[Music] welcome to math with Mr J in this video I'm going to cover how to solve percent problems using the percent equation now for the percent equation we can use the percent times the whole equals the part keep in mind the percent equation can help us with any percent problem whether we're looking for the percent the whole or the part we plug in what we are given and solve for what we are looking for we'll go through three sections we'll solve for the whole the part and the percent we will go through two examples for each and we're going to start with finding the whole let's jump into number one where we have 12 is 80% of what number I'm going to start by writing the equation using variables and then we will plug in so percent times whole equals part P for the percent W for the whole and a for the part now as far as identifying the different parts of the equation so figuring out the percent the whole and the part from the problem what I like to do is identify the percent and the whole first and I like doing that by looking for the keyword of no matter how the problem is worded what's given or what the unknown is look for the percent of the whole when working with percents we have a percent of a whole amount so I like to identify those first and fill in the equation from there so of is associated with the whole and then is is going to be associated with the part so for number one the percent is 80% and we're actually going to write the percent as a decimal within our equation in order to be able to work through everything so we want that decimal form and remember all we need to do when going from a percent to a decimal is divide by 100 and a quick way to do that is move the decimal twice to the left the decimal comes after a whole number so for 80% the decimal goes right here and we move it once twice to the left so we get 0.80 80 hundredths which we can just use 8810 zeros to the right of decimal digits don't change the value of a decimal so we can leave that zero off and use the equivalent decimal 8/10 that will give us less digits to have to work with so we plug in 8/10 4 P times and now we need the whole so look for of the percent of the whole amount well we have 80% of what number so the whole is unknown let's use our variable W to represent that so 80% as a decimal time W equals the part as far as the part is can be a helpful key word here as we think about about this 12 is 80% of what number so 12 is the part and we can plug that in right here now we have our equation set up and we need to solve we need to isolate that variable of w we are multiplying W by 8/10 so we need to use the inverse operation division in order to isolate W so let's divide the left side of the equation by 8/10 whatever we do to one side of an equation we must do to the other so divide the right side by 810s as well now the 810s on the left cancel each other out W is now isolated equals and then on the right we have 12 / 810 so let's come to the side and solve this by hand so we have 12 / 81s now remember when we divide decimals we need the divisor that outside number we're dividing by to be whole so here we need to multiply by 10 so we move the decimal once to the right to make this eight so again we need this outside number to be whole so we are multiplying it by 10 we can move the decimal once to the right and now we have eight now whatever we do to the divisor the outside number we need to do to the dividend the inside number which is 12 so we need to multiply 12 by 10 that gives us 120 or we can think through it by moving the decimal once to the right just like we did with 8/10ths the decimal comes after a whole number so right here for 12 and we move it once to the right fill this Gap with a zero and we get 120 so we have 120 / 8 let's rewrite this without the arrows here so we have 120 divided by 8 now we can divide so we start with 1 divided 8 how many whole groups of eight in one well we can't do that so we use the two and now we have 12 / 8 how many whole groups of eight in 12 well one that gets us to eight so we put one right here above the two multiply 1 * 8 is 8 subtract 12 - 8 is 4 now we need to bring down our next digit which is this zero so now we have 40 40 / 8 how many whole groups of eight in 40 well five that gets us to 40 exactly now we multiply 5 * 8 40 subtract 40 minus 40 is 0o so we get 15 W equals 15 so 12 is 80% of 15 let's move on to number two taking a look at number 2 we have 55% of what number is 33 so for this one the wording is a little bit different than number one but we can solve it the same way so let's write out our equation percent time whole equals part let's plug in our percent well we have 55% and we need this in decimal form the decimal comes after 55 here and we move it once twice to the left and we get 0.55 55 5 hunds so plug that in for the percent times the whole which is well 55% of what number is 33 the whole is unknown here so we use our variable W equals the part which is 303 now we solve so we need to isolate our variable w w is being multiplied by 55 hundredths so we need the inverse operation division in order to isolate W so let's divide the left side by 5500s that means we need to divide the right side by 5500s as well now on the left these cancel each other out W is now isolated so w equals and then on the right we have 33 / 5500 let's go to the side here and work through this so 33 / 55 hundredths now our divisor that outside number is a decimal let's make it a whole number by multiplying it by 100 for this one we need to move the decimal twice we need to multiply it by 100 to get it to a whole number so once twice that means we need to to multiply the dividend the inside number by 100 as well 33 * 100 gives us 3,300 or we can also take the decimal like we did on the outside and move it once twice to the right and fill these gaps with zeros either way we get 3,300 let's come to the side and rewrite this so we have 3,300 ided by 55 now let's divide so we start with 3 ided 55 how many whole groups of 55 in three well we can't do that so we use the other three and think of this as 33 / 55 how many whole groups of 55 in 33 well we can't do that either so we need to use the zero and do 330 / 55 so how how many whole groups of 55 in 330 well six and the six needs to go above the zero there that's actually going to hit 330 exactly now we multiply 6 * 55 is 330 subtract we get zero and now we need to bring down our next digit which is a zero so we end up with Zer there and now we do 0 / 5 5 which is 0 multiply 0 * 55 0 subtract 0 - 0 is zero so we get 60 W equals 60 so 55% of 60 is 33 so there's our section on finding the whole let's move on to finding the part here's our section on finding the part let's jump into number one where we have what is 65% of 80 basically this is saying 65% of 80 is what part of 80 is what number out of 80 I'm going to start by writing the equation using variables and then we will plug in so P for percent time W for whole equal a for part percent * whole equal part next we can plug in what we are given and keep a variable for the unknown let's start with the percent which is 65% and we actually want to write the percent as a decimal within our equation in order to work through everything we're going to end up multiplying here so we want the decimal form and remember all we need to do when going from a percent to a decimal is divide by 100 and a quick way to do that is to move the decimal twice to the left the decimal comes after a whole number so the decimal is right here for 65% and we move it once twice to the left so we get 65 65 hundreds so let's plug that in for p times the whole which is 80 so 6500s * 80 now the percent time the whole equals the part and that's our unknown here so we need a variable and we're using a for part so let's put equals a now as far as identifying the different parts of the equation so figuring out the percent the whole and the part remember we can look for that percent of a whole amount and use the keywords of and is so what is 65% of 80 what is so the part is unknown 65% so the percent is 65% of 80 so the whole is 80 now we solve well our variable a is already isolated on the right side of the equation so all we need to do is multiply on the left side of the equation so 6500s * 80 let's come to the side and multiply this by hand and and remember when we multiply decimals we can actually start by taking out any decimals then we multiply and then place the decimal in our answer at the end so we can just do 65 * 80 but I'm actually going to set this up as 80 time 65 I like putting the greater number on top when multiplying either way will work though now let's multiply 5 * 0 is 0 5 * 8 is 40 we are done with this five and we are moving over a place to the six so we need a zero here and now we do 6 * 0 which is 0 and then 6 * 8 which is 48 and now we can add 0 + 0 is 0 0 + 0 is 0 4 + 8 is 12 and then 1 + 4 is 5 and now we need to place the decimal so we go back to the original problem and see how many digits are to the right of a decimal and that's how many digits are to the right of the decimal in our answer so looking at our original problem we have one two digits to the right of a decimal so we need one two digits to the right of the decimal in our answer so we get 52.00 which is just 52 so we can leave those zeros off a equals 52 so 52 is 65% of 80 let's move on to number two taking a look at number two we have 42% of 27 is what number the wording here is a little different than number one but we can go about solving this the same exact way 42% of 27 is what part of 27 let's write our equation the percent time the whole equals the part now we plug in our percent is 42 and we need the decimal form so we need to divide div by 100 the decimal comes after a whole number so right here and we move it once twice to the left so we get 42 42 hundredths let's plug that in to the equation times the whole well we have 42% of our whole amount 27 so 27 is the whole so we need to do 42 hundredths * * 27 equal a the part the part is unknown so we need that variable there now we solve the variable is isolated so all we need to do is multiply on the left side of the equation we need to do 4200s * 27 so let's come to the side and we will take any decimals out so let's do 42 * 27 let's start with 7 * 2 which is 14 then we have 7 * 4 which is 28 + 1 is 29 we are done with the seven and this one we are moving over a place to the two so we need a zero here and then we do 2 * 2 which is 4 and then 2 * 4 gives us 8 and now we can add these 4 + 0 is 4 4 9 + 4 is 13 1 + 2 is 3 + 8 is 11 and now we can place the decimal so in our original problem we have one two digits to the right of a decimal that means our answer needs two so one two digits to the right of the decimal