Do Now Do Now (Jan 13) Fill in the blank. (page 398) 1. A(n) ___ of an equation is a number that you can substitute for the variable to make the equation true. 2. A(n) ___ is formed by the intersection of a horizontal number line, called the x-axis, and a vertical number line, called the y-axis. 3. Points on a coordinate plane are represented by ___. Write the fraction or mixed number as a decimal. 4. 3/5 5. 47 ¼ Solve the equation, check your solution 6. 6.3y = 25.2 7. w/4 = 5 Do Now (Jan 14) Fill in the blank. (page 398) 1. A(n) ___ of an equation is a number that you can substitute for the variable to make the equation true. 2. A(n) ___ is formed by the intersection of a horizontal number line, called the x-axis, and a vertical number line, called the y-axis. 3. Points on a coordinate plane are represented by ___. Write the fraction or mixed number as a decimal. 4. 3/5 5. 47 ¼ 6. 15/150 Solve the equation, check your solution 7. 6.3y = 25.2 8. w/4 = 5 Singapore Math – Daniel gave 4/5 of his stickers to Javier. Javier’s collection of stickers increased to 64. If Javier had 28 stickers in the beginning, how many stickers did Daniel have in the beginning? Do Now (Jan 15) 1. Find the unit rate for 24 ft/ 4 sec Find the average speed. 2. 119 meters in 8 minutes 30 seconds 3. 44 feet in 1 hour 20 minutes 4. Determine which is the better buy: 3 cans of cat food for $2.37, or 12 cans or cat food for $9.00 5. Mary can sew 50 quilt squares in 18 hours and 20 minutes. How long does it take her to sew one quilt square? Do Now (Jan 16) 1. Find the unit rate for 24 ft/ 4 sec Find the average speed. 2. 119 meters in 8 minutes 30 seconds 3. 44 feet in 1 hour 20 minutes 4. Determine which is the better buy: 3 cans of cat food for $2.37, or 12 cans or cat food for $9.00 5. Mary can sew 50 quilt squares in 18 hours and 20 minutes. How long does it take her to sew one quilt square? Singapore Math: The ratio of Kwame’s age to Derrick’s age is 3:4. 2 years ago, their average age was 12 years. How old is Kwame now? Do Now (Jan 19) 1. Draw the line that has the given slope, and passes through the given point. Slope= ¾, (-2, -1) 2. Draw the graph of the line that passes through the points. Then find the slope of the line. (2, 5), (5, -2) 3. Use equivalent ratios to solve 8/9 = m/45 4. Use algebra to solve 10/15 = c/27 5. It takes Taz 72 minutes to embroider a logo on a dozen baseball caps. At that rate, how long does it take her to embroider the logo on 3 dozen caps? 6. Write and then solve the proportion for 2 is to 10 as 8 is to x. Do Now (Jan 20) 1. Draw the line that has the given slope, and passes through the given point. Slope= ¾, (-2, -1) 2. Draw the graph of the line that passes through the points. Then find the slope of the line. (2, 5), (5, -2) 3. Use equivalent ratios to solve 8/9 = m/45 4. Use algebra to solve 10/15 = c/27 5. It takes Taz 72 minutes to embroider a logo on a dozen baseball caps. At that rate, how long does it take her to embroider the logo on 3 dozen caps? 6. Write and then solve the proportion for 2 is to 10 as 8 is to x. Singapore Math: The ratio of Liam’s age to his brother’s age is 4:9. Liam is 10 years younger than his brother. How old is Liam now? Quiz redo Do Now (Jan 21) Prepare for Chapter 8 test 5 minutes Do Now (Jan 24) Review Solve the proportion. 1. 8/3 = n/24 2. Draw the line that has slope 3/2 and passes through (0,1) 3. A ______ is an equation that states that two ratios are equivalent. (pg 448) Write the fraction as a decimal. 4. 5/20 Write the decimal as a fraction. (Remember to simplify!) 5. 0.95 6. 0.4 Singapore Math: Jayden, Maggy, and Ramon shared $49 in the ratio 2:5:7. How much more did Ramon get than Jayden? MS Math Do Now (Jan 26) Review Solve the proportion. 1. 8/3 = n/24 2. Draw the line that has slope 3/2 and passes through (0,1) 3. A ______ is an equation that states that two ratios are equivalent. (pg 448) Write the fraction as a decimal. 4. 5/20 Write the decimal as a fraction. (Remember to simplify!) 5. 0.95 6. 0.4 Singapore Math: Jayden, Maggy, and Ramon shared $49 in the ratio 2:5:7. How much more did Ramon get than Jayden? Do Now (Jan 27) 1. What number is 35% of 400? 2. What percent of 40 is 6? 3. 6 is what percent of 75? 4. 