CRCT Domain Review Numbers and Operations

Key Vocabulary  Rational Numbers  Any number that can be made by dividing one integer by another. The word comes from "ratio".  Absolute Value  A numbers distance from zero (always a positive distance)  Expression  A mathematical sentence that uses operations, numbers, and symbols  NO EQUAL SIGN  (simplify or evaluate)

Key Vocabulary  Equation  A statement that the values of two mathematical expressions are equal (indicated by the sign =).  Inequality  An inequality says that two values are NOT equal.  Distributive Property  Distribute the factor outside of the parenthesis to each number inside (multiply)

Ordering Rational Numbers  You must compare the numbers using the same format (decimal, percent or fraction)  Use the number line to determine order  EXAMPLE -3.5, 4, 100%, -4, 1.675, 1 2/3, -350%

Integer Rules  Addition  Same sign add and keep  Different signs subtract and keep the sign of the higher absolute value  Subtraction  Add the opposite- (change to addition and use addition rules)  Multiplication and Division  Same sign = positive  Different sign = negative -4 + (-5) = -3 – 5 = -2 x -3 = -2 x 3 =

Converting Between Fractions, Decimals and Percents  Fractions to Decimals  Divide the numerator by the denominator (top/bottom)  Decimals to Fractions  Place the number after the decimal over its place value (10’s, 100’s, 1000’s) and simplify  Keep any whole numbers  Decimals to Percents  Multiply by 100 – move decimal 2 places to the right  Percents to Decimals  Divide by 100- move decimal 2 places to the left ¾=.60= 1.20=.40= 2.45= 120%=

Operational Vocabulary SymbolsOther Words Addition+Sum All together All Increased Together Total Add More Subtraction _Minus Take away Fewer than/ less than Subtracted from Decreased Difference Is left How many more? How many less? Multiplication x, (), 3y,. Product Multiply Factor Times Division / or ÷ Quotient Dividend Average Group(ed) Divide Each Per Evenly distributed Equal=The same (as) Equals Equivalent Equal to

Properties  Commutative  Change the order  5 x 9 x 6 = 6 x 5 x 9  Associative  Change the grouping  (5 x 9) x 6 = 5 x (9 x 6)  Distributive  Distribute the common factor (multiply by EVERYTHING inside the parenthesis)  5(9 + 6) = (5 x 9) + (5 x 6)  4(x + y – z)= Works for addition and multiplication only! Order doesn’t matter

Fractions Rules  Addition & Subtraction  Must have the same denominator  If not the same find common factor  Add or subtract the numerators and keep the denominator  Multiplication  Multiply numerator times numerator and denominator time denominator  If a mixed number you can make improper first  Division  Multiply by the reciprocal  Change division to multiplication and flip the second fraction to make its reciprocal  ALWAYS SIMPLIFY TO LOWEST TERMS

Decimal Rules  Addition and Subtraction  MUST line up the decimals  If needed add zeros as place holders  Multiplication  Do not have to line up decimals  Multiply as normal and count the places behind the decimal in the numbers being multiplied  Move that many spaces left from the end of the product  Division  Make the divisor (outside) a whole number by shifting the decimal point  Shift the decimal point of the dividend (inside) the same number of places (if needed add zeros)  Move the decimal point up to the quotient (answer) so that it is in the same place  Divide like normal

Inequality Table >> Greater than Arrow points to the right << Less than Arrow points to the left -Not equal to -Open circle -Equal to -Closed circle ***** this is true if x is on the left of the inequality symbol LESS THAN ALWAYS GOES LEFT

Expressions vs. Equations  Expressions  No equal sign  Combine like terms/ Simplify  Will not get an answer like x = 5  Use substitution to EVALUATE  Equations  An equal sign or inequality sign  Can simplify before SOLVING for a variable  Will get an answer such as x = 3  Use INVERSE OPERATIONS to SOLVE