a To translate a phrase into an algebraic expression, we need to think about the meaning of each key word. The phrase the product of indicates that we should multiply two things.
... × ...The two terms that we are multiplying are 9 and a numbert. Since 9 comes first in the verbal expression, it should be to the left of the multiplication.
9 × a numbert
When we say a numbert, this is indicating an arbitrary number or a variable. If we write this number as t, we can complete our expression.
the product of & 9 and a numbert
& 9 * t
When writing the product of a number and a variable, we typically remove all symbols. This leaves us with 9t.
b This time, the key words are the difference of. This indicates that we should subtract two things.
... - ...
The two terms of the subtraction are a numberx and 12.
Since a numberx comes first in the verbal expression, it should be to the left of the subtraction symbol.
a numberx - 1/2
When we say a numberx, this is indicating an arbitrary number or a variable. If we write this number as x, we can complete our expression.
the difference of &a number $x$ and 1/2
& x - 1/2
c Now we are given the key words the sum of. These indicate that we should add two things.
... + ...The two terms that we are adding are a numberm and 7.1.
Since a numberm comes first in the verbal expression, it should be to the left of the addition symbol.
a numberm + 7.1
When we say a numberm, this is indicating an arbitrary number or a variable. If we write this number as m, we can complete our expression.
the sum of & a numberm and 7.1
& m + 7.1
d Finally, the quotient of indicates that we should divide two things. This gives us
... ÷ ...The two terms of the division are 207 and a numbern.
Since 207 comes first in the verbal expression, it should be to the left of the division.
207 ÷ a numbern
When we say a numbern, this is indicating an arbitrary number or a variable. If we write this number as n, we can complete our expression.
&the quotient of 207 and n
& 207 ÷ n
We can also express this as a fraction 207n.