60 is 20% of what number? Do Now (Jan 28) 1. What number is 35% of 400? 2. What percent of 40 is 6? 3. 6 is what percent of 75? 4. 60 is 20% of what number? Singapore Math: The mass of a jar is 750 g when it is ½ filled with orange juice. The same jar has a mass of 625 g when it is ¼ filled with orange juice. (a) What is the mass of the jar when it is ¾ filled with orange juice? (b) What is the mass of the jar when it is empty? Do Now (Jan 29) 1. Write 650% as a decimal. 2. Write 0.57 as a percent. 3. Write 8/9 as a percent to the nearest tenth. 4. What is 20% of 45? 5. 51 is 60% of what number? 6. A salesperson sold a car for $22,000. If she receives a 9% commission for all car sales, what was her commission on this sale? Do Now (Jan 30) 1. Write 650% as a decimal. 2. Write 0.57 as a percent. 3. Write 8/9 as a percent to the nearest tenth. 4. What is 20% of 45? 5. 51 is 60% of what number? 6. A salesperson sold a car for $22,000. If she receives a 9% commission for all car sales, what was her commission on this sale? Singapore Math: Nadine has 3 times as many stamps as Evan and 50 more stamps than Kate. They have 872 stamps altogether. How many more stamps does Kate have than Evan? Do Now (Feb 2) Write the fraction as a percent. 1. 11/15 2. 5/26 3. 52/10,000 Find the percent of the number 4. 0.8% of 200 5. 350% of 12 Do Now (Feb 3) Draw a circle graph for the data. Instrument Number Woodwind 200 Brass 150 String 310 Percussion 60 Singapore Math: There are 16 red buttons and some black buttons in a box. The ratio of the number of red buttons to that of black buttons is 2 : 3. If 5 red buttons are added into the box, what is the new ratio? Do Now (Feb 4) Draw a circle graph for the data. Instrument Number Woodwind 200 Brass 150 String 310 Percussion 60 Do Now (Feb 5) Use the given information to find the new price. 1. original price: $45, Discount: 20% 2. original price: $78, Markup: 150% 3. your bill at a restaurant is $28.85. You leave a 20% tip and are charged a 5% sales tax. What is the total cost of the meal? 4. A pair of hiking boots with an original price of $125 is on sale for 20% off. If a sales tax of 6% must also be paid, what is the total cost? Singapore Math: The ratio of points scored by 3 boys on a math test is 7:10:12. If the sum of their scores is 232, what is the highest score? Do Now (Feb 6) Identify the percent of change as an increase or decrease. Then find the percent of change. 1. original: $20 New: $17 2. original: 70 New: 98 3. The population of a bacteria was 25,000. The bacteria increased by 12% after 3 hours. What was the population of the bacteria after 3 hours? 4. The number of employees at a car manufacturing plant decreased from 1150 to 1104. What was the percent of decrease? Do Now (Feb 10) 1. Find the interest and balance after 2 years on an account with a principal of $1500 and a simple annual rate of 12.5% Use the simple interest formula to find the unknown quantity. 2. I = $384, P = ?, r = 15%, t = 2 years 3. I = $305.20, P = $4360, r = ?, t = 6 months 4. I = $1692, P = $5640, r = 7.5%, t = ? Begin Chapter Review pg 496-500 Do Now (Feb 11) 1. A coordinate plane is formed by the intersection of a horizontal number called the ______, and a vertical number line, called the _____. 2. A(n) _____ consists of two rays that begin at a common point, called the _____. Plot the point and describe its location in a coordinate plane. 3. A(7,0) 4. B(-3,-4) 5. C(9, -5) 6. D(-1,2) Use the cross products property to solve the proportion. 7. 3/a = 4/9 8. 2/3 = 12/m Use a protractor to draw an angle with the given measure. 9. 135º 10. 75º Do Now (Feb 12) Prepare for Chapter 9 test. Turn to page 501, do problems 1-22 Do Now (Feb 13) Tell whether the angles are complementary, supplementary, or neither. Singapore Math: The 1. 161º and 19º ratio of points scored by 3 boys on a math test is 2. 37º and 53º 7 : 10 : 12. If the sum of 3. 45º and 40º their scores is 232, what is the highest score? 4. Name two pairs of vertical angles. 5. Name two pairs of corresponding angles. 6. Find m∠2 7. Find m∠5 Do Now (Feb 25) 1. A coordinate plane is formed by the intersection of a horizontal number line called the ______, and a vertical number line, called the _____. 