A Problem Solving Approach to Mathematics for Elementary School Teachers (13th Edition)

Chapter 6

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; The given figure can be divided into equal ... more

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; To show   by using an area model, draw a circle... more

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Yes ; Use the theorem that a fraction is greater ... more

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Meter A has more time remaining; By 3 minutes. ; ... more

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Entire Proof Answer: The Fundamental Law of ... more

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Assume   to be a negative integer. Dividing   by 1... more

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; One millimeter is one thousandth of a meter. ... more

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; Calculate the number of Objects B that are ... more

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; Calculate the number of people who were male by... more

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; Take a rectangular pane and divide it into 8 ... more

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; Divide the given unit strip into 15 equal parts... more

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The denseness property for rational numbers states... more

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Entire Proof Answer:The fraction will be less ... more

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; The given diagram can be divided into equal ... more

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; To show  using an area model, take a square.... more

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; Let   be the numerator and   be the denominator... more

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; The given diagram can be redrawn and divided ... more

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For and , , where , , and are integers.For ... more

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Entire Proof Answer: Let   be any integer.Any ... more

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; Divide a ruler in 8 equal parts.The whole of ... more

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; The required number of objects B is equal to   ... more

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; Let 1 represent the whole, that is, the total ... more

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As there are 100 cents in a dollar, the 25 cents ... more

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There can be different number of students in the ... more

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The fraction obtained is equal to .If any set of ... more

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; Let   be natural numbers,  be whole numbers,  ... more

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The given law states that multiplying and dividing... more

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Let the total cross symbols in the original ... more

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; Since the diameter of the first Dish P is , the... more

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Each square can be divided in four equal parts and... more

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No. In the fraction , the GCD of 0 and 6 is not 1... more

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The second person does not know the concept of ... more

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The assertion of Individual S is wrong as there ... more

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The concept of Individual S is incorrect as the ... more

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Individual A can show   part of the total visages ... more

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The assertion of Individual I is wrong because the... more

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Individual S's assertion is incorrect because 10 ... more

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The assertion of Individual C is incorrect, as to ... more

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Since the passing ratio of both classes is equal, ... more

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The claim is incorrect as the concept of lower and... more

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The fraction with larger denominator is smaller if... more

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Individual C's assertion is incorrect because when... more

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Individual K is correct because 6 out of 8 equal ... more

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Person A has 7 siblings out of which 5 are girls. ... more

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Multiply the numerators and denominators of the ... more

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When 10 feet long object S is divided into 5 ... more

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As the denominator is greater than the numerator, ... more

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; There is a total of 16 squares. of 16 squares ... more

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; Assume the length of the fence to be .So, the ... more

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Write the fractions that are equal to the given ... more

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The approximated value of the summation can be ... more

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Person K approximated the value of the addition ... more

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NoFor instance, the fraction is closer to , which... more

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added to results in a value more than 1, whereas... more

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Individual J should choose the two pieces that ... more

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By finding the nearest numbers (benchmark ... more

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; Write each given fraction into decimals. ; The ... more

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12 ; Use grouping to add the mixed numbers.Select ... more

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; Let the total number of students in a class be... more

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; Add the fractions that represent the length of ... more

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; The total amount of item F is .The individual ... more

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; Calculate the difference between the distance ... more

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The quantity of Item M needed is cups and cups. ... more

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; Let the other fraction be .Equate the sum of ... more

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; The fraction representing the portion for rent ... more

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; The denominator of the answer will be 24 only ... more

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; The fractions , , and lie between 0 and , but ... more

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; Let the total number of students be .Write the ... more

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; The total amount of liquid M required for a ... more

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; Total fraction for the area of an item B is .... more

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; The   term of an arithmetic sequence is given ... more

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; Find the quantity of paint left after ... more

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; Write the fraction representing the portion for... more

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The fraction represents the amount taken from ... more

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It is easier to add two fractions having like ... more

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It is always true that a mixed number can be ... more

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The information is about the amount spent on ... more

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The value of the given expression is . The second ... more

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A person purchased some chocolates and ate of the... more

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The statement given by Individual K is wrong.One ... more

