Download U8-4 Guten Tag u8h04

8-4
Guten Tag
Name _____________________________
Do you know what language the following expressions come from?
1) Guten tag______________________
2) Bon jour _________________________
3) Ciao __________________________
4) Shalom __________________________
5) Hola _________________________
6) 2n + 3 __________________________
It's a lot of fun to learn other languages. The answers for numbers 1-6 are German, French, Italian,
Hebrew, Spanish and Algebra, yes Algebra! Math class is just like a foreign language class. You have
learned some of this language already. Since your elementary classes you have come to recognize what
the following symbols mean:
+
÷
add
divide
=
÷
•
subtract
equals
per
multiply
x
=
multiply
is
7) Why do you think algebra teachers prefer to use a "•" sign to represent multiplication instead
of an "x"?
8) What is an algebraic way to show 3 times Elrod's weight without the x or •?
Draw lines to match these. How much you know about the language of math?
9)
±
a)
approximately
10)

b)
11)

c)
it's wrong (so it can't be my work)
pi (a value of about 22/7 or 3.1415...)
12)

d)
plus or minus
13)

e)
infinity
14)

f)
not equal
Mathematicians write words into symbols for a variety of reasons. Symbols can make math a universal
language. (If a Hungarian mathematician used the + sign, we would all know she meant to add).
Symbols also help us translate words into math talk. The following words all represent the use of one of
these symbols: +, -, x, or ÷.
divided by
less than
sum of
is
is the same as
has
difference of
more than
quotient of
total of
times
decreased by
greater than
increased by
product of
15)
Symbols take up less room on our paper and help us to stay organized. Let's make a dictionary to
help translate English words into the Algebraic language.
___ a) Place the words from above into your very own dictionary below.
+ (add)
- (subtract)
x (multiply)
÷ (divide)
=(equals)
divided by
___ b) Think a minute and then add 6 more words that aren't on the list above. Once you get the
first one, it will be easy.16)Remember to read a little, 'rite a little. Read slowly, only two or three
words at a time as you write algebraic symbols for these.
Read 'n Rite is an important skill to develop. It takes great self-discipline,
Grasshopper, not to read too many words at once. While all problems on this page
are short, now is the time to develop that skill.
a) five
more than
_____ +
eight
b) eight more than five
_____
_____
+
_____
You'd get the same answer to both of those questions. (5 + 8 = 13 and 8 + 5 = 13) When using addition,
it doesn't matter in which order we put the numbers. The answer turns out the same for addition. We
say that addition is COMMUTATIVE. (To "commute" means to move. So the "commutative property"
allows us to reverse the order, a + b = b + a, or move around the "+".)
Exceptions
Of course, every language has exceptions. Here is the key one: less than
Less than does mean - (subtract), but you must reverse the order, watch:
We know 5 less than 8 is 3. But if we read and 'rite it , we get:
5
8 which is negative 3, not just 3.
So you must reverse the order whenever you read the two words less than.
So…
5 less than
8
is really
8
-
5
which is 3.
Just translate these to algebraic symbols; do not calculate.
17
a) four more than eight
b) four less than ten
_______________________________
__________________________________
c) ten more than eight
d) two less than five
_______________________________
__________________________________
e) one less than eight
f) four more than ten
_______________________________
__________________________________
Did we catch you on #17e? I doubt it, you're way too good at this by now.
Complete the following without looking at your dictionary. I know you can do it.
18
a) of means
b) per means
c) _____________ and _____________ and _____________ all mean to add
d) List three words which translate to "=" ____________, _____________, ___________
e) Twice a number would be written as ____•____ (You learned in Unit 6 that when we don't
know the number we are referring to, all we have to do is use a variable.)
f)
8-4
Five less than a number _________________________________
page 3
Guten Tag
Name _____________________________
19)
What is the sum of 5, 3 and 6? __________ Did you notice that the word "of" does
not mean to multiply this time?
use addition while grouping.
It means to group the numbers of 5, 3 and 6 and to
This is another EXCEPTION. If the word "of" is used with another operation, it doesn't mean to
multiply but it does mean to group the numbers with parentheses. Examples:
a) three times the sum of 3 and 5 = 3 ( 3 + 5)
Simplify the answer ___________
b)
twice the difference of 5 and 2 = 2 ( 5 - 2)
c)
double the total of a number and 7 =
Simplify the answer ___________
2 (n + 7)
You're answers should be 24 and 6 for a and b. Without parentheses you'd get 14 and 8!
20)
Go back to your dictionary on the first page. Circle the phrases that will require grouping.
Remember, if the word "of" is used with another operation name it means to group the numbers with
parentheses.
With all the practice we've been doing, I know you can translate all these expressions into symbols.
Prove to yourself how great a mathematician you've become. Remember to read a little, 'rite a little.
21)
Six times a number
You don't need a multiplication sign if the
6 is placed snugly next to the n.
___n
22)
five less than a number
23)
twice a number minus three
24)
six less than one-third of a number
25)
seven greater than double a number
26) one more than one-ninth of a number
27)
six times the sum of five and a number
28)
(
29)
+
)
twice the difference of a number and three
nine divided by a number
(don't use "÷")
30)
a number increased by 6
31) one half of the sum of four and a number
32) a number decreased by four
33) two minus the sum of four and a number
34) one less than a number divided by two
Guess what? You've just been transformed into an Algebra Guru! When a fine mathematician like
yourself can transform words into expressions, they're ready to master algebra.