TenMarks teaches you about ratios, rates and proportions.
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Learn about Ratios, Rates and Proportions In this lesson let's cover ratio, rates and proportions. We will do all three. The first problem says that add one factory, the ratio of defective light bulbs produced to total light bulb produce is about 3:700. What is the ratio? A ratio is something which is A with the ratio B, so any quantity one compared to equivalent quantity two is called the ratio. Now, if two ratios are in proportion that means they are equal. So if A is to B is equal to C is to C then these are supposed to be in proportion. That’s what we’re going to use here. So what we know is the ratio of defective to total light bulb is 3/700. You can write it as 3:700 or 3/700, it’s the same thing. This is equal to how many light bulbs are expected to be defective when 14,000 are produced. So if 14,000 of light bulbs are produced and let’s say the number of D were defective, the ratios would be equivalent. So if 700 light bulbs are produced three are defective, if 14,000 are produced D number would defective but the ratio for both of these are equivalent or these are in proportion. So if this is indeed true their cross products are equal. So 3×14000=D×700, 3×14000 is 42000=700×D. Let's divide both sides plus 700 to solve it, what do I get? So D=60, this cancels out. So D=60 is the number of defective light bulbs you will find if there are 14,000 produced and the ways we got that is by writing the two ratios and putting an equal two signs because these two ratios are the same. Let's try one more problem or a couple of more. This has to do with the rate. So it’s says John ate 52.5 hotdogs in 12 minutes so the ratio of hotdogs in minutes is 52.5/12. This is the ratio of 52.5 hotdogs in 12 minutes. If we need to find the unit rate, the unit rate is how many in one minute. Unit rate is essentially a ratio where you have two values both with different units. This is 52.5 hotdogs in 12 minutes different units, so ratio when one of the unit, the second unit equals what? The second unit should be equal to one. So if we know that 52.5 hotdogs over 12 minutes is one ratio and we need the second ratio with one unit, how many hotdogs does he eat in one minute? That’s what we need to find out. But the ratios are going to be the same so the cross multiplications are going to be the same. So 52.5 will be equal to 12×h÷12 on both sides, what do I get? 12×4 = 48, 45, 36, 9, 7, so it is about 4.38 hotdogs per minute is what he can eat. All we did was we took the first ratio 52.5 hotdogs in 12 minutes equated it to h number of hotdogs in one minute. This is the unit rate. The unit rate is always when the ratio is express in a form where the second unit is always one. So if this is equivalent then the cross products are equivalent which means 52.5×1=12×h. Then I just solve this equation to get h=4.38. So John can eat 4.38 hotdogs in one minute. Let's do the third one. We need to solve this proportion. If this is given to us as a proportion that means the cross products are equal. So 5×y-4=3×y+2. Let's just compute this, 5×y-5×4 is 20=3×y+3×2 is 6. I've got variables on both sides so let's move them one to one side. I'm going subtract 3y from both sides, what do I get? 2y-20=6, I'm going to add 20 to both sides. What do I get? 2y=this gets cancelled, 6+20 is 26 divide both sides by 2, what do I get? 2y or y is y=26/2 is 13. So the solution for this is y=13. Remember when we’re talking about ratios, rates and proportions, ratio can be express as this or 3/700. If two ratios are equal they are called and proportion and a unit rate or rate is a ratio where one of the values is one and the two values have different units.