Video Transcript
Are the ratios six pounds to 54 ounces and five pounds to 50 ounces equivalent?
As the first number of both of the ratios is in pounds and the second number is in ounces, we could just consider the numbers. We can look at the ratios six to 54 and five to 50 to determine whether the two ratios are equivalent. The usual method when dealing with two different units would be to convert them all to the same unit first. We will look at this method after.
The numbers six and 54 are both divisible by six. Six divided by six is equal to one. 54 divided by six is equal to nine. This means that the ratio six to 54 in its simplest form is one to nine. Both sides of the second ratio five to 50 can be divided by five. Five divided by five is equal to one. 50 divided by five is equal to 10. This means that the ratio five to 50 in its simplest form is one to 10. In the first ratio, for every one pound, we have nine ounces. Whereas in the second ratio, for every one pound, we have 10 ounces. As these two ratios are not the same, we can conclude that the ratios six pounds to 54 ounces and five pounds to 50 ounces are not equivalent.
As mentioned earlier, an alternative method would be to convert all four values into the same units. There are 16 ounces in one pound. This means that five pounds is equal to five multiplied by 16 ounces. Five multiplied by 16 is equal to 80. As five multiplied by 10 is 50 and five multiplied by six is equal to 30. Six pounds can be converted into ounces by multiplying six by 16. If five multiplied by 16 is 80, then six multiplied by 16 is 96. We add another 16 to 80 ounces. Our first ratio six pounds to 54 ounces can therefore be rewritten as 96 to 54.
The second ratio five pounds to 50 ounces could be rewritten as 80 to 50. 96 and 54 are both divisible by six. 96 divided by six is equal to 16. 54 divided by six is equal to nine. Therefore, 96 to 54 can be simplified to 16 to nine. As these numbers have no common factor apart from one, we cannot simplify the ratio any further. 80 and 50 are both divisible by 10. 80 divided by 10 is eight. And 50 divided by 10 is equal to five. Therefore, the ratio 80 to 50 simplifies to eight to five. As the two ratios once again are not the same, we can confirm that the ratios are not equivalent. The ratios 16 to nine and eight to five are not the same. We could add one extra line here. Eight to five is the same as 16 to 10 as we can double both sides. Clearly, 16 to nine is not the same as 16 to 10.