TenMarks teaches you how to solve multiplication equations including real world applications.
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Let’s learn how to do multiplication equations with fractions. We’re given two problems. The first one says, solve for y when I know 10/3×y=5. This is multiplication equation because 10/3 is multiplied to the variable y. Since the multiplication and division are inverse operations, I can use one to undo the other. The reason we have to undo them is we have to make sure the left side only contains y. What we will do is the left side to this says 10/3×y=5. What we’ll do is divide the left side by 10/3 and we’ll divide the right side by 5/3. If I divide the left and the right side by the same value, it makes no difference. Let’s do this. The left side becomes 10/3×y÷10/3. The right side becomes 5÷10/3. Let’s do the left side first. We’ll tackle the left hand side first which is 10/3×y÷10/3. Since I'm dividing a fraction by another fraction, it’s the same as multiplying by reciprocal. 10/3×y multiplied by the reciprocal which is 3/10 which gives me 10×3 is 30×y÷3×10 is 30 which is y. The right hand side gives me 5÷10/3 which is the same as 5/1÷10/3. 5/1÷10/3 is 5/1×3/10 which is 5×3 is 15, 1×10 is 10. What do we know? The left side says y, the right side says 15/10. My answer is y=15/10 but 15/10 is an improper fraction. I can actually divide both by the GCF which is 5. 15/5 is 3, 10/5, 10÷5 is 2, so y=3/2. Key thing to remember when I'm solving it is y=3/2. The way we did this is we looked at the equation. We divided the left and the right hand side by the same value which is to undo the operation on the left. When I divided the left side by 10/3, we got this which is y, when we divided the right hand side which is 5÷10/3; that’s the same as 5/1÷10/3. Division is the same as multiplication with the reciprocal which gave me 15/10 which is the same as 3/2. The answer is y=3/2. The second problem says, the width of a dance floor is 14 ft. The width is 2/3 of its length. We need to find the length. It says the width equals 2/3 times length, we need to find out. We know the width equals 14 ft. What equation do we have? Replacing, we know the width equals 14 ft. 14 ft.=2/3 × length. Since this is a multiplication equation, let’s divide the right hand side, divide by 2/3 and divide the left side by 2/3. This gives me 14÷2/3=2/3 × length ÷ 2/3. What do I have here? 14÷2/3 is the same as 14 multiplied by the reciprocal which is 3/2. Here, I have 2/3 × length multiplied by the reciprocal which is 3/2. Again, the left side becomes 14×3 is 42/2, the right side becomes 2×3×length. So, 6 × length over 3×2 which is 6 which means the right side is only length; the left side is 42 by 2 which means the length equals 42/2. If length equals 42/2, I can simplify this by dividing the numerator and the denominator by there greatest common factor which is 2 which gives me 21 by 1 equals 21. The length equals 21 or the length of the dance floor equals 21 ft. It was a simple multiplication equation. Once we knew was the width is 2/3 of length and the width is 14 ft. that means 14=2/3 of length. It’s a simple multiplication equation which we have to undo by dividing both sides by 2/3. Division is the same as multiplication by the inverse or the reciprocal which gave me the length equals 42/2 or 21 ft.

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