{"id":114,"date":"2017-09-03T23:56:41","date_gmt":"2017-09-04T03:56:41","guid":{"rendered":"http:\/\/iblog.dearbornschools.org\/kourank\/?page_id=114"},"modified":"2017-10-08T11:36:52","modified_gmt":"2017-10-08T15:36:52","slug":"pre-algebra","status":"publish","type":"page","link":"https:\/\/iblog.dearbornschools.org\/kourank\/pre-algebra\/","title":{"rendered":"Algebra Concepts"},"content":{"rendered":"<p>Practice vocabulary through this Site<\/p>\n<p><a href=\"https:\/\/www.armoredpenguin.com\/wordmatch\/Data\/best\/math\/pre-algebra.vocabulary.01.html\">https:\/\/www.armoredpenguin.com\/wordmatch\/Data\/best\/math\/pre-algebra.vocabulary.01.html<\/a><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>SUM<\/p>\n<p>sum \u2013 the answer to an addition problem<\/p>\n<p>Ex. 4 + 5 = 9\u2026The sum is 9.<\/p>\n<p>DIFFERENCE<\/p>\n<p>difference \u2013 the answer to a subtraction problem<\/p>\n<p>Ex. 8 \u2013 2 = 6\u2026The difference is 6.<\/p>\n<p>PRODUCT<\/p>\n<p>product \u2013 the answer to a multiplication problem<\/p>\n<p>Ex. 3 \u00d7 4 = 12\u2026The product is 12.<\/p>\n<p>QUOTIENT<\/p>\n<p>quotient \u2013 the answer to a division problem<\/p>\n<p>Ex. 18 \u00f7 6 = 3\u2026The quotient is 3.<\/p>\n<p>ESTIMATE<\/p>\n<p>estimate (noun\/verb) \u2013 an answer that is close to the real answer; to quickly perform an<\/p>\n<p>approximation<\/p>\n<p>Ex. 28.7 + 42.25 \u2248 30 + 40 = 70\u2026The estimate is 70.<\/p>\n<p>COMPATIBLE NUMBERS<\/p>\n<p>compatible numbers \u2013 numbers that can be divided evenly; useful in estimating quotients<\/p>\n<p>Ex. 27.2 \u00f7 4.14 \u2248 28 \u00f7 4 = 7\u202628 and 4 are compatible #s.<\/p>\n<p>PROPER FRACTION<\/p>\n<p>proper fraction \u2013 a fraction that represents a positive number that has a value less than 1 (denominator is larger than numerator)<\/p>\n<p>IMPROPER FRACTION<\/p>\n<p>improper fraction \u2013 a fraction that represents a positive number that has a value more than 1 (numerator is larger than denominator) is an improper fraction.<\/p>\n<p>EQUIVALENT FRACTION<\/p>\n<p>equivalent fraction \u2013 a fraction that has the same value as a given fraction are equivalent fractions.<\/p>\n<p>SIMPLEST FORM<\/p>\n<p>simplest form (of a fraction) \u2013 an equivalent fraction for which the only common factor of the<\/p>\n<p>numerator and denominator is 1<\/p>\n<p>MIXED NUMBER<\/p>\n<p>mixed number \u2013 the sum of a whole number and a fraction<\/p>\n<p>RECIPROCAL<\/p>\n<p>reciprocal \u2013 a number that can be multiplied by another number to make 1 (numerator and denominator are switched)<\/p>\n<p>PERCENT<\/p>\n<p>percent \u2013 a ratio that compares a number to 100<\/p>\n<p>SEQUENCE<\/p>\n<p>sequence \u2013 a set of numbers that follow a pattern<\/p>\n<p>Ex. 4, 6, 8, 10, 12\u2026is a sequence of numbers.<\/p>\n<p>ARITHMETIC SEQUENCE<\/p>\n<p>arithmetic sequence \u2013 a sequence where each term is found by adding or subtracting the exact same<\/p>\n<p>number to the previous term<\/p>\n<p>Ex. 4, 6, 8, 10, 12\u2026is an arithmetic sequence (add 2)<\/p>\n<p>GEOMTRIC SEQUENCE<\/p>\n<p>geometric sequence \u2013 a sequence where each term is found by multiplying or dividing by the exact<\/p>\n<p>same number to the previous term<\/p>\n<p>Ex. 2, 6, 18, 54, 162\u2026is a geometric sequence (multiply 3)<\/p>\n<p>GROUPING SYMBOLS<\/p>\n<p>Ex. (parenthesis), [brackets], {braces}, long division bar<\/p>\n<p>ORDER OF OPERATIONS<\/p>\n<p>order of operations \u2013 the procedure to follow when simplifying a numerical expression<\/p>\n<p>1 \u2013 