ACT Math : How to evaluate rational expressions

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #1 : Rational Expressions

Find the product of  and .

Possible Answers:

Correct answer:

Explanation:

Solve the first equation for .


Solve the second equation for

The final step is to multiply  and .

      

 

Example Question #2 : Rational Expressions

The following table shows the temperature of a cup of coffee at different times

Time                           1:09    1:11    1:13    1:15    1:17   

Temperature (ºF)            187.1  184.4  181.7  179.0  176.3

If this trend continues, what will the temperature of the coffee at minute 1:25?

Possible Answers:

165.5°F

162.9°F

171.0°F

160.2°F

168.3°F

Correct answer:

165.5°F

Explanation:

The table shows that for every two minutes, the temperature of the coffee lowers 2.7ºF. At 1:25, 16 minutes, or eight 2-minute intervals have passed, and the temperature of the coffee has lowered by 8*2.7ºF, reaching a temperature of 165.5ºF.

Example Question #1 : How To Evaluate Rational Expressions

Amy buys concert tickets for herself and her friends. She initially buys them at $40/ticket. Weeks later, her other friends ask her to buy them tickets, but the prices have increased to $54. Amy buys 7 tickets total and spends $350. How many tickets has she paid $40 on?

Possible Answers:

Correct answer:

Explanation:

Amy has bought 7 tickets, x of them at $40/ticket, and the remaining 7-x at $54/ticket. She spends at total of 

Example Question #2 : How To Evaluate Rational Expressions

What is 

?

Possible Answers:

Correct answer:

Explanation:

To find an equivalency we must rationalize the denominator.

To rationalize the denominator multiply the numerator and denominator by the denominator.

 

  

To simplify completely, factor out a three from the numerator and denominator resulting in the final solution.

 

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