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Multiplying integers

Multiplying integers. By Rose Eisenmenger. What Is Multiplication?. A number of groups of a number Example: 6 x 3 is the same as saying 6 groups of 3 This could be shown as:. What Is Multiplication?.

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Multiplying integers

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  1. Multiplying integers By Rose Eisenmenger

  2. What Is Multiplication? • A number of groups of a number • Example: 6 x 3 is the same as saying 6 groups of 3 • This could be shown as:

  3. What Is Multiplication? • It could also be said in a word problem, Mary had 5 friends coming over, and she wanted each person, including herself, to have 3 chocolates. How many chocolates would she need to buy? • Therefore, multiplication can be shown as: • an equation • 6 x 3 • word problem • Mary had 5 friends … • picture

  4. Example 1Multiplying A Positive By A Negative • Let’s try another problem using equation, word problem, and a picture • Equation • 6 x -4 • Word Problem • Suzie owed 6 of her friends 4 dollars. How much money did she owe?

  5. Example 1Positive x Negative Picture • Here are 6 boxes of 4, but we need six boxes of negative four • Another way to say negative is, the opposite of, so we need the opposite of 4 Opposite of… Opposite of… Opposite of… Opposite of… Opposite of… Opposite of… 4 4 4 4 4 4 *Since we are doing the opposite of 6 x 4 which equals 24, our product will be the opposite! What do you think the answer is? -24

  6. Example 2Multiplying A Negative By A Positive • We will also use an equation, word problem, and picture for this problem • Equation • -8 x 5 • Word Problem • 8 people got a letter in the mail from the bank stating that they received 5$. One week later, the same eight people got another letter saying that the bank made a mistake and meant to say that they owed the bank 5$.

  7. Example 2Negative x Positive Picture • Here are 8 boxes of 5, but we need negative 8 boxes of 5 • Another way to say negative is, the opposite of, so we need the opposite of 8 boxes • Since we are doing the opposite of 8 x 5 where we would get a positive answer, we will get an negative product. What do you think the answer is? Opposite of… Opposite of… Opposite of… Opposite of… Opposite of… Opposite of… Opposite of… Opposite of… 5 5 5 5 5 5 5 5 -40

  8. Example 3Multiplying A Negative By A Negative • Guess what? We are going to use the same method for this problem too! • Equation • -9 x -2 • Word Problem • There were many people at the dog park, but only nine of the people brought two dogs each. All 18 of those dogs found a way to escape under a fence, and became lost. The owners of the dogs went home dog-less and felt “negative” or sad. The next day, all the dogs returned home, which made the owners feel positive!

  9. Example 3 Negative x Negative • We have 9 boxes of two, but we need negative nine boxes of negative two. • Another way to say that is… Opposite of… Opposite of… Opposite of… Opposite of… Opposite of… Opposite of… Opposite of… Opposite of… Opposite of… Opposite of… Opposite of… Opposite of… Opposite of… Opposite of… Opposite of… Opposite of… Opposite of… Opposite of… 2 2 2 2 2 2 2 2 2 *We have one “opposite of” for each negative number per box *Since there are two negative numbers or “Opposite of…” per box, they cancel each other out *Therefore, your answer will be positive *What do you think your answer will be? 18

  10. Let’s Try Some! • 6 x -7 • -8 x 4 • -3 x 5 • -6 x -1 • Challenge: -2 x 0 = -42 = -32 = -15 =6 =0

  11. Multiplying Integers Rules • A positive times a negative equals a negative(pxn) • A positive times a positive equals a positive (pxp) • A negative times a negative equals a positive(nxn) • Between the two factors and the product, there should either be 2 negative numbers or zero negative numbers

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