How can you figure this out? You can divide the entire amount (let's say, $76.02) by the amount shown on your receipt (say, $12.67), which is the amount of one charge. You want to confirm the number of over-charges before you call your bank to correct the situation. Some portion of that total debit (being a negative on your account) is wrong. You can tell from the amount that, yes, he actually charged you way more than once. When you get home, you check your bank account online. He swipes it six times before finally returning the card to you. When you go to pay, the kid has trouble running your debit card. Since it is sum, we will be adding all the values. Firstly stepwise writing the expression based on mentioned information. But in what context could dividing a negative by a negative (and getting a positive) make any sense? The expression equivalent to the statement is B - negative eleven fourths times n minus one eighth. In this context, getting a negative answer makes sense. When subtraction occurs several times in an expression, rewrite each. So, for instance, if you owe $10 to six people, your total debt would be 6 × $10 = $60. negative 4 plus positive 2 equals negative 2. ✅ The above explanation can be described as intuitive □įinally a video from Mathologer explaining the above problem (that was a base for the above post).Some people like to think of negative numbers in terms of debts. In this situation, multiplying two negative numbers means reducing the loss, ie the total positive effect of the action. None of the traditional parts of speech fits them perfectly, but in my opinion preposition comes closest. Suppose we multiply two numbers, where the interpretation of the first is the value of profit or losses, while the meaning of the second one is the multiplication (increase / decrease) of the first value. The mathematical operations minus, plus, times have a different syntax than most of English, and this apparently confuses grammarians. ⭐️ Multiplication of negative numbers as a reduction of loss based on the arithmetic of positive numbers and zero, the commutative property of multiplication, the distributive property of multiplication over addition, we are able to justify why multiplying negative numbers must be a positive number. The above has nothing to do with intuition, but it is consistent, i.e. To solve the above, we will use a trick based on the distributive property of multiplication over addition. Time to go to the main point – let’s try to answer the question: If I see -3-4 it means 'start from zero' and take out 4 groups of negative 3s from the number. I think that the '0' always has to be at the center of the two sides (negative/positive infinity) in order for them to be balanced. I visualize the number line as a scale with a pivot on the 0. The signs are different so we must have a. This is a way I think of a negative times a negative. Now using theĬommutative property of multiplication we get:Īt this point, the intuition is a bit more difficult, but the consistency has been preserved. In this case we have a number that is positive multiplied by a negative number (minus times positive gives a minus). ![]() “By adding debt to debt,” we get more debt – intuitive. Based on the interpretation of the short notation of repeated addition, we can easily justify the following: ![]() Mathematicians, defining the arithmetic of negative numbers, wanted to be consistent with the already developed arithmetic of positive numbers and zero. These two fundamental multiplication properties can be written as followsĭistributive property: a × (b + c) = a × b + a × cĮxample: 3 × 4 = 3 × (1 + 3) = 3 × 1 +3 × 3 = 3 + 9 = 12 ⭐️ Negative numbers multiplication from the mathematician point of view ![]() It is said that multiplication is a short notation of repeated addition, which is absolutely true and, with a limitation to integers, a fairly obvious fact.Ĥ × 3 = 3 + 3 + 3 + 3 = 4 + 4 + 4 = 3 × 4 = 12 ⭐️ The commutative property of multiplication and the distributive property of multiplication over addition ⭐️ Multiplication as a short notation of repeated addition 1 Their use has been extended to many other meanings, more or less analogous. In addition, + represents the operation of addition, which results in a sum, while represents subtraction, resulting in a difference. negative seven times negative seven equals 49. The plus sign + and the minus sign are mathematical symbols used to represent the notions of positive and negative, respectively. However, the teachers have forgotten to explain why this is the case, and to pass the motivation of mathematicians who defined the arithmetic of negative numbers. positive, you can replace both minus signs with a plus sign. The formula “minus times a minus is a plus” or “negative times a negative is a positive” was put into our heads during the early school years. Surely everyone knows that the result of multiplying two negative numbers is positive.
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