Visual Math: See How Math Makes Sense

Visual Math: See How Math Makes Sense

Jessika Sobanski

Language: English

Pages: 208

ISBN: 1576854043

Format: PDF / Kindle (mobi) / ePub


Visual math: see how math makes sense is for anyone who is bothered by all the written rules of mathematics. Specifically designed for the visual learner, this book explores shapes from many different perspectives. Questions and answers explanations are presented as pictures so that students will be able to respond to math questions quickly and confidently.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Well, you’re right: “What percent” means: ᎏ I don’t know ᎏ 100 Well, for the most part, we mathematicians don’t go around writing, “I don’t know” in the place of the numbers that we don’t know. We are partial to letting x represent the “unknowns” that we come across. “What percent” means: ᎏ xᎏ 100 Here’s an example: What percent of 250 is 30? Let’s break this down: “What percent” means: ᎏ xᎏ 100 “of 250” means: • 250 “is 30” means: = 30 So you have: ᎏ xᎏ • 250 = 30 100 ᎏ x • 250

(R × × 1 T) + (R2 T) You know the dog walks at 5 m/min (this is R1) and the turtle walks at 1 m/min (this is R2), so put these two rates into the equation: 80 = 5T + 1T 80 = 6T algebra 151 Dividing both sides by 6 yields T = 13ᎏ1ᎏ minutes. 3 One-third of a minute = ᎏ1ᎏ • 60 minutes = 20 seconds. The answer can also 3 be written as 3 minutes and 20 seconds. Suppose Tamara is standing on the corner with her two pups, and one gets loose. The pup takes off at a rate of ᎏ 4 m ᎏ. By

this case since wd > WD, the plank will tilt to the left: factoring Sometimes expressions are easier to deal with when you “pull out” common factors from the terms. For example, if you had 6 xy 2 + 3 xy, you could notice that each term is divisible by 3. Each term is also divisible by x. And each term is divisible by y as well. 154 visual math You can “pull out” a 3 xy from each term to yield 3 xy(2 y + 1). You can check your work by distributing the 3 xy: = 3 xy • 2y + 3 xy • 1 = 6

radical. ͙8ෆ • ͙2ෆ = ͙8•2 ෆ = ͙16 ෆ = 4 3. When dividing two roots (with the same index) you can combine them under the same radical. ͙242 ෆ ÷ ͙2ෆ = ͙242 ÷ ෆ2ෆ = ͙121 ෆ = 11 4. You can take a “division problem” out from under the radical and place each “piece” under its own radical. Ίᎏ15ᎏ ๶ = ͙15 ෆ ÷ ͙4ෆ = ͙15 ෆ ÷ 2 4 5. You can only add roots if they have the same index and radicand. Recall: 2͙3ෆ + 3͙3ෆ = 5͙3ෆ 6. Also, you can only subtract roots if they have the same index

it’s a viable option. But what if you had an unknown? Let’s say you had 12 − ( x − 1). First, you could get rid of the subtractions by turning each “minus” into “plus a negative. ” So, 12 − ( x − 1) = 12 + −1( x + −1). [Note that there was an “invisible one” in front of the parentheses 12 − ( x − 1) = 12 − 1 ( x − 1) = 12 + −1( x + −1).] 42 visual math Next, apply the distributive property . . . 12 plus −1 times x plus −1 times −1 equals 12 + −1 x + (−1 (−1), or 12 − x + 1. Once you

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