What I Learned Today 11/5/2014

Grammar:

I learned about the two parts of a sentence. There is a subject, which is what the sentence is about, and the predicate, which is what we are saying about the subject. My mom wrote out sentences that I had to cut where the subect ends and the predicate starts. You need to be careful because a subject isn't the first word or so. It can be be really long, about half of the sentence sometimes. I got them all right!

Pre-Algebra:

I moved into harder exponents after learning squares. I learned to add, subtract, multiply, and divide integers with exponents. Here are the rules I learned:

Definition: Let a be any number and let n be a positive integer. The power a^n, pronounced “a to the n,” is defined by the equation

A^n = a * a * … * a.

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V

N copies of a

For example, a^5 = a * a * a * a * a

Important: let a and b be numbers. Let n be a positive integer

Power of product: (a*b)^n = a^n*b^n

Power of reciprocal: if b is nonzero, then (1/b)^n = 1/b^n

Power of quotient: If b is nonzero, then (a divided by b)^n = a^n divided by b^n

WARNING!! Suppose a and b are nonzero numbers, and n is an integer greater than 2. Just as (a + b)^2 is not equal to a^2 + b^2, the expression (a + b)^n is not necessarily equal to a^n + b^n.

Important: Cube of negation: Let a b any number. Then

(-a)^3 = -a^3

Important: Power of negation: Let a be any number. Let n be a positive integer. If n is even, then (-a)^n = a^n if n is odd, then (-a)^n = -a^n.

Important: Product of powers (same base): Let a be any number. Let m and n be positive integers. Then

A^m · a^n = a^m+n.

Quotent of powers (same base): Let a be a nonzero number. Let m and n be positive integers such that m is greater than n. then

A^m divided by a^n = a^m–n

Important: Power of power: Let a be any number. Let m and n be positive integers. Then

(a^m)^n = a^mn

Ancient Civilization:

I learned how to make peasant girdle bread this time. I thought it was pretty good with butter. Grama Tina liked hers with jam. Here is the recipe for you to try:

Ingredients

• a cup of warmed ale
• wholemeal flour
• an egg

1. Bolt the flour through a cloth, to make the flour white (this makes manchet (white) bread)
2. Add the warmed ale – the yeast in this will make the bread rise. Mix to make a dough
3. Into the centre of the dough, add the egg and fold this into the dough
4. On a floured board, knead half of the dough into a flat circle
5. Repeat with the rest of the dough
6. Set a griddle pan on the fire to heat. When it is hot put a piece of fat in and coat the pan
7. Place one bread in at a time a cook. The bread will need to be turned from time to time to stop it burning
8. Wrap the cooked breads in a clean cloth to keep warm while the rest cook
9. When they are all cooked, serve hot