Grouping symbols<\/p>\n<p>2 \u2013 Exponents<\/p>\n<p>3 \u2013 Multiplication and Division (from left to right)<\/p>\n<p>4 \u2013 Addition and Subtraction (from left to right)<\/p>\n<p>NUMERICAL EXPRESSION<\/p>\n<p>numerical expression \u2013 a mathematical phrase that contains numbers and operation symbols<\/p>\n<p>Ex. 14 + 8 \u00f7 4 \u2013 21<\/p>\n<p>VARIABLE EXPRESSION<\/p>\n<p>variable expression \u2013 a mathematical phrase that contains variables, numbers, and operation<\/p>\n<p>symbols<\/p>\n<p>Ex. 45 \u2013 (x + 3y)<\/p>\n<p>EVALUATE<\/p>\n<p>evaluate \u2013 to replace variables with numbers and then simplify an expression<\/p>\n<p>Ex. To evaluate 4x + 10 when x = 3, replace \u201cx\u201d with 3 and simplify: 4(3) + 10 = 12 + 10 = 22<\/p>\n<p>ABSOLUTE VALUE<\/p>\n<p>absolute value \u2013 the distance a number is from zero on the number line<\/p>\n<p>Ex. |-3| = 3; \u201cThe absolute value of -3 is 3.\u201d<\/p>\n<p>OPPOSITES<\/p>\n<p>opposites \u2013 pairs of numbers that have the same absolute value<\/p>\n<p>Ex. 4 and -4 are opposites because they are 4 units from 0.<\/p>\n<p>INTEGERS<\/p>\n<p>integers \u2013 the set of numbers that includes whole numbers and their opposites<\/p>\n<p>X-AXIS \u2013 the horizontal number line that, together with the y-axis, establishes the coordinate plane<\/p>\n<p>Y-AXIS \u2013 the vertical number line that, together with the x-axis, establishes the coordinate plane<\/p>\n<p>COORDINATE PLANE<\/p>\n<p>coordinate plane \u2013 plane formed by two number lines (the horizontal x-axis and the vertical y-axis)<\/p>\n<p>intersecting at their zero points<\/p>\n<p>QUADRANT<\/p>\n<p>quadrant \u2013 one of four sections on the coordinate plane formed by the intersection of the x-axis and the y-axis<\/p>\n<p>ORDERED PAIR<\/p>\n<p>ordered pair \u2013 a pair of numbers that gives the location of a point in the coordinate plane. Also referred to as the \u201ccoordinates\u201d of a point<\/p>\n<p>Ex. The ordered pair (3, 2) describes the location that is found by moving 3 units to the right of zero on the x-axis and then 2 units up from the x-axis.<\/p>\n<p>ORIGIN<\/p>\n<p>origin \u2013 the intersection of the x-axis and the y-axis on the coordinate plane<\/p>\n<p>Ex. The origin is described by the ordered pair (0,0).<\/p>\n<p>X-COORDINATE<\/p>\n<p>x-coordinate \u2013 the number that indicates the position of a point to the left or right of the y-axis<\/p>\n<p>Ex. The 4 in (4,3) is the x-coordinate, and tells you to move 4 places to the right of the y-axis<\/p>\n<p>Y-COORDINATE<\/p>\n<p>y-coordinate \u2013 the number that indicates the position of a point above or below the x-axis<\/p>\n<p>Ex. The 3 in (4,3) is the y-coordinate, and tells you to move 3 places above the x-axis<\/p>\n<p>EQUATION<\/p>\n<p>equation \u2013 a mathematical sentence that uses an equals (=) \u00a0sign to indicate that the side to the left of the equals \u00a0sign has the same value as the side to the right of the equals sign<\/p>\n<p>Ex. The equation x + 4 = 10 has a solution of x = 6.<\/p>\n<p>INVERSE OPERATION<\/p>\n<p>inverse operations \u2013 operations that undo each other Ex. Addition and subtraction are inverse operations.<\/p>\n<p>Multiplication and division are also inverse operations.<\/p>\n<p>INEQUALITY<\/p>\n<p>inequality \u2013 a mathematical sentence that uses a symbol (&lt;, &gt;, \u2264, \u2265, \u2260) to indicate that the left and right<\/p>\n<p>sides of the sentence hold values that are different<\/p>\n<p>Ex. The inequality x &gt; 8 has an infinite number of solutions.