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Individual K thought that there were a total of 12... more

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Individual J gave a wrong statement. One should ... more

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The given area model is incorrect. To display the ... more

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To perform addition, separate the integer and ... more

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Individual N’s statement is incorrect. If the ... more

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There are 27 bones in one hand of a human, so both... more

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The fractions of the form are equivalent to for ... more

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; Let the total number of Food Item C be .The ... more

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On the number line, the number on the right is ... more

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; In the given image, fill in the first 4 rows ... more

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; In the given image, fill in the first row out ... more

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; In the given image, fill in the first 2 rows ... more

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; Draw an image with 4 rows and 8 columns. Fill ... more

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; Draw an image with 9 rows and 10 columns. Fill ... more

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; Draw an image with 7 rows and 3 columns. Fill ... more

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  ; Draw an image with 5 rows and 6 columns. Fill ... more

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; Draw an image with 6 rows and 4 columns. Fill ... more

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; Draw an image with 8 rows and 2 columns. Fill ... more

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; Draw an image with 12 rows and 5 columns. Fill ... more

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; Draw an image with 2 rows and 9 columns. Fill ... more

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Assume there were 4 apples in a basket.Suppose one... more

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Entire Proof Answer: Apply the algorithm for ... more

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; Draw an image with 1 shaded block out of 4 ... more

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Width: mile ; Determine the width of the ... more

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The cost of yard of material is and cost of ... more

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; Assume that there are   number of students in ... more

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; Assume a fraction of stock that is neither ... more

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; Let   be the original price.The discount price ... more

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; Suppose   were there originally in the savings ... more

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32 ; Let Individual A have Object M.Find the ... more

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Entire Proof Answer: Let and be rational numbers ... more

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; Find the number of cups mixed to make 1 batch ... more

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3 ; Let   be the required number of persons.Every ... more

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; Add   and , to find the required fraction. ; ... more

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; Each individual gets  th part of the  th of the... more

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; Assume the fraction to be .Add numerator and ... more

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; Let the number be .Multiply   by 3 and find the... more

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; Let   represent the initial number of teachers.... more

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246 ; Let the total number of pages in the book be... more

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41 weeks ; Calculate of 52 weeks to find the ... more

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; From the given information, 8 students are ... more

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34 ; To find the number of Utensil C contained in ... more

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; Find the total fraction of Animal D in the two ... more

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; Find the required part of stocks by calculating... more

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The point   best reflects the product of the ... more

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The other number is less than 1 and the reciprocal... more

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Both the method and the result are incorrect. The ... more

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Individual A’s statement is incorrect. Taking the ... more

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Individual N’s statement is correct. If a number... more

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The student’s statement is incorrect. If 5 is ... more

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The fraction can be simplified as and not . and... more

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Both ways of writing “17 divided by 5” in the ... more

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Individual J’s statement is correct. The fractions... more

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Individual J's statement is incorrect as division ... more

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Individual B's statement is correct. A positive ... more

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Write as the sum of a whole number and a fraction... more

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1.      ;   2.    ;   3.     ; ; Draw a rectangle ... more

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  ; Draw two rectangles.Divide one rectangle into ... more

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; Calculate the unit rate of cutting the grass by... more

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; According to the given information, the ratio ... more

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Fruit G for ; The cost of 4 Fruit G is 80 cents.... more

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; The ratio of distance in the map to the real ... more

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; The ratio of reading pages to minute is .Assume... more

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; Assume   to be constant such that the ... more

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Person S: ; Person D:   ; Calculate the ratio ... more

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; Assume a constant   so that the success of ... more

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; Multiply both side of the proportion by   and ... more

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; The ratio of the length to the wingspan is .... more

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; The ratio of the length to the electrical ... more

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; From the given information, it can be said that... more

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; The ratio of the mass of pure metal to the ... more

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Vehicle C ; Mileage of a vehicle can be obtained ... more

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Person N ; Divide 20 by 2 to find the distance ... more

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; Assume that the total number of appliances is .... more

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Object OT: 85; Object RT: 17 ; Assume a variable... more

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No; It is because   is the required amount of Item... more

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Each unit of stick B represents , so the length of... more

