Number Assigned DueTopicProblem Description
14 Monday
210615 		Tuesday
210616		Fractions

  1.     A Hyundai 2021 car costs 280,000 pesos. A Mazda 2021 car costs 320,000 pesos. What fraction of the Mazda is the Hyundai?

  2.     A wedding party will have 200 guests. Each table fits 10 persons and costs 6,000 pesos, dinner included. The music will cost 15,000 pesos. What is the total cost of the wedding party?

  3.     Peru has 26 departments, which are equivalent to states in Mexico. Ten (10) of them are along the Pacific Coast. Three (3) of them are in the low-lying Amazon jungle. What fraction of the departments are in the highlands (mountains, without coast)?

  4.     South America has 13 countries, 10 of which speak Spanish as the primary language. The other three (3) countries are French Guiana (French), Guyana (English), and Surinam (Dutch). What fraction of the South American countries do not speak Spanish as the primary language?

Number Assigned DueTopicProblem Description
13 Monday
210614 		Tuesday
210615		Fractions

  1.     The American Continent has 25 countries. 20 of them speak Spanish as the primary language. What fraction of countries in America are non-Spanish speaking?

    Total number iof countries = 25
    Number of countries speaking Spanish = 20
    Fraction of non-Spanish = (25 - 20)/25 = 5/25 = 1/5

  2.     The population of the world is 8 billion persons (1 billion = 1000 million). The population of the American continent is 1 billion. What fraction of the world does not live in the American continent?

    World population = 8 billion
    Population in America = 1 billion
    Population in the rest of the world = 8 - 1 = 7 billion
    Fraction of population not living in America = 7/8

  3.     Mexico has 120 million people, of which 20% are identified as indigenous. Five (5) percent of the indigenous Mexican people speak a language other than Spanish. How many Mexicans identified as indigenous do not speak an indigenous language?

    Population of Mexico = 120 million
    Population of indigenous people living in Mexico = 120 × (20/100) = 24 million
    Population of indigenous people speaking a language other than Spanish = 24 × (5/100) = 1.2 million
    Population of indigenous Mexicans that do not speak an indigenous language = 24 - 1.2 = 22.8 million

  4.     Peru has many languages, but 83% of the population of 30 million speak Spanish. Quechua, the language of the Incas, is spoken by 15% of the population. How many people in Peru speak a language other than Spanish or Quechua? What fraction is it?

    Peru has 30 million people.
    Percentage or Peruvians speaking either Spanish or Quechua = 83 + 15 = 98
    Percentage of people speaking language other than Spanish or Quechua = 100 - 98 = 2
    Number of people speaking language other than Spanish or Quechua = 30,000,000 × (2/100) = 600,000 persons. Fraction = 600,000/30,000,000 = 6/300 = 1/50

Number Assigned DueTopicProblem Description
12 Thursday
210610 		Monday
210614		Fractions

  1.     A neighborhood has 50 houses, 40 percent were built before 1950 (old); the remainder (new) were built after 1950. One-fourth of old houses undergo renovation. What fraction of the total number of houses have been renovated?

    50 × (40/100) = 20 houses were built before 1950.
    50 - 20 = 30 houses were built after 1950.
    20 × (1/4) = 5 old houses are renovated.
    5/50 = 1/10 of the total number of houses have been renovated.

  2.     A car dealership has 80 cars to sell. One-eight of them are red color. Ten of the others (not originally red) are repainted in red color. What fraction of the total number of cars are now red color?

    Number of red cars = 80 × (1/8) = 10
    Number of cars that are not red = 80 - 10 = 70
    Number of the 70 cars that are painted red = 10
    New total number of red cars = 10 + 10 = 20
    New total fraction of red cars = 20/80 = 1/4

  3.     A class has 25 students, 13 boys and 12 girls. Two (2) of the boys and three (3) of the girls call in sick. What fraction of the total number is now the group of remaining )not sick) students, boys and girls together?

    Boys remaining in class = 13 - 2 = 11
    Girls remaining in class = 12 - 3 = 9
    Students remaining in class = 11 + 9 = 20
    Fraction of original number of students, remaining in class= 20/25 = 4/5

  4.     A girl has eighteen (18) dresses, fifteen (15) old and three (3) new. She gives away to charity three (3) of the old dresses. After this gift, what fraction of the original number of dresses (20), is the number of dresses that remain?

