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Category: math

Math: simplification with a rational exponent

By Jack Posted on May 3, 2014 Posted in math Tagged with radicals, rational exponents

Tutoring math, this topic is perennial.  The math tutor works an example. Imagine you are posed the following question: Simplify 32^(6/5) First, realize the following: 32^(6/5)=5√(32)^6 5√(32)=2, since 2*2*2*2*2 = 2^5 = 32. Therefore, 32^(6/5)=5√(32)^6=2^6=64 So 32^(6/5)=64. I’ll be saying …

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Math: simplifying cube roots

By Jack Posted on April 20, 2014 Posted in math Tagged with cube roots, simplifying cube roots

Tutoring high school math, cube roots come up a few times a year. The math tutor opens the discussion on simplifying them. By way of introduction, you might want to read my short article here on perfect cubes and cube …

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Math: multiplying with algebra tiles

By Jack Posted on April 16, 2014 Posted in math Tagged with algebra tiles, multiplying with algebra tiles

The tutor continues with algebra tiles. Tutoring math, you see them especially in grades 9 or 10. I began discussing algebra tiles here. Recall that they are meant to model numbers, variables, and operations you can perform to them. Recalling …

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Math: adding and subtracting radicals

By Jack Posted on April 13, 2014 Posted in math Tagged with adding radicals, radicals, subtracting radicals

Tutoring high school math, radicals are prominent.  The math tutor introduces addition and subtraction of them. Adding radicals is much like adding variables. Note that x=1x; the 1 is understood to be there, but never written. Similarly, √3=1√3. Therefore, 2√5 …

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Math: algebra tiles

By Jack Posted on April 7, 2014 Posted in math Tagged with algebra tiles

Tutoring math, you might explain algebra tiles a few times a year.  The math tutor introduces them.   If algebra tiles existed when I was in school, I never saw them. Everything back then was symbolic, and teaching didn’t have …

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Math: counting: multiply or add

By Jack Posted on March 29, 2014 Posted in math Tagged with counting

Tutoring math 12, you may discuss counting problems.  The tutor offers a quick guide for when to multiply vs when to add. One question you’re sometimes asked about counting is when you multiply, vs when you add.  The answer is …

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Math: div and mod

By Jack Posted on March 25, 2014 Posted in computer science, math

Tutoring math, you know that div and mod are also fundamental to computer science.  The tutor presents them with an example. Consider the age-old long division situation: In this case, the question posed is “30 divided by 7”. The answer …

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Math: radicals: rationalizing the denominator

By Jack Posted on March 22, 2014 Posted in math Tagged with radicals, rationalizing the denominator

Tutoring math, you cover this topic with students in late middle school or early high school.  The math tutor shows the first case. This article assumes that the reader is familiar with multiplying radicals. If necessary, see my article here …

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Math: multiplying radicals

By Jack Posted on March 18, 2014 Posted in math Tagged with multiplying with radicals, radicals, simplifying radicals

Tutoring high school math, you realize that radicals are a problem for many. Today the math tutor gives brief coverage of multiplying radicals. Consider the following example: Simplify 3√(6)*4√(7) Multiplying with radicals goes “number times number, radical times radical.” Like …

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Math: Finding the slope of a line

By Jack Posted on March 10, 2014 Posted in math Tagged with slope, slope of a line

Tutoring math, you know this skill is essential.  The math tutor provides a quick explanation and example. The concept of slope is known to all in everyday life.  In math, it is defined as follows: slope=rise/run=m=(y2-y1)/(x2-x1) Indeed, slope is often …

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