we get 11.34 11 and 34 100 so our part A equals 11 34 11 and 34 hundredths so 42% of 27 is 11 and 34 hundredths so there's our section on finding the part let's move on to finding the percent here's our section on finding the perc let's jump into number one where we have 21 is what percent of 30 I'm going to start by writing the equation using variables and then we will plug in so we have percent times whole equals part now as far as identifying the different parts of the equation 21 is what percent of 30 so 21 is 21 is the what percent the percent is unknown of 30 30 is the whole amount with the percent being the unknown we keep the variable P times the whole which is 30 equals the part which is 21 and now we need to solve this equation so we need to isolate that variable of P now p is being multiplied by 30 so we need to use the in inverse operation in order to isolate the variable the inverse operation of multiplication is division so we need to divide the left side of the equation by 30 now whatever we do to one side of an equation we must do to the other so divide the right side by 30 as well now the 30s on the left cancel each other out p is now isolated so we have P equals and then on the right we have 21 over 30 21 / 30 now 21 / 30 is going to give us a decimal that we can convert to a percent so let's come over to the side and do 21 / 30 and let's divide we have 21 / 30 so how many whole groups of 30 in 21 how many 30s in 21 well we can't do that so we need to use a decimal and a zero in order to work through this once we have the decimal and the zero we can bring the decimal straight up into where the quotient the answer will be and now we can think of this as 210 / 30 so how many whole groups of 30 in 210 how many 30s in 210 well seven that actually hits 210 exactly and we need to put the seven right here above the zero since we used that zero and thought of this as 210 that will line us up correctly now we multiply 7 * 30 is 210 subtract 210 - 210 is 0er so we have that clean cut zero there at the bottom and we went all the way over within our division problem so we are done we get 77 710 now that answer is in decimal form we are looking for a percent so let's convert this decimal to a percent and remember all we need to do to convert a decimal to a percent is multiply by 100 and a quick way to do that is move the decimal twice to the right so for 710s and I'm going to write this off to the side here we need to move the decimal once twice to the right and we can fill this Gap this place with a zero so 710 equal 70% so P equals 710 as a decimal which equals 70% as a percent so 21 is 70 perent of 30 let's move on to number two taking a look at number two we have what percent of 16 is 10 so the wording is a little different than number one but it's the same type of problem let's write our equation so percent times whole equals part and now we can plug in well what percent of 16 is 10 so what percent the percent is unknown of 16 so 16 is the whole is 10 so 10 is the part so with the percent being the unknown we can keep the variable P times the whole which is 16 equals the part which is 10 and now we can solve so we need to isolate the variable p is being multiplied by 16 so we need to use the inverse operation division so divide the left side by 16 whatever we do to one side of an equation we must do to the other so divide the right side by 16 as well now the 16s on the left cancel each other out p is now isolated equals and then on the right we have 10 over 16 10 10 / 16 let's divide in order to get a decimal and then we can convert that decimal to a percent so we have 10 / 16 so let's divide we have 10 / 16 how many whole groups of 16 in 10 how many 16s in 10 well we can't do that so we need a decimal and a zero in order to work through this once we the decimal and the zero bring the decimal straight up into where the quotient the answer will be and I'm actually going to extend this division bar here and now we can think of this as 100 / 16 so how many whole groups of 16 in 100 how many 16s in 100 well six that gets us to 96 so that six needs to go above the zero since we used that zero and we thought of this as 100 and that's going to line us up now we need to multiply 6 * 16 is 96 subtract 100 - 96 is 4 now we don't have a clean cut zero there at the bottom so we need to continue on by using another zero that we can bring down and now we have 40 so we have 40 ID 16 how many whole groups of 16 and 40 well two that gets us to 32 multiply 2 * 16 32 40 - 32 is 8 so again we don't have that clean cut zero there at the bottom so let's use another zero that we can bring down and now we have 80 80 / 16 that's going to be five and that will hit 80 exactly now we multiply 5 * 16 is 80 80 - 80 is 0 so we get that clean cut0 there at the bottom and we went all the way over within our division problem so we are done 625 625,000 now let's convert this decimal to a percent by multiplying it by 100 so I'm going to rewrite it off to the side here and move the decimal once twice to the right so the decimal is going to go in between the two and the five that gives us 62.5% so P equals 625,000 which equals 62.5% so that means 62.5% of 16 is 10 in other words 10 is 62.5% of 16 so there you have it there's how to solve percent problems using the percent equation I hope that helped thanks so much for watching until next time peace