2. A(n) _____ consists of two rays that begin at a common point, called the _____. Plot the point and describe its location in a coordinate plane. 3. A(7,0) 4. B(-3,-4) 5. C(9, -5) 6. D(-1,2) Use the cross products property to solve the proportion. 7. 3/a = 4/9 8. 2/3 = 12/m Use a protractor to draw an angle with the given measure. 9. 135º 10. 75º Do Now (Feb 26) Classify the triangle by the length of it’s sides. 1. 10 cm, 5 cm, 10 cm 2. 10 cm, 4 cm, 12 cm 3. A non-regular quadrilateral has four congruent sides. Sketch and classify it. Classify the polygon and tell if it is regular. If it isn’t regular, explain why not. 4. 5. 6. Singapore math: Lucas had $272, and Kelly had $804. Both of them spent the same amount of money. The ratio of Lucas’s money to Kelly’s money then became 2:9. How much money did they spend together? Prepare for Chapter 10 quiz (10.1 – 10.4) Do Now (Feb 27) Tell whether the angles are complementary, supplementary, or neither. 1. 161º and 19º 2. 37º and 53º 3. 45º and 40º 4. Name two pairs of vertical angles. 5. Name two pairs of corresponding angles. 6. Find m∠2 7. Find m∠5 Do Now (March 2) 1. Two polygons that have the same shape but not necessarily the same size are ____ polygons. 2. When two similar polygons have congruent corresponding angles and congruent corresponding sides, the polygons are _____. Page 539: 3, 5 – 9 Singapore Math: The ratio of the number of chickens to the number of ducks on a farm was 3:8.. There were 40 more ducks than chickens. When half the chickens and some of the ducks were sold, the ratio of the number of chickens to the number of ducks became 3:4. How many ducks were sold? Do Now (March 3) Classify the triangle by the length of it’s sides. 1. 10 cm, 5 cm, 10 cm 2. 10 cm, 4 cm, 12 cm 3. A non-regular quadrilateral has four congruent sides. Sketch and classify it. Classify the polygon and tell if it is regular. If it isn’t regular, explain why not. 4. 5. 6. Singapore math: Lucas had $272, and Kelly had $804. Both of them spent the same amount of money. The ratio of Lucas’s money to Kelly’s money then became 2:9. How much money did they spend together? Prepare for Chapter 10 quiz (10.1 – 10.4) Do Now (March ) 1. Two polygons that have the same shape but not necessarily the same size are ____ polygons. 2. When two similar polygons have congruent corresponding angles and congruent corresponding sides, the polygons are _____. Page 539: 3, 5 – 9 Literacy week! Drop Everything And Read 20 minutes Do Now (March 4) Page 550 1-7, 11-18 Singapore Math Cameron and Peter shared a box of markers in the ratio 5:3. Cameron gave half of his share to Peter. Peter then had 30 more markers than Cameron. How many markers did Cameron give to Peter? Do Now (March 5) 1. Two polygons that have the same shape but not necessarily the same size are ____ polygons. 2. When two similar polygons have congruent corresponding angles and congruent corresponding sides, the polygons are _____. Page 539: 3, 5 – 9 International Day Do Now (March 5) Page 561: 1-5 Singapore Math: Tierra and Joey shared some stamps in the ratio 7:5. Tierra gave Joey 12 stamps. If each of them had the same number of stamps in the end, how many stamps did Tierra have in the beginning? Intl Day Study for the quiz 10.5 – 10.8 Do Now (March 9) Page 545 15-17 Do Now (March 10) Tessellations Page 569 1-18 evens Study for the test Begin by 1:00 Do Now (March 11) Page 561: 1-5 Study for the quiz 10.5 – 10.8 Do Now (March 13) Prepare for Chapter 10 Test calculators Do Now (March 16) Intl Day 1. Find the two square roots of 144. 2. Evaluate the square root -√(196) 3. Evaluate the expression √(x²-4y) when x = 6 and y=5. 4. Solve the equation 2m² = 72 5. Find the side length of a square having an area equal to 169 m² Singapore Math: The ratio of Victoria’s weight to Kazuki’s weight was 4:5. If Victoria’s weight increased by 5 lb. and Kazuki’s weight decreased by 1 lb., Victoria would have the same weight as Kazuki. What was Victoria’s original weight? Survey 1. Write 2 things that you liked so far this semester in this class. 2. Write something you didn’t like, or one of your least favorite things. 3. If you could change something in our class, what would you change? Do Now (March 17) Intl Day Test Corrections Page 576 1-15 Do Now (March 18) 1. Approximate the square root to the nearest whole number and then to the nearest tenth. 