The first things you should know about me: I don't talk about "me" very well. I am a realist to the T and don't sugar coat things. But I do try to look at the positive side of things as much as possible, or at least try to find a positive spin on just about everything.
I was born to be a teacher. As a young child, I always wanted to play school with my friends. However, I never wanted to be the student! Later, I realized that the best teachers were always the best lifelong students. How thankful I am to have learned that lesson early in life.
Although I once dreamed of being a teacher, I decided to not become a classroom teacher. I did obtain my teaching degree, but circumstances changed, and I decided to teach in other ways.
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| Reading Games on the laptop |
My first students were my own children! I started teaching them as soon as they gave me a curious look or noise. I fed them whatever they were hungry for - numbers, letters, stories, animals, space, etc. They taught me so much about what it means to learn.
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| Science Fun |
I realized within the first 3 years of our homeschooling journey, that the books and curriculum we chose were not as important as the time we spent exploring. This is when my love for interactive learning began.
When my children were all in their primary school years, I also taught classes to homeschool groups. Then I decided to start tutoring on the side and I fell in love!
It was such a blessing to be able to work one-on-one with these kids who were struggling in the classroom! I quickly learned that there aren't a whole lot of resources and materials out there to support tutoring, or at least they aren't easy to find! So I began to make the things I needed to support my learners. That led me to TeachersPayTeachers.
Over the past year and a half I have made some wonderful connections with teachers, tutors, homeschooling parents, coaches, interventionists, and others who are just as passionate about teaching as I am. I've grown as an educator, and as a creator. I am now thrilled to bring all of these areas together into this site!
y ÷ y = ?
ReplyDeleteObviously, the quotient of that division statement is 1.
Remember back to 9th grade basic algebra & recall what a term is.
from byjus.com:
"A term [in this case, a monomial] can be a number, a variable, product of two or more variables or product of a number and a variable."
"A coefficient is an integer that is written along with a variable or it is multiplied by the variable. In other words, a coefficient is the numerical factor of a term containing constant and variables. For example, in the term 2x, 2 is the coefficient.
The variables which do not carry any number along with them, have a coefficient of 1. For example, the term y has a coefficient of 1."
So y ÷ y is really 1y ÷ 1y
Like-variables can be cancelled out (the "y's"), so the division statement becomes 1 ÷ 1 which of course equals 1.
Using PEMDAS to evaluate 1y ÷ 1y:
1 * y ÷ 1 * y
Step-by-Step:
1 * y = 1y
1y ÷ 1 = 1y
1y *y = 1y^2
And we know that y ÷ y does not equal y squared. And 1y ÷ 1y doesn't equal 1y squared, either (since those two division statements are the same thing). So using PEMDAS in which a monomial is pulled apart (no longer one value -- no longer the product of the coefficient & variable) is the wrong way to solve a linear division statement containing monomials.
Now take the division statement 60/5(7-5)
Factor out 60 to 30(7-5), so the division statement now reads:
30(7-5) / 5(7-5)
Replace what's inside the parentheses [7-5] with the variable "y" & the division statement now reads:
30y / 5y
Cancel out the "y's" & do the division:
30/5
which equals 6.
6 is the quotient of that division statement because division statements are FRACTIONS! Fractions are evaluated by first doing all the operations indicated in the numerator (dividend), then doing all the operations in the denominator (divisor) & then finally dividing the numerator (dividend) by the denominator (divisor) to find the quotient.
Vertical fractions (something-over-something) can be written as a linear division statement on a single horizontal line (e.g. one-half can be written as 1 over 2 or as 1/2). Written linearly, everything to the left of the division symbol (obelus or slash) is the numerator & everything to the right of the division symbol is the denominator. No additional parentheses or brackets are necessary to differentiate what is the numerator & what is the denominator -- the division symbol is the separator!