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; The ratio of Person A to Person T is .Assume ... more

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; In 12 minutes, the burnt length of Object C is ... more

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Length: ; Width:   ; Assume a constant number   ... more

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; The ratio of the insect's height to its jumping... more

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; The ratio of the number of months worked to the... more

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; Let   be the number of teachers currently ... more

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; The ratio of the length of the tree to the ... more

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; Ignoring the units, the given proportion can be... more

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; The ratio of the number of weeks to the ... more

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; Assume a constant variable   to be the width (... more

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; Assume a constant variable   to be the distance... more

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; Assume a variable   that denotes the actual ... more

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, , , if . ; The variables   and   cannot be equal... more

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; Assume a constant variable   to be the amount ... more

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; Substitute 173 for , 68 for , and 21 for into... more

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Vehicle C ; Mileage of a vehicle can be obtained ... more

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Person N ; Divide 18 by 2 to find the distance ... more

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; Assume the total number of appliances to be .... more

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Object OT: 96; Object RT: 16 ; Assume a variable... more

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Assume that is the required amount of Item F that... more

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; Assume a constant variable   to be the weight (... more

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Each unit represents 2 Object B. So, the original ... more

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The proportion indicates that the price of the ... more

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Two ratios are equal if they are reducible to a ... more

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Reduce the ratio of dimensions of the first Object... more

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Two ratios are equal, that is, they form a ... more

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; Assuming   as the total number of adult men and... more

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  There is more water in Recipe A as compared to ... more

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By asking Person D to interchange the numerator ... more

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Yes, Person N is correct because two ratios are ... more

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By asking Person A to change the units of each ... more

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Let and 43 feet be the nose length and arm length... more

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Both the mixtures have different ratios of colors... more

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; Assume the constant variables   and , which ... more

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is a proper fraction because the denominator is ... more

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Rational numbers are those numbers that can be ... more

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The ratio   can be simplified to . The reason ... more

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; At 6, the hands of the clock form a straight ... more

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The given ratios are equivalent if they are in ... more

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Entire Proof Answer:Use the fact that   if and ... more

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People G used the ratio   in the construction of ... more

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As the old length of the object is 5 inches and ... more

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Assume a constant number such that the number of ... more

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 Assume a constant number   such that the number ... more

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From the given information, it can be said that ... more

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; A proportion is defined as the equality of ... more

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; Multiply both the numerator and the denominator... more

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; The simplest form of   is .To compare the ... more

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Yes, by using the laws of multiplication, ... more

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Let Individual A have 4 children and 37 cookies. ... more

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; Multiply the numerator and denominator of the ... more

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Write the given number as . After this, press the ... more

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; Compute   of half. ; Multiply   by 2000 to find... more

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; If side H was obtained 376 times, which was ... more

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; The fraction of obtaining side H 240 times to ... more

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Not reasonable: The sum of the given fractions ... more

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; Assume to be the required distancein feet.Set ... more

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The simplest form of the given fraction is which ... more

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; Write   in the simplest form. ; Multiply the ... more

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; To calculate the required number, multiply   by... more

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; This is because when is subtracted from, the ... more

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The conclusion drawn from the diagram is correct. ... more

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Neither bottle is a better buy since both cost the... more

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No; The ratio of metal G to other metals is not ... more

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44 ; Write the ratio of 11 people to 4 people to ... more

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; Let the length of the house be   meters.Convert... more

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; Let there be   ounces of chemical H in   of ... more

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No; If the percentage of the obtained defective ... more

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; Substitute 1 for   into the formula . ; ... more

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; Let   be the boys in Ms. G's class.Write the ... more

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; All the ratios can be considered as fractions ... more

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; Assume that the two numbers are   and .Form an ... more

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; Let the required number be .Form an equation ... more

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Person D: 45Person M: 75 ; The total number of ... more

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; Compute the perimeter of the first triangle by ... more

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Mug with  of cream ; The mug with   of cream has ... more

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; Compute   of 121 by multiplying   by 121. ; ... more

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The total sum of fractions must be 1.Let the total... more

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; Let   be the number of containers left at a ... more

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