Tag Archives: Fractions

January 2019 Algebra I Regents, THE WHOLE TEST SOLUTIONS, Premiering now!

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Is 16/7 rational or irrational? THE ANSWER MIGHT SURPRISE YOU!

Is 16/7 irrational? The answer might seem obvious to you, but in fact the vast majority of students get this wrong!

I’ve even spoken to adults, and adults who know the difference between rational and irrational numbers get this question wrong.

What is it about this number that tricks so many people? I discuss the cause in this video. By the end of this video, you’ll end up a little bit smarter, and a little bit more ready for the ACT and every other test that your school throws at you, so that you can get into the college of your choice and achieve the career you deserve.

Is the product of the square root of 16 and the fraction 4/7 rational or irrational?

A. Yes, because the product of two rational numbers is always rational.
B. Yes, because the product of two irrational numbers is rational.
C. No, because the product of a rational number and an irrational number is irrational.
D. No, because the product of two irrational numbers is irrational.
E. Yes, because the product is both rational and irrational.

SAT/ACT problem of the week, September 15, 2016 solution

Hint for process of elimination: Memorize the slope formula: $latex m=\dfrac{y_2 -y_1}{x_2 -x_1} &s=1$, where $latex m &s=1$ is the slope of the line, and $latex (x_1,y_1) &s=1$ and $latex (x_2,y_2) &s=1$ are two points on the line. You should also be able to recognize what lines look like when they have positive versus negative slopes, and large versus small slopes.

The line in the diagram has a positive slope less than 1, making D the only possible choice.

Read on for a full solution.

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SAT/ACT problem of the week, September 15, 2016

In the figure above, which of the following expressions can be used to calculate the slope of line $latex \overline{AB} &s=1$?

  1. $latex \dfrac{2-1}{-4+3} &s=1$ (check answer)
  2. $latex \dfrac{2+4}{1+3} &s=1$ (check answer)
  3. $latex \dfrac{-4+3}{2-1} &s=1$ (check answer)
  4. $latex \dfrac{1+3}{2+4} &s=1$ (check answer)
  5. $latex \dfrac{1-3}{2-4} &s=1$ (check answer)

Solutions, hints, and questions are welcomed. A full solution will be posted on September 21st. If you would like to learn how to enter math formulas into this blog, visit the WordPress LaTeX tutorial page.