1. √(41) 2. √(96) Tell whether the number is rational or irrational. 3. – (4/9) 4. √(67) 5. You are building a ramp. Use the formula h = √(c² - a²) where a = 7 feet and c = 8 feet to find the height, h, of the ramp to the nearest tenth. Prepare for the Quiz (11.1-11.3) you can work with the person next to you. Page 592: 1 – 16 Quiz at 10:55 Do Now (March 19) 1. Find the two square roots of 144. 2. Evaluate the square root -√(196) 3. Evaluate the expression √(x²-4y) when x = 6 and y=5. 4. Solve the equation 2m² = 72 5. Find the side length of a square having an area equal to 169 m² Do Now (March 20) Quiz corrections Page 590 7 – 17 Singapore math: Last year, the ratio of the number of boys to the number of girls in the computer club was 1:2. This year, 70 new members joined the computer club. There are now 4 times as many boys and 3 times as many girls as last year. How many members were in computer club last year? Do Now (March 23) Page 590 7 – 17 Study for the quiz (11.1-11.3) When you are finished, preview 11.4 Do Now (March 24) Use the area A of the parallelogram to find its base b or height h. 1. A = 144 m², b = 4 m, h = ? 2. A = 200 ft², b = ?, h = 25ft Page 598; 31 – 37 Singapore Math: A square plot of land has an area of 196 m², while a rectangular plot of land with a length of 12 m has an area of 96 m². What is the ratio of the length of the square plot of land to the width of the rectangular plot of land? Do Now (March 25) Use the area A of the parallelogram to find its base b or height h. 1. A = 144 m², b = 4 m, h = ? 2. A = 200 ft², b = ?, h = 25ft Page 598; 31 – 37 International Day Do Now (March 26) Find the unknown base of the trapezoid. A = 24 km², b1 = 5 km, b2 = ?, h = 6km Page 605 25 – 27, 31, 33, 34 Singapore Math: Andrew had $93. With his money, he could buy 3 CDs and 4 books. However, he bought only 2 CDs and 3 books and had $27 left. What was the cost of each CD? Do Now (March 26) Find the unknown base of the trapezoid. A = 24 km², b1 = 5 km, b2 = ?, h = 6km Page 605 25 – 27, 31, 33, 34 Do Now (April 13) Find the circumference of the circle. 1. diameter = 49km 2. radius = 2.3 in. Find the diameter and the radius of the circle with the given circumference. 3. C = 18.84cm 4. C = 7 1/3ft 5. A map shows the protected area around a community’s water source. The area is a circle with a radius of 200 feet from the center of the water source. What is the circumference of the protected area? Singapore Math – The ratio of Carlos’s money to Ava’s money to Zach’s money is 4:5:9. If Zach has 168 more than Ava, A) how much money does Ava have? B) how much money will Zach have left if he spends 1/3 of it? International Day project due WEDNESDAY Do Now (April 14) Find the circumference of the circle. 1. diameter = 49km 2. radius = 2.3 in. Find the diameter and the radius of the circle with the given circumference. 3. C = 18.84cm 4. C = 7 1/3ft 5. A map shows the protected area around a community’s water source. The area is a circle with a radius of 200 feet from the center of the water source. What is the circumference of the protected area? International Day project due THURSDAY Do Now (April 16) Prepare for Chapter 11 test Page 621 25- 40 odds When you are finished, work on your international day project. DUE TODAY Do Now (April 17) Bring your International Day project on Wednesday to present to the class. Test redo Page 630 1-12 Singapore Math: Jamila and Akiko had the same amount of money to spend. After Jamila spent $33 and Akiko spent $42, Jamila had 4 times as much money left as Akiko. How much money did each of them have in the beginning? Now (April 20) Bring your international day project to present to class on Wednesday. Quiz redo Prepare for Chapter 11 test. Look at formulas Finish review When you are finished with the test: Page 630 1-12 Do Now: Pre AP MS Math (April 21) 1. Sketch a square pyramid 2. Page 639 25 -31 Singapore Math: For every watch Sarah sells, she earns $4. She gets an additional bonus of $40 for every 25 watches she sells. Last month, Sarah received a total of $506. How many watches did she sell last month? International Day