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Multiplying Integers Word Problem

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Integers Recap Zero Negative integers Positive integers The numbers –1, –2, –3, … (to the left of zero) are called negative integers The numbers 1, 2, 3,… (to the right of zero) as positive integers. The new set of numbers …, -3, -2, -1, 0, 1, 2, 3,… are called Integers. ‘–’ symbol in front of a number is read as ‘negative’ or ‘minus’. For example, –5 is read as negative 5 or minus 5. A number without a sign is considered as a positive number. For example, 5 is considered as +5.

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Terminologies Positive Negative Above sea level Above ground Increase

Gain/Profit Deposit Positive Marking Kept back Raises Below sea level Below ground Decrease Loss Withdraw Negative Marking Taken Out Descends

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+ ( + ) = + + ( – ) = – – ( – ) = + – ( + ) = –

Rules of Addition and subtraction Rule 1 Two numbers have same sign Add the numbers Copy bigger number sign Rule 2 Two numbers have different sign Subtract the numbers Copy bigger number sign Rules of multiplication Converting 2 symbols into 1 Rule 1 Multiply same sign Answer is + + ( + ) = + – ( – ) = + Rule 2 Multiply different sign Answer is – + ( – ) = – – ( + ) = –

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Example 1:On a mountain the temperature decreases by 5°c for every 10m ascent.

What will be the temperature 100m above point A. If the temp at A is 6°c. Given: Temp at A = 6°c Temp decreases by 5°c for every 10m ascent. To find: Temp at 100m above point A Solution: Temperature decreases by – 5°c for every 10m for every 10 m = – 5°c temp drop To reach 100m ,10 should be multiplied with 10 m m x 10 = – 5°c x 10 m At 100m, temperature reduces by – 50°c The temperature reduces by – 50°c above 100 m from point A At point A the temperature was +6°c. So, exact temp at 100m, above point A = = – 44 °c The exact temperature above 100m from point A = – 44°c

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Example 2: In a test containing 15 questions, 4 marks is given for correct answer and

-2 for wrong answer. Mohan attempted all the questions and only 9 of his answers were correct. What was his test score? Given: Total number of question = 15 No. of correct answers given by Mohan = 9 Mark for one correct answers = 4 (i.e. +4) Mark for one wrong answers = -2 To find: Total marks scored by Mohan Soln: Marks scored by Mohan on 9 correct answers = 9 x 4 = 36 Marks scored by Mohan on 6 (=15-9) wrong answers = 6 x -2 = -12 Test Score = Correct answers marks + Wrong answers marks = 36 + (-12) = 36 – 12 = 24 By sign rule, (+) x (+) = + (+) x (-) = – Answer: The test score is 24 By rule + (-) = –

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Try these A company manufactures 16m of cloth every hour. After 7

hours it is seen that due to a worker’s fault 7m of cloth is spoiled. At present how many meters of cloth does the company has for sale A chocolate company earns a profit of Rs.8 per dark chocolate and profit of Rs.5 per white chocolate. What is the earnings if it sells 300 dark and 800 white chocolates in a month?

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