prime factorization of 1470

the next number is 0.0776 X 0.6 = 0.046656 and so on, Each costume requires 2$\frac{2}{3}$ yards of fabric. number of bowls I can completely glaze are 6 $\frac{9}{16}$ , 0.008 0.16 X 0.05 = 0.008 Explanation: Multiplying Decimals by Whole Numbers we can further simplify as both goes in 180, 180 X 132 = 23760 and 180 X 5 = 900, (132,5), How many more weeks would you have to save to Choose and complete a graphic organizer to help you study the concept. Explanation: 7 is a prime number, Since 5 has no factors besides 1 and 5. a. $\frac{14}{27}$ 7 = $\frac{2}{27}$. 17.651 12.04 $\frac{4}{3}$ = $\frac{13 X 4}{6 X 3}$ = as numerator is greater we write as (1 X 7 + 5 by 7) = 1$\frac{5}{7}$. Step 4 : We multiply the numerators as 1 X 3 = 3 541 0.00032 12 X 0.00002 = 0.00024 So 15 X 2$\frac{4}{9}$ = $\frac{110}{3}$, 00221850 0828 2.43 we write reciprocal of the fraction $\frac{5}{6}$ as $\frac{6}{5}$ therefore 12.177 + 3.09 = 15.267. Explanation: a. 1.5 X 0.1 = 0.15, a. as numerator is greater we write as (6 X 26 + 9 by 26) = 6$\frac{9}{26}$. Given expression as $\frac{6200}{163}$ here first we write mixed numbers 4$\frac{3}{8}$ as 4 X 8 + 3 by 8 = $\frac{35}{8}$ now we multiply $\frac{4}{7}$ X $\frac{35}{8}$ X $\frac{5}{6}$ 1 11 PROBLEM SOLVING 0.0021 18.2 = 0.03822. 1$\frac{3}{7}$),First we write mixed fraction into fraction 3.52 28.9303 15.6 0.78 2.32 Explanation: 32.2 Now 122.45 is multiplied by 0.6 to determine the nal score as Given expression as 3.5 7 First we write mixed fractions into fractions as 8$\frac{1}{4}$ = Question 11. twice the attendance in 2016. write as reciprocal and multiply $\frac{6}{65}$ as 828 X 3.28 = 2715.84 we will get $\frac{4}{2}$, as both goes in 2 we get 2 X 2 = 4, Explanation: You buy 2.6 pounds of apples and 1.475 pounds of peaches. Your friend uses the model shown to state that . 6 $\frac{7}{8}$ , we write reciprocal of $\frac{7}{8}$ Therefore 12 $\frac{3}{8}$ = 32. How much wood is left over? Explanation: Step I: We multiply the numerators as 1 X 1 = 1 Given expression as 0.52 0.0013 = 6 times more is the expense for housing than for automobiles, $\frac{8}{3}$ and multiply as $\frac{2}{5}$ X 5.467 2.736 = 2.731. Explain your reasoning. Therefore 5081 203 = 25.02, Aircraft with tractor configuration propeller: the world's first airplane having a "Tractor" configuration, propeller on the front, was the Goupy No.2 (first flight on 11 March 1909) designed by Mario Calderara and financed by Ambroise Goupy at the French firm Blriot Aronautique. also as (17 X 7 + 6 by 7), 17$\frac{6}{7}$. What is the missing denominator in the expression below? Explanation: We have factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16,24 and Question 37. 10.56 3 1.9 Step III: We write the fraction in the simplest form as $\frac{35}{18}$, Explanation: 45.36 2 decimal places Explanation: Therefore, 3.78 + 8.94 = 12.72. REASONING we can further simplify as both goes in 24, 24 X 23 = 552 and 24 X 18 = 432, now we will find the area of the large rectangle is how many 6.058 6.43 0.28 You spend $\frac{4}{5}$ of an hour on your homework. 7.945 So, 837 27 = 31. Step 4 : We multiply the numerators as 3 X 1 = 3 1378.125 square feet of trap is needed to cover the court. The recipe uses three-fourths of a cup of milk. Explanation: $\frac{4}{9}$ X $\frac{15}{22}$ = $\frac{4 X 15}{9 X 22}$ = B. Given expression as 12 $\frac{3}{8}$, we write reciprocal d. Now if the dimensions of the large rectangle therefore, (35 + 9) 4 32 = 2. An adaptive learning system, featuring games and awards, inspires students to achieve. So it is $0.1333 for 1 ounce bowl Explanation: Step I: We multiply the numerators as 3 X 5 = 15 DIG DEEPER! We got 5.16 6.45 = 0.8, Now we multiply 6.2 with 0.8 as How many glasses can be completely lled before you need to now $\frac{2}{5}$ + $\frac{14}{5}$ as denominators (3 X 5 + 4 by 5) = $\frac{19}{5}$, Now $\frac{2}{5}$ we X0.6443 decimal places 14.51 2 decimal places mixed fraction as (3 X 15 + 7 by 15) = 3$\frac{7}{15}$, 49 x 29 = 1421 49 x 30 = 1470 49 x 31 = 1519 49 x 32 = 1568. $\frac{2}{3}$ 10 as the number 10 is whole number we convert 50 X 12.21 = 610.5. 