Solving Proportions with Decimal Solutions | Math with Mr. J

[Music] welcome to math with mr j [Music] in this video i'm going to cover how to solve proportions with decimal solutions in other words the unknowns within the proportions are going to be decimals not all proportions work out to include only whole numbers we are still going to use cross multiplication to solve these so we need to cross multiply set the cross products equal to each other and solve let's jump into number one where we have x to 20 equals three to eight x is our unknown so we need to figure out what x equals we will start by cross multiplying so multiplying diagonally this will give us a one step equation that we can solve for x first let's do x times 8 and we can write this as 8x so 8x bring our equal sign straight down and now we have 20 times 3 so 20 times 3. i'm going to use a dot to represent multiplication that way we avoid any confusion between x's that are variables and x's that are multiplication signs next we can do 20 times 3 which is 60. so let's bring down our 8x the equal sign and then 20 times 3 again that's 60. so we have 8x equals 60. we have a one-step equation to solve for x so we need to isolate the variable x we can do that by dividing both sides by eight eight x divided by eight and sixty divided by eight eight x divided by eight gives us x equals 60 divided by 8 equals 7 and 5 10 or 7.5 so x equals 7 and 5 10. now before we move on to number two i do want to mention that when we cross multiply to solve a proportion don't get too held up on what to multiply first or which cross products go on which side of the equal sign it will all work out the same either way just make sure to multiply diagonally and have the equal sign in between your cross products let's move on to number two where we have 6 to x equals 32 to 15. we'll start by cross multiplying first we'll do 6 times 15. so 6 times 15 equals and then we have x times 32 which we can write as 32 x now we can do 6 times 15 that equals 90. so we have 90 equals 32x now we have a one-step equation to solve for x we need to isolate that variable of x we can do this by dividing both sides by 32 so 32x divided by 32 and 90 divided by 32 32x divided by 32 will isolate our variable that will give us x equals 90 divided by 32 gives us 2 and eight thousand one hundred twenty-five ten thousandths now we can rewrite that as x equals two and eight thousand one hundred twenty five ten thousandths or x equals two point eight one two five now that decimal goes to the ten thousandths place so i'm going to round it to the hundredths this decimal isn't too long but i wanted to mention rounding because there is the possibility of a very long decimal or even a repeating decimal in those cases you'll need to round so as far as rounding to the hundredths place we have x and i'm going to put is approximately because we are rounding the hundredths place we have a 1 the digit to the right is a 2 so that 1 is going to stay the same in the hundredths place we are not going to round it up to a two so x is approximately two point eight one or two and eighty-one hundredths here is our exact answer and then here is our rounded approximate answer so there you have it there's how you solve proportions with decimal solutions i hope that helped thanks so much for watching until next time peace