project presentations Quiz today 12.1-12.3 International day project presentations 1. Test redo 2. sketch a square pyramid 3. page 639 25 -31 Quiz Friday 12.1-12.3 Do Now (April 24) Page 638 1 – 14 Quiz today 12.1-12.3 MS Math (April 29) A small box of rice is 11 cm long, 3 cm wide, and 16 cm high. A larger box is 16 cm long, 6 cm wide, and 22 cm high. 1. Find the volume of each box. 2. How many small boxes do you have to buy to equal the amount of rice in a large box? Pg 658; 23-28 Singapore math: 5 people can sit on each side of a square table. If 4 tables are pulled together to form a large square table, how many people can sit around the large table? 1. find the surface area of the rectangular prism with the given dimensions A. 3cm by 3 cm by 1 cm B. 2.5 m by 1.5 m by 0.5 m Page 647: 1-7 Do Now (April 30) 1. Find the height of a cylinder with radius 12 centimeters and surface area 1281 square centimeters. 2. How much wrapping paper is needed to wrap a poster tube that is 30 inches long and has a diameter of 5 inches? 3. Find the surface area of the cylinder with radius 5 inches and height 3 feet. Use 3.14 for π. Page 653 30 – 36 Do Now (May 5) 1. a cylinder has a volume of 1356.48 cubic feet and a radius of 6 feet. Find its height. Use 3.14 for pi. 2. a circular swimming pool is 20 feet in diameter and 4 feet deep. What is its volume? Use 3.14 for pi. Page 666 1 – 7 Prepare for Quiz 2 12.4-12.6 Do Now (May 7) Prepare for Chapter 12 test Page 673 1-15 Do Now (May 11) Page 680 Prerequisite skills 1-6 Test Redo Do Now (May 12) Each letter in PROBABILITY is placed in a bag. One letter is randomly chosen from the bag. Find the probability of the event. Write the probability as a fraction. 1. The letter B is chosen. 2. The letter Y is chosen. A number cube is rolled once. 3. What is the probability of rolling a prime number? 4. What is the probability of rolling a number less than 5? Page 685: 21-22, 26-28, 29-33 Singapore Math: Abby and Hakeem had the same number of CDs. After Abby gave away 28 CDs and Hakeem sold 17 CDs, the ratio of the number of Abby’s CDs to the number of Hakeem’s CDs became 2:3. How many CDs did they have altogether in the beginning? Do Now (May 13) Each letter in PROBABILITY is placed in a bag. One letter is randomly chosen from the bag. Find the probability of the event. Write the probability as a fraction. 1. The letter B is chosen. 2. The letter Y is chosen. A number cube is rolled once. 3. What is the probability of rolling a prime number? 4. What is the probability of rolling a number less than 5? Page 685: 21-22, 26-28, 29-33 Do Now (May 14) 1. Find the probability that two even numbers are rolled when rolling two number cubes. Paintings at an art store include oils and watercolors. They come with a wood frame, a metal frame, or unframed. 2. Make a tree diagram to show the different types of paintings. 3. If a painting is randomly chosen, what is the probability that it has a metal frame? Page 693 #9, 22, 23 Do Now (May 15) 1.Paintings at an art store include oils and watercolors. They come with a wood frame, a metal frame, or unframed. 2. Make a tree diagram to show the different types of paintings. 3. If a painting is randomly chosen, what is the probability that it has a metal frame? Do Now (May 18) Use the number of outcomes of the events to find the number of ways that the events can occur together. 1. Events C, D, and E each have 5 outcomes. 2. A 5-character password is randomly generated so that the first and last characters are digits and the others are letters. If any character can be repeated, what is the probability of generating the password 7GBS7? Prepare for the quiz Page 700 1-5 Do Now (May 19) Use the number of outcomes of the events to find the number of ways that the events can occur together. 1. Events C, D, and E each have 5 outcomes. 