Operations With Integers

concepts · 19

1. 01

   Rakesh's Puzzle: Two Numbers From A Sum And A Difference

   Find two numbers when you know only their sum and their difference, and see why the order of the numbers decides the sign.

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2. 02

   Carrom Coin Moves On A Number Line

   Turn each carrom strike into a positive or negative number, find where the coin lands with P = a + b, and read jump diagrams.

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3. 03

   Subtracting With Tokens And Zero Pairs

   Take away a bigger number from a smaller one by adding zero pairs, and see why subtracting is the same as adding the opposite.

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4. 04

   Multiplying With A Token Bag

   See multiplication as putting the same group of tokens into a bag again and again, and find out why 4 × (−2) = −8.

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5. 05

   When The Multiplier Is Negative

   A negative multiplier means taking tokens out of the bag. Use zero pairs to see why (−4) × (−2) = +8.

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6. 06

   Same Number, Different Tokens

   Different-looking token sets can stand for the same number. Find out whether the product changes when the tokens look different.

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7. 07

   Sign Rules From Patterns

   Continue a steady pattern of products below zero and see the four sign rules for multiplying integers appear.

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8. 08

   Brahmagupta's Rules: Fortune And Debt

   How Brahmagupta wrote the sign rules for multiplying and dividing in 628 CE, using fortunes and debts.

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9. 09

   Times 1, Times −1, And Swapping The Order

   Multiplying by 1 keeps a number, multiplying by −1 gives its opposite, and swapping the two numbers never changes a product.

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10. 10

    Exam Marks And Profit And Loss

    Use positive and negative integers to total exam marks with negative marking, and to find a company's profit or loss.

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11. 11

    Mine Lifts And Falling Temperatures

    Write a speed with a direction as an integer, and find where a mine lift or a temperature ends up with start + rate × time.

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12. 12

    The Magic Grid Of Integers

    Play the grid game from the start of the chapter, multiply four integers with the right sign, and find out why everyone gets −30240.

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13. 13

    Division Of Integers

    Divide integers by turning each division into a multiplication question, and use the same sign rules as multiplication.

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14. 14

    Multiplying Three Or More Integers

    Multiply three or more integers in any order, and predict the sign of a long product by counting the negative numbers.

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15. 15

    The Distributive Property With Integers

    See with tokens why a × (b + c) = a × b + a × c works for negative numbers, and use it to find products quickly.

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16. 16

    Pick The Pattern: Number Machines

    Find the hidden rule of a number machine by testing your guess on every row, then use it on the missing row.

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17. 17

    Integer Puzzles: Collatz And Consecutive Numbers

    Follow a Collatz-style rule with negative numbers until it loops, and find three consecutive integers with a given product.

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18. 18

    Integer Puzzles: Alien Coins And Expressions

    Pay exact amounts with +13 and −9 coins, then use brackets and signs to make expressions as big or as small as possible.

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19. 19

    Review: Operations With Integers

    Check what you can now do with integers, revise every rule, and solve mixed problems from the whole chapter.

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