In algebra, there are many different ways to represent multiplication. The following expressions all mean "two times ":
When a number is next to a variable, it means that we multiply them together. We can also represent multiplication using the dot symbol () or the familiar "times" symbol (), though we tend to avoid using the () symbol because it looks a lot like the variable
Translate the phrase "a number minus the product of three and another number" into an algebraic expression.
If we denote the first number by and the second number by , we can write "the product of three and another number" as
So, the phrase "a number minus the product of three and another number" can be written as
Translate the following phrase into an algebraic expression: "The product of three and a number."
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a
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$\dfrac{x}{3}$ |
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b
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$\dfrac{3}{x}$ |
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c
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$3x$ |
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d
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$x-3$ |
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e
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$3+x$ |
The algebraic expression $2k+4j$ can be translated into a sentence as
|
a
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Twice a number minus four times another number |
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b
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Three times a number plus twice another number |
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c
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Twice a number plus four times another number |
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d
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Twice a number plus four times that number |
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e
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Twice a number plus three times another number |
The quotient of two numbers means that we need to divide the first number by the second number.
For example, "the quotient of and two" means the same thing as " divided by two" and can be written as either expression below:
In algebra, we prefer to represent division using the fraction bar instead of the () symbol.
Translate the phrase "the quotient of a number and seven" into an algebraic expression.
"The quotient of a number and seven" means the same thing as "a number divided by seven." If we call our number then we can express this mathematically as
Write "the quotient of a number and five" as an algebraic expression.
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a
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$\dfrac{5}{m}$ |
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b
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$\dfrac{m}{5}$ |
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c
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$m-5$ |
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d
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$5m$ |
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e
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$5-m$ |
Translate the following phrase into an algebraic expression: "The quotient of a number and one fewer than that number."
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a
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$\dfrac{x-1}{x}$ |
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b
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$\dfrac{x}{x-1}$ |
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c
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$\dfrac{x+1}{x}$ |
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d
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$x-1$ |
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e
|
$\dfrac{x}{1}$ |
Translate the following phrase into an algebraic expression: "The quotient of a number and twice another number."
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a
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$\dfrac{r}{2}$ |
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b
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$\dfrac{2r}{r}$ |
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c
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$\dfrac{r}{2r}$ |
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d
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$\dfrac{2s}{r}$ |
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e
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$\dfrac{r}{2s}$ |