Equivalent rational expressions (SAT) Practice Questions (Grade 9)

Question 1easy

Which expression is equivalent to $\dfrac{15p}{r} + 15p$ , where $r > 0$ ?

Write $15p$ with denominator $r$ : $\dfrac{15p}{r} + \dfrac{15pr}{r} = \dfrac{15p + 15pr}{r} = \dfrac{15p(r + 1)}{r}$ .

Question 2easy

Which expression is equivalent to $\dfrac{24n}{w} + 24n$ , where $w > 0$ ?

Write $24n$ with denominator $w$ : $\dfrac{24n}{w} + \dfrac{24nw}{w} = \dfrac{24n + 24nw}{w} = \dfrac{24n(w + 1)}{w}$ .

Question 3easy

Which expression is equivalent to $\dfrac{50x}{h} + 50x$ , where $h > 0$ ?

Write $50x$ with denominator $h$ : $\dfrac{50x}{h} + \dfrac{50xh}{h} = \dfrac{50x + 50xh}{h} = \dfrac{50x(h + 1)}{h}$ .

Question 4easy

Which expression is equivalent to $\dfrac{28z}{f} + 28z$ , where $f > 0$ ?

Write $28z$ with denominator $f$ : $\dfrac{28z}{f} + \dfrac{28zf}{f} = \dfrac{28z + 28zf}{f} = \dfrac{28z(f + 1)}{f}$ .

Question 5medium

Which expression is equivalent to $\dfrac{18m}{t} + 36m$ , where $t > 0$ ?

Write $36m$ with denominator $t$ : $\dfrac{18m}{t} + \dfrac{36mt}{t} = \dfrac{18m + 36mt}{t} = \dfrac{18m(1 + 2t)}{t}$ .

Question 6medium

Which expression is equivalent to $\dfrac{12y}{c} + 24y$ , where $c > 0$ ?

Write $24y$ with denominator $c$ : $\dfrac{12y}{c} + \dfrac{24yc}{c} = \dfrac{12y + 24yc}{c} = \dfrac{12y(1 + 2c)}{c}$ .

Question 7medium

Which expression is equivalent to $\dfrac{10u}{g} + 30u$ , where $g > 0$ ?

Write $30u$ with denominator $g$ : $\dfrac{10u}{g} + \dfrac{30ug}{g} = \dfrac{10u + 30ug}{g} = \dfrac{10u(1 + 3g)}{g}$ .

Question 8medium

Which expression is equivalent to $\dfrac{35v}{k} + 70v$ , where $k > 0$ ?

Write $70v$ with denominator $k$ : $\dfrac{35v}{k} + \dfrac{70vk}{k} = \dfrac{35v + 70vk}{k} = \dfrac{35v(1 + 2k)}{k}$ .

Equivalent rational expressions (SAT) practice