2. A 5-character password is randomly generated so that the first and last characters are digits and the others are letters. If any character can be repeated, what is the probability of generating the password 7GBS7? Page 699 21, 23, 24, 26 When finished, keep the quiz at your desk and work on: Page 700 1-5 Page 701 Do Now (May 20) Final touches on menu presentation. (5 min) You need to give me your rubric when you present Quiz corrections Page 701: 1-7 Exchange and Respond You will exchange menus with another group. Create 5 questions about your poster that the other group will need to answer. Examples How many possibilities are there if you chose one drink, one soup, one entrée, and one dessert? If I am on a budget, but I want to get one thing of each category, what is the cheapest meal I can buy, and how much is it? You have $15, can you buy a drink, salad, and entrée? Which can you buy? Do Now (May 21) Page 701 1-7 Do Now (May 22) Counting Principle practice Singapore Math: The ratio of the number of cars to the number of SUVs in a parking lot is 3:1. The ratio of the number of SUVs to the number of minivans is 3:5. A. Find the ratio of the number of cars to the number of SUVs to the number of minivans in the parking lot. B. if there are 20 minivans, how many vehicles are there altogether? Do Now (May 25) 1. Find the number of combinations of two sandwiches to be chosen from a vending machine that offers 5 different kinds of sandwiches. 2. How many ways can you play 3 CDs from a set of 12 CDs if the order matters? How many ways can you choose 3 CDs if order does not matter? Tell whether the situation describes a permutation or a combination. Then answer the question. 3. How many ways can 8 members of the string section in an orchestra be introduced at a concert? Page 706: 20,21, 23, 28, 30-38 Singapore Math: The ratio of Beatriz’s savings to Savannah’s savings is 4:7. The ratio of Savannah’s savings to Julia’s savings is 3:5. The three girls have a total savings of $136. How much more money has Julia saved than Beatriz? Do Now (May 28) Are events A and B disjoint or overlapping? 1. Event A: A student is on the baseball team. Event B: A student is on the soccer team. 2. Event A: Today is Wednesday. Event B: It is the month of May. 3. Events c and D are disjoint events, with P(C) = 0.18 and P(D) = 0.77. Find P(C or D). 4. Events E and F are complementary events, and P(E) = 4/7. Find P(F). 5. You randomly choose a letter from the word DISJOINT. Find the probability of choosing an I or a T. Textbook page 713: 23-28, 33-36 Singapore Math: Ally and Tony had a total of $44. After Ally spent ¼ of her money and Tony spend $5, the ratio of Ally’s money to Tony's money became 1:2. How much money did Tony have in the beginning? Do Now (May 29) 1. Events C and D are dependent events. Find P(D given C) if P(C) = 0.6 and P(C and D) = 0.3. Tell whether the situation describes independent events of dependent events. Then answer the question. 2. A box contains 3 red, 2 white, and 5 blue balls. Two balls are drawn without replacement. What is the probability that the first ball is red and the second is white? 3. Two balls are drawn without replacement. What is the probability that both are red? 4. What is the probability that both are white? 5. What is the probability that the first is white and the second is red? Page 719: 20-29, 31-42 Singapore Math: Sam, Jimmy, and Andre shared a number of pennies in the ratio 8:5:3. Sam and Andre received a total of 671 pennies. How many more pennies did Jimmy receive than Andre? When you are finished, work on the problems on Page 722: 1-3 You may work with your partner after everyone is finished with the quiz Turn in the homework (1-3) Quiz corrections Singapore Math: The ratio of the number of boys to the number of girls at an elementary school is 3:2. If each boy receives 2 pieces of paper and each girl receives 3 pieces, a total of 1,992 pieces of paper are needed. How many children are there altogether? Page 723 – 726 Page 727 test practice (1-15) Singapore Math: Jessica has 3 times as many postcards as Antonio. After Jessica gave 30 postcards to her friend and Antonio received 15 more postcards from his friend, Antonio had ¾ as many postcards as Jessica. How many postcards did they have altogether in the beginning? Test today Page 732: 1 – 23 Test corrections Study guide Survey Page 732: 1 – 42 Singapore Math: Danny, Amira, and Tyler shared a sum of money in the ratio 6:4:3. Amira used ½ of her money to buy a watch that cost $30, and Danny gave 1/3 of his money to his sister. How much money did they have left altogether? 1-10 11-20 21-30 31-40 41,42