<\/p>\n<p>PERIMETER<\/p>\n<p>perimeter \u2013 the distance around the outside of a figure<\/p>\n<p>Ex. The perimeter of a rectangle whose length is 18 feet and width is 5 feet is: 18+5+18+5 = 46 feet.<\/p>\n<p>CIRCUMFERENCE<\/p>\n<p>circumference \u2013 the distance around a circle<\/p>\n<p>Ex. The circumference of a circle whose radius is 4 inches is:<\/p>\n<p>2\u03c0(4) = 8\u03c0 inches or approximately 25.12 inches.<\/p>\n<p>AREA<\/p>\n<p>area \u2013 the number of square units inside a 2-dimensional figure<\/p>\n<p>Ex. The area of a rectangle whose length is 18 feet and width is 5 feet is: 18\u00d75 = 90 square feet.<\/p>\n<p>VOLUME<\/p>\n<p>volume \u2013 the number of cubic units inside a 3-dimensional figure<\/p>\n<p>Ex. The volume of a rectangular prism whose length is 10 feet, width is 4 feet, and height is 2 feet is: 10\u00d74\u00d72 = 80 cubic\u00a0feet.<\/p>\n<p>RADIUS<\/p>\n<p>radius \u2013 a line segment that runs from the center of the circle to somewhere on the circle<\/p>\n<p>CHORD<\/p>\n<p>chord \u2013 a line segment that runs from somewhere on the circle to another place on the circle<\/p>\n<p>DIAMETER<\/p>\n<p>diameter \u2013 a chord that passes through the center of the circle<\/p>\n<p>CENTRAL TENDENCY<\/p>\n<p>central tendency \u2013 an attempt to find the \u201caverage\u201d or \u201ccentral value\u201d of a given set of data.<\/p>\n<p>Ex. In statistics, there are three main measures of central tendency: MEAN, MEDIAN, MODE<\/p>\n<p>MEAN<\/p>\n<p>mean \u2013 the sum of the data items divided by the number of data items<\/p>\n<p>Ex. The mean of (16, 10, 13, 11, 10) is 60\/5 = 12.<\/p>\n<p>MEDIAN<\/p>\n<p>median \u2013 the middle data item found after sorting the data items in ascending order; could be the mean of two middle numbers if the data set has an even number of items<\/p>\n<p>Ex. The median of (10, 10, 11, 13, 16) is 11.<\/p>\n<p>MODE<\/p>\n<p>mode \u2013 the data item that occurs most often; there could be no mode, one mode, or multiple modes<\/p>\n<p>Ex. The mode of (10, 10, 11, 13, 16) is 10.<\/p>\n<p>RANGE<\/p>\n<p>range \u2013 the difference between the highest and the lowest data item<\/p>\n<p>Ex. The range of (10, 10, 11, 13, 16) is 16 \u2013 10 = 6.<\/p>\n<p>OUTLIER<\/p>\n<p>outlier \u2013 a data item that is much higher or much lower than all the other data items<\/p>\n<p>Ex. The outlier of (2, 3, 5, 5, 6, 7, 10, 45) is 45.<\/p>\n<p>RATIO<\/p>\n<p>ratio \u2013 a comparison of two quantities by division<\/p>\n<p>Ex. The ratio of students to staff members at a given school is 16:1 (also 16 to 1\u2026or 16\/1).<\/p>\n<p>RATE<\/p>\n<p>rate \u2013 a ratio that compares quantities measured in different units<\/p>\n<p>Ex. The student\u2019s typing rate was 200 words per 6 minutes.<\/p>\n<p>UNIT RATE<\/p>\n<p>unit rate \u2013 a rate that has a denominator of 1<\/p>\n<p>Ex. The unit rate describing his speed was 14 meters per\u00a0second.<\/p>\n<p>PROPORTION<\/p>\n<p>proportion \u2013 a statement (equation) showing two ratios to be\u00a0equal<\/p>\n<p>CONGRUENT FIGURES<\/p>\n<p>congruent figures \u2013 figures that have the same size AND same shape<\/p>\n<p>SIMILAR FIGURES<\/p>\n<p>similar figures \u2013 figures that have the same shape BUT different size. The corresponding sides of<\/p>\n<p>similar figures are proportional in length.<\/p>\n<p>SCALE DRAWING<\/p>\n<p>scale drawing \u2013 an enlarged or reduced drawing that is similar to an actual object or place<\/p>\n<p>SCALE<\/p>\n<p>scale \u2013 the ratio of the model distance to the actual distance<\/p>\n<p>Ex. The scale on the map is 1 in. to 25 mi.