Maharashtra Board Class 7 Chapter 2 Set 9 Multiplication and Division of Integers Solutions

Question 1. Solve
(i) (-96) ÷ 16
(ii) 98 ÷ (-28)
(iii) (-51) ÷ 68
(iv) 38 ÷ (-57)
(v) (-85) ÷ 20
(vi) (-150) ÷ (-25)
(vii) 100 ÷ 60
(viii) 9 ÷ (-54)
(ix) 78 ÷ 65
(x) (-5) ÷ (-315)
Answer:
Solution:
i. (-96) ÷ 16
\( \frac{-96}{16} = \frac{(-1)\times96}{16} \)
\( = (-1) \times (6) = -6 \)
ii. 98 ÷ (-28)
\( \frac{98}{-28} = \frac{98}{(-1)(28)} \)
\( = \frac{7}{(-1)\times(2)} = \frac{-7}{2} \)
iii. (-51) ÷ 68
\( \frac{-51}{68} = \frac{(-1)\times(51)}{68} \)
\( = \frac{(-1)\times(3)}{4} = \frac{-3}{4} \)
iv. 38 ÷ (-57)
\( \frac{38}{-57} = \frac{38}{(-1)\times(57)} \)
\( = \frac{2}{(-1)\times(3)} = \frac{-2}{3} \)
v. (-85) ÷ 20
\( \frac{-85}{20} = \frac{(-1)\times(85)}{20} \)
\( = \frac{(-1)\times17}{4} = \frac{-17}{4} \)
vi. (-150) ÷ (-25)
\( \frac{-150}{-25} = \frac{(-1)\times150}{(-1)\times25} \)
\( = 6 \)
vii. 100 ÷ 60
\( \frac{100}{60} = \frac{5}{3} \)
viii. 9 ÷ (-54)
\( \frac{9}{-54} = \frac{9}{(-1)\times54} = \frac{-1}{6} \)
ix. 78 ÷ 65
\( \frac{78}{65} = \frac{6}{5} \)
x. (-5) ÷ (-315)
\( \frac{-5}{-315} = \frac{(-1)\times5}{(-1)\times315} = \frac{1}{63} \)
In simple words: Division of integers follows rules of signs: negative divided by positive is negative, positive divided by negative is negative, and negative divided by negative is positive. Simplify fractions to their lowest terms.

🎯 Exam Tip: Pay close attention to the signs of the numbers and simplify fractions to their simplest form to score maximum marks.

Question 2. Write three divisions of integers such that the fractional form of each will be \( \frac{24}{5} \).
Answer:
Solution:
1. \( \frac{24}{5} = \frac{24\times1}{5\times1} = 24 \div 5 \)
2. \( \frac{24}{5} = \frac{24\times2}{5\times2} = \frac{48}{10} = 48 \div 10 \)
3. \( \frac{24}{5} = \frac{24\times(-10)}{5\times(-10)} = \frac{-240}{-50} = (-240) \div (-50) \)
In simple words: To find equivalent fractional forms for a given fraction, multiply both the numerator and the denominator by the same non-zero integer. This also applies to expressing them as divisions of integers.

🎯 Exam Tip: Remember that multiplying the numerator and denominator by the same number (positive or negative) does not change the value of the fraction, allowing you to create various equivalent division expressions.

Question 3. Write three divisions of integers such that the fractional form of each will be \( \frac{-5}{7} \).
Answer:
Solution:
1. \( \frac{-5}{7} = \frac{-5\times2}{7\times2} = \frac{-10}{14} = (-10) \div 14 \)
2. \( \frac{-5}{7} = \frac{-5\times(-5)}{7\times(-5)} = \frac{25}{-35} = 25 \div (-35) \)
3. \( \frac{-5}{7} = \frac{-5\times7}{7\times7} = \frac{-35}{49} = (-35) \div 49 \)
In simple words: Similar to positive fractions, multiplying both the numerator and denominator of a negative fraction by the same non-zero integer generates equivalent fractions and corresponding division expressions.

🎯 Exam Tip: Be careful with signs when multiplying by negative integers; for example, a negative numerator multiplied by a negative number becomes positive.

Question 4. The fish in the pond below, carry some numbers. (Choose any 4 pairs and carry out four multiplications with those numbers. Now, choose four other pairs and carry out divisions with these numbers.
Examples:
i. (-13) × (-15) = 195
ii. (-24) ÷ 9 = \( \frac{-24}{9} = \frac{-8}{3} \)

ℹ️ चित्र व्याख्या (Diagram Explanation): एक तालाब में विभिन्न मछलियाँ हैं जिन पर अलग-अलग पूर्णांक संख्याएँ लिखी हुई हैं, जैसे -13, +41, -15, -8, 24, +9, -27, +12, 37, -28, -18, +13। छात्रों को इन संख्याओं के जोड़ों का उपयोग करके गुणा और भाग के उदाहरण हल करने हैं।
Answer:
Solution:
1. (-13) × 9 = -117
2. 12 x 13 = 156
3. 9 × (-37) = -333
4. (-15) × (-8) = 120
5. (-28) ÷ 12 = \( \frac{-28}{12} = \frac{(-1)\times(28)}{12} = \frac{-7}{3} \)
6. 12 ÷ 9 = \( \frac{12}{9} = \frac{4}{3} \)
7. 9 ÷ (-24) = \( \frac{9}{-24} = \frac{9}{(-1)\times24} = \frac{-3}{8} \)
8. (-18) ÷ (-27) = \( \frac{-18}{-27} = \frac{(-1)\times18}{(-1)\times27} = \frac{2}{3} \)
In simple words: This problem requires selecting pairs of integers from the diagram and performing both multiplication and division operations, remembering the rules for signs in integer arithmetic.

🎯 Exam Tip: Carefully select distinct pairs for multiplication and division. Show all steps for simplification, especially for division of negative numbers, to ensure accuracy.