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Parent’s Cheat Sheet # 2A fraction is a part of something larger and is made up of a numerator (top number) and a denominator (bottom number). Fractions fall between whole numbers on the number line and can be positive or negative.Fractions combined with whole numbers to make mixed numbers. Fractions whose numerator is larger than their denominator are called improper fractions.A fraction is in simplest form when there is no number (other than 1) that can be divided into the numerator and the denominator.General Rules for Adding and Subtracting Fractions or Mixed Numbers:1. Change any mixed numbers to improper fractions:Multiply the denominator (bottom number) by the whole number. Add this answer to the numerator (top number). This is your new numerator.The denominator (bottom number) stays the same.2. Determine a common denominator: a number that both denominators fit evenly into.Rewrite the fractions using the common denominator:Do this by multiplication. Whatever you multiply the bottom by, you MUST multiply the top by (there’s a reason for this involving equality and the multiplicative identity property).3. Add the numerators.4. Keep the common denominator.5. Simplify:If there is a number that divides into the numerator (top) and the denominator (bottom) evenly, then divide both by that number.********The integer rules for all operations apply to fractions as well!!!!!*********General Rules for Multiplying Fractions or Mixed Numbers:1. Change any mixed numbers to improper fractions.2. Cross Simplify (simplify the numerator of the first fraction with the denominator of the second, and vice versa) or simplify the answer at the end.3. Multiply the numerators straight across.4. Multiply the denominators straight across.5. Simplify (if you haven’t already).General Rules for Dividing Fractions or Mixed Numbers:1. Change any mixed numbers to improper fractions.2. Keep the first fractions as it is.3. Change the division to multiplication.4. Flip the second fraction (this is called the multiplicative inverse, or reciprocal)5. You can cross simplify here or do it at the end.6. Multiply the numerators straight across.7. Multiply the denominators straight across.8. Simplify if you haven’t already.The information above is the method we arrive at after some practice and exploring, and most often the most efficient method to solve these problems. There are various models to show adding and subtracting, multiplying and dividing fractions including using pattern blocks, the number line and the area model. If your student needs more guidance, you could try searching these items online for more information. We have touched on them in class. Solving Equations:An equation is a mathematical sentence that has an equal sign such as x + 4 = 3. It is usually made up of some terms, separated by an operation, an equal sign, and the answer. At least one term usually includes a variable. A variable is a symbol that represents a number. Common variables are x and n. The number in front of a variable is called a coefficient. In the example of 3n, 3 is the coefficient and n is the variable. A number by itself is called a constant.The goal when solving equations is to isolate the variable. In other words, we want the variable alone on one side of the equal sign. We achieve this by moving the other pieces, or terms around. We can move them using the opposite operation in most cases. In the example of x + 4 = 3, we can get x alone by moving 4. We can move 4 by subtracting it from BOTH SIDES. When we subtract 4 from 4 it makes zero, or cancels out. When we subtract 4 from 3, we get -1.X + 4 – 4 = 3 – 4X + 0 = -1X = -1When we add zero to any number, the answer is just that number (additive identity property).The idea is to keep the equation “true” at all times and we can do that by making sure whatever we do to one side, we do to the other. Inverse operations are as follows:OperationInverseAdditionSubtractionSubtractionAdditionMultiplicationDivisionDivisionMultiplicationExponentRootInverse operations should be used when isolating the variable.Two step equations can be solved by the same process, working backwards and dealing with the term with the variable last.Resources Worth Checking Out: ................
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