    Remaining number of old dresses, after gift to charity = 15 - 3 = 12
    Remaining number of dresses = 12 + 3 = 15
    Fraction of original number remaining = 15/18 = 5/6

Number Assigned DueTopicProblem Description
11 Wednesday
210609 		Thursday
210610		Angles - fractions

  1.     What is the value of the inner angle of an isosceles triangle (three equal-length sides)?

    There are three angles; the sum is 180 degrees. They are all equal; therefore, each angle is 60 degrees.

  2.     A triangle has angles of 100 and 50 degrees. What is the value of the third angle?

    Third angle = 180 - 100 - 50 = 30 degrees.

  3.     A ballet company has 3 male dancers and 12 female dancers. Three female dancers call in sick. What fraction of the remaining group of dancers is now composed of men?

    remaining female dancers = 12 - 3 = 9
    total number of dancers after sick leaves = 9 + 3 = 12
    fraction of male dancers = 3/12 = 1/4

  4.     A group of 47 musicians in an orchestra is divided into groups of four. How many complete groups are they? How many musicians remain in the last, incomplete group?

    47 / 4 = 11 + 3/4.
    Therefore, 3 musicians remain the twelveth, incomplete group.

Number Assigned DueTopicProblem Description
10 Tuesday
210608 		Wednesday
210609		Angles

  1.     A rectangular triangle has one acute angle of 30 degrees. What is the value of the other acute angle?

    180 - 90 - 30 = 60
    60 degrees is the other acute angle.

  2.    A square of 10 cm side length, contains a circle inside, completely filling an inside circle. What is the radius of the circle?

    The radius of the circle inside the square is 5 cm.

  3.     A rectangle has dimensions: length = 20 cm, and height = 10 cm. How many circles of radius r = 5 cm can you fit inside the rectangle?

    Two circles of radius = 5 cm can fit into the rantangle of length = 20 cm.

  4.     An isosceles triangle has a side length = 10 cm. How many of these triangles can confortably fit into a rectangle of 10 m height × 20 cm length?

    Two sitting on the bottom length and one hanging (inverted) from the top length. Total of three (3) isosceles triangles.

Number Assigned DueTopicProblem Description
9 Monday
210607 		Tuesday
210608		Fractions -- rulers

  1.    A ruler is 40 cm long. What fraction is 10 cm?

    10/40 = 1/4

  2.    What is the total length of a ruler if 1/5 of it is 12 cm?

    If 1/5 equal 12 cm; 1 = 5/5
    5 × 12 = 60 cm

  3.     Two rulers are 60 and 100 cm respectively. What fraction of the second is the first?

    60/100 = 6/10 = 3/5

  4.     Three rulers are 30, 50 and 100 cm. What fraction of the third is the sum oif the first two?

    Sum of the first two = 30 + 50 = 80
    Fraction of first two over third = 80/100 = 8/10 = 4/5

Number Assigned DueTopicProblem Description
8 Friday
210604 		Monday
210607		Fractions -- rulers

  1.    A ruler is 30 cm long, divided into six (6) fractions or portions of 5 cm each. It is desired to measure 9 cm. What fraction of the total ruler does this amount? What fraction of the second portion does it amount?

    The ruler is 30 cm long. It has six sections of 5 cm each. 9 cm is 9/30 od the total rular = 3/10. The fraction of the second portionis = (9 - 5) / 5 = 4/5

  2.    A measuring stick is 36 inches long. We want to measure 6 inches. What fraction of the total stick is this measure?

    The stick is 36 inches long. 6 inches is = 6/36 = 1/6 of the total length of the ruler.

  3.     A ruler is 50 cm long. We want to measure 1/4 of the ruler. How many centimeters does this 1/4 amount to?

    The ruler is 50 cm. 1/4 of the total length of the ruler is = 50 / 4 = 12.5 cm

  4.     A ruler is 100 cm long. We want to measure 1/5 of the ruler. How many centimeters does this 1/5 amount to?

    The ruler is 100 cm long. 1/5 of the total is - 100/ 5 = 20 cm.

