Translating Sentences into Equations (Level
1) Many applications in algebra require you to
translate word sentences into equations. Recall that equations contain an equal sign between
numerical and or variable expressions. In the last video we practiced translating words
into symbols converting the words into algebraic expressions. Now we are going to add an additional
level of difficulty, not only do we need to translate words into algebraic expressions
we also need to determine if the sentences describe an equation.
Usually the tell tell sign that you are face to face with an equation is by scanning the
sentence for phrases containing the word “is”, as in “5 more than a number is 10.” After
reading this sentence we find the key word “is” this means that we are face to face with
an equation so we must not forget to include an equal sign in our final expression.
Let’s try this example, the first part should be fairly easy if it’s not, I recommend you
to check the previous video titled “translating words into symbols”. Alright let’s go ahead
and translate this sentence into an equation. The expression 5 more than a number translates
to n + 5 or 5 + n because of the key word more and remembering that when you add two
numbers the order is not important. Next, we add an equal sign because of the key word
“is” and finally we include the number ten. The final expression is written as: n + 5
=10 or 5 + n=10. Both expressions are acceptable ways of writing this equation.
Alright let’s try some more examples: fifty decreased by a number is 20
We see the key word decreased so we are dealing with a subtraction between two numbers specifically
fifty and a number. So this expression is written as follows 50 – n, we also see the
key word “is” so we write an equal sign followed by the number 20. Remember when dealing with
expressions with the subtraction operator you need to be careful unlike addition where
the order between the two numbers does not matter, subtraction is order sensitive and
the expression n – 50=20 is totally different as well as totally wrong for this particular
example. So the correct answer is written as 50 – n=20. Ok let’s try the next example: seven less
than a number is twelve once again we have the key words less so we
have a subtraction, notice that the key word is less than, remember be careful with subtraction
operators at times you can’t just translate the expression in order. For this example
the expression 7 less than a number is written as n – 7 , once again we see the key word
“is” so we are dealing with an equation so we insert an equal sign and finally we include
the number 12. So the final equation is written as, n – 7=12
Let’s try the next example: the sum of one third of a number and ten is thirty.
Here we have a couple of key words, the first key word is sum so we need to add two expressions,
the first expression one third of a number is denoted as: one third times n because of the key word “of” which translates to multiplication, then we add the second expression in this case the
number 10 and then we add the equal sign because of the key word “is” and finally the number
30. So the final equation is expressed as one third n plus 10 equals 30, or written another way as 10 plus one third n equals 30. Let’s move along to the next example: a third of the sum of a number and ten is thirty.
This problem seems to look exactly like the previous example but notice that its actually
different and requires the use of grouping symbols. We first have a product because of
the key word “of” so it’s going to be a third times the sum of a number and 10 so
we use grouping symbols as follows, then we include the equal sign because of the key
word is, so we include the number 30 after the equal sign. The final expression is written
as: one third times the quantity n plus 10 equals 30 or written another way as, one third times the quantity 10 plus n equals 30. Keep in mind that some phrases require the use of grouping symbols so make sure you read
the sentence as many times as you need to completely understand the problem.
Ok notice that every single example up to this point contained an equal sign immediately
after some sentences let’s try an example where the equal sign appears first. Like the
following example: three is ten more than five times a number. In this example we first
write 3=because of the key word “is” which appears first, followed by a sum of two expressions
specifically 10 and 5n because of the key word more and times. The Final expression
is written as 3 equals 10 plus 5n or alternatively we can also write this expressions by flipping
the expression on the left side of the equal sign with those of the right side of the equal
sign as follows: 10 plus 5n equals 3. Both of these equations are essentially the same. Some sentences actually describe equations
that contain variables on both sides of the equal sign. Like the following example: Twice
a number is ten more than a number. We first write 2n followed by the equal sign because
of the key word twice and “is” which denote multiplication and an equal sign respectively.
Followed by the sum of 10 and a number n. Once again we can write this equation by
switching the expression from either side of the equal sign as follows. Alright let’s try the final example: nine
less than three times a number is 10 more than the number.
So here we have multiple things occurring on both sides of the equal sign. On the left hand
side we have a multiplication and subtraction specifically 3n – 9 followed by the equal sign
and the sum of two numbers which include 10 and n so the final expression is 3n – 9=10
+ n or 3n – 9=n + 10 either form is acceptable, because the order in which you add numbers
is not important but the order in which you subtract numbers is important, so keep this
important detail in mind. Alright In our next video we will continue translating
sentences into equations especially those that require the use of formulas.