00:00Please see the link in the description to download a worksheet for this video.
00:05If you've not already done so, we suggest that before you watch this video,
00:09you watch the video introducing the order of operations.
00:13This is Ms. Anderson and her fifth grade class at Jackson Elementary School.
00:17One day, Ms. Anderson had to stay home so Mr. Jones taught her class.
00:21Mr. Jones is a substitute teacher.
00:24Ms. Anderson and Mr. Jones are both certified teachers, so they are equal in their jobs.
00:29They can fill in for each other.
00:31When two people or things are equal, and we have one fill in for the other, we call that substitution.
00:37That's why we call Mr. Jones a substitute.
00:40This is Susie. She's a student in the class.
00:43Susie is not equal in skill to Ms. Anderson.
00:46That means Susie can not be a substitute for Ms. Anderson.
00:50If we left Susie in charge of the class, then the students might learn nothing.
00:55In math, we also use the word substitute.
00:57We use substitution a lot when applying a formula to a specific problem.
01:01For example, you may have used substitution when applying the formula for a rectangle's area
01:06to calculate the area of a specific rectangle.
01:10In this video, we'll
01:11Learn how to substitute letters with numbers.
01:14Learn how we substitute operations symbols for other symbols.
01:18And practice with a sample test question.
01:20We'll begin with learning how to substitute letters with numbers.
01:23We'll learn about this by using a formula which helps us figure out the distance
01:27that somebody or something has traveled.
01:30Here's the formula.
01:31Distance traveled equals the rate multiplied by the time.
01:35In math, we use the word rate rather than the word speed.
01:40What distance did this train travel?
01:42It's traveling at a rate of 30 miles per hour, and it's been traveling for one hour.
01:47The formula is, distance equals rate multiplied by time.
01:53Next, we substitute the number 30 for the word rate, and we substitute the number 1 for
01:58the word time.
01:59Then we do the multiplication.
02:0130 times 1 equals 30.
02:04So the distance this train traveled in one hour was 30 miles.
02:07We often use abbreviations in math formulas.
02:12We do this by writing only the first letter of a word.
02:15So the distance formula becomes, D equals R multiplied by T.
02:20What distance did this ship travel?
02:23Its rate is 20 miles per hour.
02:25Its time is 4 hours.
02:27We know the formula is D equals R multiplied by T.
02:31Next, we substitute the number 20 for the letter R,
02:34and we substitute the number 4 for the letter T.
02:38Then we do the multiplication.
02:4020 times 4 equals 80.
02:43So the distance this ship traveled in 4 hours was 80 miles.
02:47In math, we use the equals sign instead of the word is.
02:51So we might get a problem like this.
02:53What distance did this car travel?
02:56R equals 50 miles per hour.
02:58T equals 2 hours.
03:00The distance formula is D equals R multiplied by T.
03:04Next, we substitute the number 50 for the letter R,
03:08and we substitute the number 2 for the letter T.
03:11Then we do the multiplication.
03:1450 times 2 equals 100.
03:16So the distance this car traveled in 2 hours was 100 miles.
03:21Next, we'll learn how we substitute operation symbols for other symbols.
03:26In everyday talking, we might use the word operation to refer to a surgery that people or pets
03:31get to make them better.
03:33In math, we also use the word operation,
03:36but we use it as a general word to refer to a way that we can do a calculation.
03:41We learn 4 operations in elementary school.
03:44We learn how to add, subtract, multiply, and divide.
03:48Please note that the symbol for multiplication can be the letter X.
03:52This can cause some students to make mistakes.
03:54That's because many math problems involve formulas that contain the letters X and Y.
03:59You may have already encountered these formulas when you were learning about how to graph points
04:03and not line graphs.
04:05Here's a typical formula involving X and Y.
04:08It says that the value of Y equals 2 multiplied by X.
04:13This format can be very confusing to students because the letter X appears twice.
04:18The first time, the X stands for multiplication.
04:21The second time, the X stands for a letter that can be substituted with a number.
04:26To avoid confusion, we suggest that when solving formulas,
04:30you write the multiplication operation with an asterisk symbol,
04:34rather than use the letter X.
04:35When you learn to write software programs,
04:38you'll see that we use the asterisk symbol to mean multiplication.
04:42So this is a very common way to write multiplication.
04:45Here are the most common ways we write that two numbers are being multiplied.
04:49We can say the word times.
04:51We can use the letter X.
04:53Or we can use an asterisk.
04:55These multiplication symbols also apply to letters.
04:59Here, M stands for any number.
05:01We can write two times M in words.
05:04We can write it using the letter X.
05:05We can write it using an asterisk.
05:08And we can also put the number and the letter alongside each other.
05:11All of these mean the same thing.
05:13We recommend that you use the asterisk symbol to avoid errors.
05:17In the prior examples of outdistance,
05:19we used the multiplication sign written as an X,
05:23because that's how most students learn to do multiplication.
05:27But in future, we suggest that you rewrite this using the asterisk symbol when you solve math problems.
05:32For example, a test question could ask what distance did these friends travel?
05:39R equals 5 miles per hour.
05:41T equals 3 hours.
05:44The distance formula is D equals R multiplied by T.
05:48Please note how we're using an asterisk as the multiplication symbol.
05:52Next, we substitute the number 5 for the letter R.
05:57And we substitute the number 3 for the letter T.
06:00Then, we do the multiplication.
06:025 times 3 equals 15.
06:05So, the distance they traveled was 15 miles.
06:09Likewise, there are many ways we can show the division operation.
06:12We can use words like 6 divided by 3.
06:16We can use a division symbol.
06:17We can use a forward slash.
06:19And we can use a horizontal bar.
06:22If we were using a letter, like the letter M,
06:25then we would write 6 divided by M.
06:27We could write this using the division symbol.
06:30We could write this using a forward slash.
06:32Or we could write this using a horizontal bar.
06:35All of these mean the same thing.
06:37All mean due division.
06:38If possible, we suggest that you use the division symbol.
06:42This will help avoid confusion and errors.
06:45Our last topic is to practice substitution with a sample test question.
06:50What is the value of the following expression, when S equals 2?
06:55First, we'll rewrite the expression by substituting the X multiplication sign with an asterisk.
07:01This helps prevent confusion about what's a multiplication operation versus what's a letter.
07:06Next, we rewrite the expression by substituting the letter X with a number 2.
07:12Finally, we solve the expression by doing the calculation.
07:15We multiply 4 times 2, which equals 8.
07:19The value of this expression is 8.
07:22Thanks for your attention.