Number Assigned DueTopicProblem Description
7 Thursday
210603 		Friday
210604		Fractions -- rulers

  1.    A ruler is 30 cm long. If one (1) inch is approximately equal to 2 (1/2) cm, what fraction of the ruler, in centimeters, is occupied by 6 inches?

    Six inches occupies 6 × 2 (1/2) = 15. The fraction of the ruler occupied by 6 inches is = 15/30 = 1/2.

  2.    My Dad weights 60 kilograms; my sister weights 20 kilograms. Does my sister weight 1/3 or 1/2 of my Dad?

    My sister weighs 20/60 of my Dad, that is, 1/3.

  3.    A large piece of luggage is H = 30 inches, L = 20 inches, and W = 10 inches. The sum of length and width should not exceed the height. Does this piece of luggage agree with the specifications?

    The sum of length L and width
    W = 20 + 10 = 30 inches. The height
    H = 30 inches. The sum of L + W agrees with the specification of 30 inches.

  4.     A ruler is 1 m long. It is divided into ten (10) equal segments. How many segments should a 30 cm length encompass?

    The ruler is 1 m long, which is equal to 100 cm. A length of 30 cm is 30/100 = 3/10 of the ruler.

Number Assigned DueTopicProblem Description
6 Wednesday
210602 		Thursday
210603		Fractions -- rulers

  1.    A ruler is 20 cm long, composed of two parts, each 10 cm long. What fraction of the entire ruler is the first 5 cm?

    5/20 = 1/4

  2.    A ruler is 30 cm long, composed of five parts, each 6 cm long. What fraction of the entire ruler is the first 18 cm?

    18/30 = 3/5

  3.    A ruler is 12 cm long, composed of two parts, each 6 cm long. What is the measure in the ruler (cm) corresponding to 1/3 of its total length?

    (1/3) 12 = 12/3 = 4 cm

  4.    A ruler is 25 cm long, composed of five parts, each 5 cm long. What is the measure in the ruler (cm) corresponding to 4/5 of its total length?

    (4/5) 25 = 100/5 = 20 cm

Number Assigned DueTopicProblem Description
5 Tuesday
210601 		Wednesday
210602		Fractions -- operations

  1.    9 (1/3) + 5 (1/2) =

    28/3 + 11/2 =

    56/6 + 33/6 =

    89/6 = 14 (5/6)

  2.    7 (5/8) - 3 (1/2) =

    61/4 - 7/2 =

    61/4 - 14/4 =

    47/4 = 11 (3/4)

  3.    7 (1/3) - 4 (1/5) =

    22/3 - 21/5 =

    110/15 - 63/15 =

    47/15 = 3 (2/15)

  4.    9 (1/4) - 7 (3/5) =

    37/4 - 38/5 =

    185/20 - 152/20 =

    33/20 = 1 (13/20)

Number Assigned DueTopicProblem Description
4 Monday
210531 		Tuesday
210601		Fractions -- operations

  1.    5 (3/4) + 8 (1/2) =

    23/4 + 17/2 =

    23/4 + 34/4 =

    57/4

  2.    7 (5/8) - 3 (3/4) =

    61/8 - 15/4 =

    61/8 - 30/8 =

    31/8

  3.    7 (1/4) - 4 (1/8) =

    29/4 - 33/8 =

    58/8 - 33/8 =

    25/8

  4.    11 (1/2) - 7 (3/4) =

    23/2 - 31/4 =

    46/4 - 31/4 =

    15/4

Number Assigned DueTopicProblem Description
3 Wednesday
210526 		Thursday
210527		Fractions 3

  1. The game of soccer has eleven (11) players. Five (5) play forward, two (2) play mid-field, and three (3) play defense. There is also one (1) goalkeeper. What fraction of the number of players play forward?

    ANSWER: Total number of players = 11. Number of players playing forward = 5. Fraction of players playing forward = 5/11.

  2. A ballet company has 18 dancers, half of which are younger than 6 years old, while one-third of the dancers are older than 9 years old. What fraction of the dancers are in the middle range of age, that is, between 9 and 12 years of age?

    ANSWER: Total number of dancers = 18. Number of dancers less than 6 years old = 18/2 = 9. Number of dancers greater than 9 years old = 18/3 = 6. Number of dancers in between 6 and 9 years old = 18 - 9 - 6 = 3. Fraction of dancers between 6 and 9 years old = 3/18 = 1/6.

