TenMarks teaches you how to apply multiplication equations to solve real life problems.
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Learn about Applications of Multiplication Equations Multiplication equations. So this first problem states that solar cells convert energy from the sun into useful electricity. The amount of electricity produced to measure in units called watts. If it costs $5 for each watt produced, how many watts can be produced for $700? In this problem we can use a multiplication equation to solve the problem. So here we’re going to use a multiplication equation to solve this problem. So steps that we’re going to take, the first one is we need to write our equation. So to write our equation, let’s let w represent the number of watts that can be produced. So w = the number of watts that can be produced. Now let’s set up this equation. So we’re going to take the cost to produce one watt, so the cost to produce 1 watt times the number of watts produced will equal the total cost. So this is our equation, the cost to produce 1 watt × the number of watts produced will give us our total cost. So now let’s go ahead and plug our information in. So the cost to produce 1 watt is $5. So we’re going to go ahead and plug in 5× the number of watts produced, that’s what we’re looking for so we’re going to put a w in there, because w equals the number of watts produced, we’ll equal our total cost which is $700.00. So now, we have our equation set up. So our second step is to isolate the unknown or the variable. So we need to isolate our variable. To do so we’re going to use inverse operation to isolate the unknown, so when you isolate the unknown, you’re using inverse operation. Inverse operation. So for instance, here we’re multiplying, right? So if you are multiplying, your inverse operation will be division. So division is the inverse of multiplication so we’re going to take our original equation and if we divide both sides by the same number the equation will still be true. So since we multiplied here, we’re going to divide both sides. So we’re going to divide both sides by 5. So I'm going to take 5×w and divide it by 5. So when I do that, these will cancel out, and we will have w, and then 700 divided by is 140. So our answer is the number of watts produced, is 140. Before we move on, let’s check our answer. We always want to double check to see if we’re right. So to double check, to check our answer, what we’re going to do is we’re going to substitute 140 for w in our equation and then we’re going to see if it’s true. So we’re going to take our original equation, 5 × w = 700 and we’re going to substitute 140 for w. So 5 × 140 = 700. So if I multiply 5 × 140, I get 700 = 700. So since both sides on this equation are the same, our answer is correct. So how many watts can be produced? We can produce 140 watts. Let’s move on to our second problem. Here, we need to solve (1/2)a = 40. So (1/2)a = 40 is a multiplication equation. So to solve the equation, we need to isolate the unknown. So remember to solve it, you need to isolate the unknown. And the unknown is your variable. So when we isolate the unknown, remember that we’re going to use inverse operation, so inverse operation is the opposite. So for instance if we’re multiplying here, since we’re multiplying the inverse operation will be division. So let’s go ahead and divide both sides by the same number of the equation. So we’re going to take our equation, (½)a = 40. And what we’re going to do is we’re going to divide by ½ so I'm going to divide both sides by ½. So I'm going to take ½a ÷ ½ = 40 ÷ 1/2. Now remember that dividing by a fraction is the same as multiplying by its reciprocal. So these two are going to cancel out and I'm going to be left with a, and then dividing by a fraction is the same as multiplying by its reciprocal. So this is the same as multiplying by the reciprocal. So 40 × 2 is 80. So 40 ÷ 1/2 would be 80. So a = 80. Things to remember and to keep in mind is that a quantity on the left side of the equal—so the quantity on left side of the equal sign is balanced with the quantity