Scale DrawingDistance, Speed, and DistanceSolve ProportionEquivalent RatiosRates
ratiosChapter 7
Equation with FractionEquation with Multiplication and DivisionEquation with Addition and SubtractionWrite Expression with FractionWrite Multiplication and Division ExpressionWrite Addition and Subtraction ExpressionEvaluate Expression with FractionDistributive PropertyThe Distributive Property gives you another way to evaluate a number multiplied by a sum or a difference
Order of OperationsP = Parentheses
E = Exponent M = Multiplication D = Division A = Addition S = Subtraction |
Multiplication propertyZero Property - a product of a number and 0 is 0
Identity Property - the sum of any number and zero is the number Associative Property – the way in which the numbers are grouped doesn’t affect the sum Commutative Property - the order of how you arrange the number, it doesn’t affect the sum Addition propertyIdentity Property - the sum of any number and zero is the number
Associative Property – the way in which the numbers are grouped doesn’t affect the sum Commutative Property - the order of how you arrange the number, it doesn’t affect the sum |
Chapter3
Rational NumbersDivide IntegersNegative integer x Positive integer = Negative Integer
Positive integer x Negative Integer = Negative Integer Negative integer x Negative integer = Positive integer Positive integer x Positive integer = Positive integer Multiply IntegersNegative integer x Positive integer = Negative Integer
Positive integer x Negative Integer = Negative Integer Negative integer x Negative integer = Positive integer Positive integer x Positive integer = Positive integer Subtract IntegersThe basic rule for Subtracting an integers
1.Subtracting an integer is the same as adding its opposite Add IntegersFor each pair of one positive and one negative they get canceled out
The remaining positive or negative is the answer. Compare and Order IntegersThe easiest way to compare integers is to put it on the number line. integers increase value from left to right.
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Chapter2
Divide Mixed NumbersStep 1: Write the mixed numbers as improper fractions.
Step 2: Rewrite the division problem using the improper fractions. So to divide mixed numbers you should change the fractions to improper fraction and the convert the problem to a multiplication question. Then you will be ready to solve. Divide Whole numbers and fractions
Divide fractions
Multiply Mixed Number1.Convert the mixed number into an improper fraction
2.Multiply the numerators to get a new numerator 3. Multiply the denominators to get a new denominators 4. Simplify the fraction (if needed) 5.Convert improper fraction into mixed number multiply fractions1.Multiply the numerators to get a new numerator
2. Multiply the denominators to get a new denominators 3. Simplify the fraction (if needed Add fraction and mixed number with unlike Denominator1.Multiply the numerators to get a new numerator
2. Multiply the denominators to get a new denominators 3. Simplify the fraction (if needed) Subtract Fraction and mixed number with unlike Denominator
1.Find the least common multiple (LCM) for the denominators.
2.Multiply the numerator and denominator to get like denominators. 3.Turn the other fractions into equivalent fractions. 4.Subtract the numerators but leave the denominators the same. 5.Simplify or reduce the answer if necessary. Add Fraction with like Denominator
Subtract Fraction with like Denominator
Terminating and Repeating FractionJust divide the numerator by the denominator . If you end up with a remainder of 0 , then you have a terminating decimal. Otherwise, the remainders will begin to repeat after some point, and you have a repeating decimal.
Compare and Order FractionStep 1: Find the LCM of all the denominators of given numbers.
Step 2: Multiply numerator and denominator of each fraction by a number in order to make denominator equal to LCM. Step 3: Now since all the denominators are same, we can compare numerators and write them in required order either ascending or descending. Simplest FormFraction in its simplest form is one that cannot be simplified any more
Equivalent FractionOne way to find an equivalent fraction is to multiple or divide the numerator and denominator by the same counting number.
You can multiply. Multiply numerator and denominator by the same counting number. You can divide. Divide numerator and denominator by the same counting number Least common multiple (LCM)How to find Least Common Multiple (LCM)
A common multiple is a number that is a multiple of two or more numbers. The Least common multiple (LCM) of two numbers is the smallest number (Not zero) that is a multiple of both Greatest common factor (GCF)How to find the Greatest common multiple (GCF)
First you have to list the factors of both numbers. Then cross the common factors of 18 and 24. The greatest factor crossed is the GCF. Then make the diagram Divisibility Rule |