Question

translating phrases: single - variable
translate each verbal phrase into an algebraic expression.

1. two - ninths of h
2. g reduced by 1
3. the quotient of the square of r and 6
4. combine the cube of k and 27
5. y raised to the fourth power
6. 10 multiplied by m
7. one - half of the cube of k
8. the square of d
9. add x to 4
10. j diminished by two - thirds

Explanation:

Step1: Translate "Two - ninths of h"

"Of" means multiplication in math, so it is $\frac{2}{9}h$.

Step2: Translate "g reduced by 1"

"Reduced by" means subtraction, so it is $g - 1$.

Step3: Translate "The quotient of the square of r and 6"

The square of r is $r^{2}$, and the quotient means division, so it is $\frac{r^{2}}{6}$.

Step4: Translate "Combine the cube of k and 27"

It likely means addition, so it is $k^{3}+27$.

Step5: Translate "y raised to the fourth power"

This is written as $y^{4}$.

Step6: Translate "10 multiplied by m"

Multiplication gives $10m$.

Step7: Translate "One - half of the cube of k"

The cube of k is $k^{3}$, and one - half of it is $\frac{1}{2}k^{3}$.

Step8: Translate "The square of d"

This is $d^{2}$.

Step9: Translate "Add x to 4"

It is $4 + x$.

Step10: Translate "j diminished by two - thirds"

"Diminished by" means subtraction, so it is $j-\frac{2}{3}$.

Answer:

1. $\frac{2}{9}h$
2. $g - 1$
3. $\frac{r^{2}}{6}$
4. $k^{3}+27$
5. $y^{4}$
6. $10m$
7. $\frac{1}{2}k^{3}$
8. $d^{2}$
9. $4 + x$
10. $j-\frac{2}{3}$