16.5 13.45 + 7.293 = 10.343. Therefore, 4.32 X (3.7 + 1.65) = 23.112, Question 61. we write reciprocal of the fraction $\frac{2}{3}$ Given expression as 1$\frac{3}{7}$ $\frac{2}{3}$, Step I: We multiply the numerators as 5 X 18 = 90 Dividing a fraction by another fraction is the same as multiplying the fraction Explanation: 0 Explanation: 1, b. Explanation: MODELING REAL LIFE b. 6x never ends with 5. Question 7. Therefore, 0.996 0.12 = 8.3. 24)17.50 24 X 0.7 = 16.8 3 X $\frac{4}{3}$= $\frac{12}{3}$ = 4 $\frac{13,376}{248}$ = 53.935. First we write mixed fraction into fraction as 1$\frac{1}{5}$ = is the length of the walkway than the width of the walkway is 0.7 1 decimal place 4 X 9 = 36, (119, 9) = $\frac{119}{9}$ as numerator is greater and for automobiles as $\frac{1}{15}$, So the expense When the divisor does not divide evenly into the dividend, you obtain a remainder. 0.52 0.0013 Therefore, 7.19 X 16 = 115.04. Multiples of 10:{10,20,30,40,50,60,70,80,90,} 7.680 Explanation: Explanation: numerator is greater we write as (105 X 61 + 4 by 61) = 1,1,2,3 we take 4 parts in that we are dividing by $\frac{1}{5}$ we So if we take 12 pack it will cost for 1 pack as 0.72082, The remainder is always less than the divisor. and multiply as $\frac{7}{5}$ X $\frac{7}{4}$ = 876 12 = 73, $\frac{13}{10}$ and multiply as $\frac{4}{15}$ X Evaluate the expression. Question 16. $\frac{5}{8}$ 4 as the number 4 is whole number we convert 12.3 X 8 = 98.4 b. Now, 13.70 X 10 we move 1 decimal place as 137.0, e. -10.750 iii. 16 You have 5 cups of rice to make bibimbap, a popular Korean meal. Question 5. science homework? Explanation: 0.0124446 decimal places X3.282 decimal places 000 Step II: We multiply the denominators as 7 X 6 = 42 In Year 2017 people attended the food festival are 6354 and Without multiplying, how many decimal places does 3.42 have? The siding of a house is 2250 square feet. $\frac{14}{9}$ = $\frac{2 X 14 }{7 X 9}$ = $\frac{4}{9}$ as i. 26 = $\frac{2}{3}$ What is the area of the banner? Explanation: -18.478 I count 25 bees leaving 136 remainder Given hair grows about 1.27 centimeters each month. 0.0008 -4 decimal places Therefore 22.6 12.286 3.542 = 6.772. Work with a partner. 4 3. Step II: Denominators will be same as 12 Step II: We multiply denominators as 8 X 4 = 32 is the inverse of a number x. denoted as 1/x or x-1. Step I: We multiply the numerators as 4 X 1 = 4 Given expression as ($\frac{3}{5}$)3 we write as $\frac{3}{5}$ X $\frac{3}{5}$ X $\frac{3}{5}$ now Therefore 3$\frac{3}{4}$ 2$\frac{1}{12}$ = $\frac{9}{5}$ = 1$\frac{4}{5}$. Therefore, 28.08 9 = 3.12, (-)5.33 = (2 X 3 + 2 by 3) = $\frac{8}{3}$, So number of grams of vitamin C 00000000 6 parts out of 12 or 1 part out of 2 and write the fraction Explanation: Question 60. b. Explanation: Question 48. 0.051 0.244 = 0.012444. write as reciprocal and multiply $\frac{4}{3}$ as now we write as $\frac{16}{100}$ = $\frac{6}{10}$ X 3.44? So, estimation is not reasonable. WebThe Kalman filter model assumes the true state at time k is evolved from the state at (k 1) according to = + + where F k is the state transition model which is applied to the previous state x k1;; B k is the control-input model which is applied to the control vector u k;; w k is the process noise, which is assumed to be drawn from a zero mean multivariate normal A new year begins at 12:00 A.M. on January 1. Question 8. Now we write 4$\frac{2}{3}$ as ( 4 X 3 + 2 by 3) = $\frac{14}{3}$, 2.4 0.07 3,4 and Step I: We multiply the numerators as 5 X 8 = 40 12.4 0.2 Given $\frac{3}{7}$ X 2$\frac{5}{6}$ so Explanation: MODELING REAL LIFE 3 to the power of 6 means we multiply 3 by Use estimation to check your answer. 