<\/p>\n<p>OUTCOMES<\/p>\n<p>outcomes \u2013 possible results of action<\/p>\n<p>EVENT<\/p>\n<p>event \u2013 an outcome or a group of outcomes<\/p>\n<p>COMPLEMENT<\/p>\n<p>of an event complement (of an event) \u2013 the opposite of the event<\/p>\n<p>PROBABILITY<\/p>\n<p>probability \u2013 a ratio that explains the likelihood of an event<\/p>\n<p>THEORETICAL PROBABILITY<\/p>\n<p>theoretical probability \u2013 the ratio of the number of favorable outcomes to the number of possible<\/p>\n<p>outcomes (based on what is expected to occur).<\/p>\n<p>EXPERIMENTAL PROBABILITY<\/p>\n<p>experimental probability \u2013 the ratio of the number of times an event occurs to the number of times<\/p>\n<p>an experiment is done (based on real experimental data).<\/p>\n<p>DISTRIBUTIVE PROPERTY<\/p>\n<p>distributive property \u2013 a way to simplify an expression that contains a single term being multiplied<\/p>\n<p>by a group of terms.<\/p>\n<p>***For any numbers a, b, and c, a(b + c) = ab + ac<\/p>\n<p>Ex. 5(2x + 3) = 10x + 15<\/p>\n<p>TERM<\/p>\n<p>term \u2013 a number, a variable, or product of a number and a variable(s)<\/p>\n<p>Ex. There are 3 terms in the expression: 4x + y + 2<\/p>\n<p>CONSTANT<\/p>\n<p>Constant \u2013 a term with no variable part (i.e. a number)<\/p>\n<p>COEFFICIENT<\/p>\n<p>Coefficient \u2013 a number that multiplies a variable<\/p>\n<p>Ex. For the term 8x, the 8 is the coefficient.<\/p>\n<p>LIKE TERMS<\/p>\n<p>like terms \u2013 terms with the same variable part (including exponent)\u2026like terms can be combined using<\/p>\n<p>the distributive property in reverse<\/p>\n<p>Ex. 4x + 6x = (4 + 6)x = 10x<\/p>\n<p>DISCOUNT<\/p>\n<p>discount \u2013 the amount by which a price is decreased<\/p>\n<p>Ex. If shoes marked at $56 have a discount of $10, the new price is now $46.<\/p>\n<p>MARKUP<\/p>\n<p>Markup \u2013 the amount by which a price is increased<\/p>\n<p>Ex. If the jacket was purchased at $25 from the manufacturer, and a $50 markup is applied, the new price is $75.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Practice vocabulary through this Site https:\/\/www.armoredpenguin.com\/wordmatch\/Data\/best\/math\/pre-algebra.vocabulary.01.html &nbsp; &nbsp; SUM sum \u2013 the answer to an addition problem Ex. 4 + 5 = 9\u2026The sum is 9. DIFFERENCE difference \u2013 the answer to a subtraction problem Ex. 8 \u2013 2 = 6\u2026The difference is 6. PRODUCT product \u2013 the answer to a multiplication problem Ex. 3 [&hellip;]<\/p>\n","protected":false},"author":2023,"featured_media":0,"parent":0,"menu_order":3,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-114","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/iblog.dearbornschools.org\/kourank\/wp-json\/wp\/v2\/pages\/114","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/iblog.dearbornschools.org\/kourank\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/iblog.dearbornschools.org\/kourank\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/iblog.dearbornschools.org\/kourank\/wp-json\/wp\/v2\/users\/2023"}],"replies":[{"embeddable":true,"href":"https:\/\/iblog.dearbornschools.org\/kourank\/wp-json\/wp\/v2\/comments?post=114"}],"version-history":[{"count":0,"href":"https:\/\/iblog.dearbornschools.org\/kourank\/wp-json\/wp\/v2\/pages\/114\/revisions"}],"wp:attachment":[{"href":"https:\/\/iblog.dearbornschools.org\/kourank\/wp-json\/wp\/v2\/media?parent=114"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}