question 25 Marks
Write the reciprocals of the following numbers:
(1) 7
(2) $\frac{11}{3}$
(3) 2
(4) $\frac{6}{7}$
Answer
Write the reciprocals of the following numbers:
(1) 7
(2) $\frac{11}{3}$
(3) 2
(4) $\frac{6}{7}$
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Question 35 Marks
Ramanujan’s Magic square.

22121887
8817925
10248916
19862311
  • Add the four numbers in the rows, the columns and along the diagonals of this square.
  • What is the sum?
  • Is it the same every time?
  • What is the peculiarity?
  • Look at the numbers in the first row, 22 – 12 – 1887. Find out why this date is special.

Obtain and read a biography of the great Indian mathematician Srinivasa Ramanujan.

Answer
Sum of the numbers in each row:
i. 22 + 12 + 18 + 87 = 139
ii. 88 + 17 + 9 + 25 = 139
iii. 10 + 24 + 89 + 16 = 139
iv. 19 + 86 + 23 + 11 = 139

Sum of the numbers along the diagonals:
i. 22 + 17 + 89 + 11 = 139
ii. 87 + 9 + 24 + 19 = 139

Sum of the numbers in each column:
i. 22 + 88 + 10 + 19 = 139
ii. 12 + 17 + 24 + 86 = 139
iii. 18 + 9 + 89 + 23 = 139
iv. 87 + 25 + 16 + 11 = 139

∴ We observe that the sum of the numbers in each of the rows, the columns and along each diagonal remains the same every time. The numbers in the first row 22 – 12 – 1887 is the birth date of Srinivasa Ramanujan.

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Question 45 Marks
Write the proper signs >, < or = in the boxes below:
  1. -4 __ 5
  2. 8 __ -10
  3. +9 __ +9
  4. -6 __ 0
  5. 7 __ 4
  6. 3 __ 0
  7. -7 __ 7
  8. -12 __ 5
  9. -2 __ -8
  10. -1 __ -2
  11. 6 __ -3
  12. -14 __ -14
Answer
  1. -4 < 5
  2. 8 > -10
  3. +9 = +9
  4. -6 < 0
  5. 7 > 4
  6. 3 > 0
  7. -7 < 7
  8. -12 < 5
  9. -2 > -8
  10. -1 > -2
  11. 6 > -3
  12. -14 = -14
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Question 55 Marks
Complete the table given below:
+84-3-5
-2-2 + 8 = +6
6
0
-4
Answer
+84-3-5
-2(-2) + (+8) = +6(-2) +(+4) = 2(-2) +(-3) =-5(-2) +(-5) =-7
6(+6) + (+8) = 14(+6) + (+4) = 10(+6) + (-3) = 3(+6) + (-5) = 1
00 + (+8) = 80 + (+4) = 40 + (-3) = -30 + (-5) = -5
-4(-4) + (+8) = 4(-4) +(+4) = 0(-4) + (-3) = -7(-4) + (-5) = -9
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Question 65 Marks
Add:
  1. 8 + 6
  2. 9 + (-3)
  3. 5 + (-6)
  4. – 7 + 2
  5. – 8 + 0
  6. – 5 + (-2)
Answer
1. 8 + 6 = (+8) + (+6) = +142. 9 + (-3) = (+9) + (- 3) = +63. 5 + (-6) = (+5) + (-6) = -1
4. -7 + 2 = (-7) + (+2) = -55. -8 + 0 = (-8) + 0 = -86. -5 + (-2) = (-5) + (-2) = -7
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