  3. Mexico has 48 active volcanoes. Six (6) of them have erupted within the past five (5) years. Ten (10) other volcanoes have erupted within the past fifty 50 years. What fraction of them have remained inactive in the past 50 years?

    ANSWER: Total number of volcanoes in Mexico = 48. Number of volcanoes that have not erupted = 48 - 6 - 10 = 32. Fraction of volcanoes that are inactive = 32/48 = 2/3.

  4. The total population of Mexico is 120 million people (1 million is equal to 1,000,000 persons) The population of its capital, Mexico City, is 20 million people. Half of the city's population live within limits of the federal district. What fraction of the Mexican nationals lives within the limits of the federal district?

    ANSWER: Total population of Mexico = 120 million. The population of Mexico City is 20 million. The population of Mexico City that lives in federal district = 10 million. The fraction of Mexican nationals that live within the federal district is = 10/120 = 1/12.

Number Assigned DueTopicProblem Description
2 Tuesday
210525 		Wednesday
210526		Fractions 2

  1. In the New Continent Section 3A class there are 24 students, 12 girls, and the rest are boys. Half of the girls are vaccinated. Only a third of the boys are vaccinated. What fraction of all the students in the class are vaccinated?

    ANSWER: Number of boys: 24 - 12 = 12 boys. Vaccinated girls = 12 / 2 = 6. Vaccinated boys = 12 / 3 = 4. Total number of vaccinated children = 6 + 4 = 10. Fraction of vaccinated children = 10/24 = 5/12.

  2. There are 80 automobiles in the Los Angeles Automobile Museum, of which 30 of them are old models, produced before 1950. The rest are newer models, produced after 1950. If a third of vintage (old) cars and a fifth of the new cars are red. What fraction of all cars in the museum is red?

    ANSWER: Old model cars: 30. New model cars: 50. Red old model cars = 30 / 3 = 10. Red new model cars = 50 / 5 = 10. Total number of red cars: 10 old + 10 new = 20 red cars. Fraction of read cars = 20 / 80 = 1/4.

  3. Seven of the twelve months of the year have 31 days, four have 30 days, and one (February) has 28 days, and 29 in a leap year, which occurs very four years (the next leap year is 2024). What fraction of the months of the year has a 30-day length?

    ANSWER: Total number of months in a year: 12. Months with 31 days: 7. Months with 30 days: 4. Fraction of months with 30 days / total of months in a year = 4/12 = 1/3.

  4. The real length of a year is not 365 days, but 365 + 1/4 days. Every how many years do we have to add another day (Februay 29) to correct the error in time incurred every year?

    ANSWER: Error in one year = 1/4. Error in four years = 4/4 = 1. Threfore, every four (4) years we need to add one year to correct the calendar.

Number Assigned DueTopicProblem Description
1 Monday
210524 		Tuesday
210525		Fractions 1

  1. The game of domino, with nine (9) numbers, has a total of 55 pieces. There are three players, and each take seven (7) pieces to start. What fraction of the total number of pieces (55) remain in the Abracadabra pile?

    ANSWER: 3 × 7 = 21 pieces removed. Pieces remaining = 55 - 21 = 34. Fraction renaining = 34/55.

  2. There are 21 countries in Mexico, Central, abd South America. Three of them (French Guiana, Guyana, and Belize) do not speak Spanish as the first language. What fraction of the countries are Spanish-speaking?

    ANSWER: Countries speaking Spanish = 21 - 3 = 18. Fraction speaking Spanish = 18/21 = 6/7.

  3. There are one-hundred (100) attractions in Puebla. The Roly Polys have already visited ten (10) of these atractions. What fraction (or percentage) remain to be visited in the future?

    ANSWER: Attractions not visited = 100 - 10 = 90. Fraction not visited = 90/100, or 9/10, or 90%.

  4. Mexico has 31 states and one federal district, making a total of 32. Seventeen (17) states have coast to either the Pacific or Atlantic oceans. What fraction of the 32 (31 states and one federal district) does not have a limit with either ocean?

    ANSWER: States with no coast = 32 - 17 = 15. Fraction with no limit to oceans = 15/32.