I learned a lot in Math 9 this year, however, I had to narrow it down to 5 things.
1. Fractions-How to find common denominators, adding, subtracting, multiplying and dividing.
Add and subtract-Need common denominators
Multiply-Do not need common denominators
Divide-Switch the sign and flip the fraction on the right.
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2. Exponents. Exponent rules are very important to remember, since you can do an exponent question many ways, but only one way will be correct. Writing an exponent is a lot more efficient then writing for example, 3x3x3 instead of 33.
-An exponent to the power of 0 is always 1
-If the base is the same, the exponent numbers preform the usual functions, (+,-, x, ÷)
-An exponent is telling you how many copies you have to make of the base
-When it is a multiplication question you add the exponents, when it is a division question then you divide them
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3. Distributive Property. I thought this was important to include because this can make algebraic questions easier. You can have a different approach on longer and more complex questions.
-First, you multiply 5 and 7x, and do the same with the 5 and 11. Then, you repeat this on the other side, being mindful of the -2 that is being multiplied with the 4. You then write it out again, and then group the like terms.
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4. Scale factor/ratio. This method, using the Butterfly method, really helped me pick up what we were learning, and it was an easy way for me to remember it. The scale factor ratio is the original size: the measurements made. In example here, you would multiply 1/3 by x/24. By cross multiplying, you would get 3x is equal to 24. If you divide by 3 in order to isolate x, you would get 8. The answer would be, 8m=24km.
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5. This last one was hard to pick. I chose to do linear equations. The first part was quite simple. You start off with an equation and add or subtract ‘x’ or the constant. By adding 6x to a -6x, this cancels out, and makes a zero pair. I also added 8, which then made the equation, 11=12x. Since it is not easy to divide, I can leave it as a fraction. After this, I chose to represent this visually. The long skinny rectangles are ‘x’, and the small squares are the constant. The shaded in tiles are the positive, the non-shaded are the negative.
