All ACT Math Resources
Example Question #1 : Rational Expressions
Find the product of and .
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?
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?
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
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.