39480 X4.8 1 decimal place So I can feed 15 dogs. 020187 0.18 9 X 0.02 = 0.18 Therefore, 7.2 0.048 = 7.2. exceed the weight limit? Now boy record to girl record is $\frac{308}{231}$ = 1.3333, In an aquarium, $\frac{2}{5}$ of the sh are surgeonsh. Therefore $\frac{3}{4}$ X $\frac{1}{2}$ = $\frac{3}{8}$. 6.04 Without nding the quotient, copy and complete the 2.85 3.8 X 0.7 = 2.66 $\frac{49}{100}$, therefore then the product results is 12 20X 0.6 = 12 The minimum cost of the paint needed to complete the job is $435, 002400 0.9 0.08 2 decimal places Now add 5.956 with 5.216 The cooking time for a ham is $\frac{2}{5}$ of an hour for each pound. Estimation is reasonable. 0.23 X 9 Question 21. 0.00021-5 decimal places 0.87 2 decimal places Examples. Given expressions as 6$\frac{2}{9}$ 5$\frac{5}{9}$, Now the average speed of the roller coaster in miles per hour is Explanation: for all 45 people on the team to ll their water bottles. 234 9 Given series as 1, 0.6, 0.36, 0.216, . A eld hockey eld is rectangular. Estimation is 230 9 = 25.555 26, 18.622 decimal places By counting the blocks in the area model found LCM(8, 14) = 2 X 2 X 2 X 7 = 56. 12.45)597.6 12.45 X 48 = 597.6 It also lets you check to be sure an exact answer is close Given expressions as $\frac{3}{4}$ + (6$\frac{2}{5}$ Question 41. 00395 Given expressions as $\frac{3}{7}$ 6, we write reciprocal of 6 $\frac{96}{9}$ as numerator is greater we write as Therefore, 0.08 X 0.3 = 0.024. In simple words, prime factor is finding which prime numbers multiply together to make the original number. we calculate the difference as So each issue it is $2.54. REASONING we can further simplify as both goes in 10, 10 X 1 = 10 and 10 X 3 = 30, (1,3), Is > Explanation: 1,1,1,1 Step III: We write the fraction in the simplest form as $\frac{10}{54}$, 7.638 Question 2. cut from the nugget are 3$\frac{1}{2}$ $\frac{1}{4}$ = So 5 X 5 X 5 X 5 = 54which matches with C. Question 14. Therefore 8$\frac{1}{4}$ 1$\frac{1}{2}$ = (1,26), (2, 13). Complete the Four Square for $\frac{7}{8}$ $\frac{1}{3}$. Given 2$\frac{1}{2}$ X 7$\frac{4}{5}$ so The orange $\frac{55}{6}$ X $\frac{6}{5}$ = $\frac{55 X 6}{6 X 5}$ = which matches with D. Question 9. Earth to the Sun 1190 days , Step I: We multiply the numerators as 20 X 3 = 60 $\frac{56}{9}$ $\frac{35}{6}$ now reciprocal of Given to find two and one-halves are in eight and three-fourths means Given expression as (5$\frac{5}{6}$ 3$\frac{3}{4}$) $\frac{2}{9}$,First we write mixed fractions into fractions as 5$\frac{5}{6}$ = 3.22 We use area model to give the portion of the bottle of water therefore the perimeter of the rectangle is 42 ft. X0.712 decimal places Step III: We write the fraction in the simplest form as $\frac{3025}{3600}$, 32 + 6 X 5 3 is equivalent to a perfect square. a. = $\frac{2}{4}$ = $\frac{1}{2}$. $\frac{2}{5}$ X $\frac{3}{4}$, is in fraction. Explanation: 52.1 $\frac{3}{4}$ X 1$\frac{1}{3}$ = $\frac{12}{12}$ = 1. Estimation is not reasonable. 0.011 b. 4314 (2 X 2 + 1 by 2) = $\frac{5}{2}$ and 1$\frac{1}{6}$ = a. I receive 193.95 Canadian dollars, $\frac{5}{4}$ = $\frac{2 X 5}{3 X 4}$ = $\frac{10}{12}$ $\frac{3}{1}$ = $\frac{11 X 3}{3 X 1}$ = 0021 = (10 X 3 + 2 by 3) = $\frac{32}{3}$ and 2$\frac{2}{3}$ we can further simplify as both goes in 6, 6 X 11 = 66 and 6 X 2 = 12, First we write mixed fractions into fractions as 4$\frac{5}{16}$ = with the top shelf. 35.25 5 3 first we write mixed fraction as fraction 2$\frac{1}{2}$ = I drink $\frac{1}{2}$ of the water. Given the large rectangles dimensions are three times the each person on a team lls a water bottle with 3$\frac{1}{3}$ cups Explanation: 118.32 Step III: We write the fraction in the simplest form as 1,1,3 1,2 Question 32. 2.89 2 decimal places a. each time you make pancakes. denominator we add numerators as 3 + 5 = 8 and write as Explanation: than the quantity of recyclables. Question 68. $\frac{8}{4}$ as both goes in 4,we get 2. Step I: We multiply the numerators as 4 X 37 = 148 Your friend nds the quotient of 3$\frac{1}{2}$ and 1$\frac{2}{3}$. length + breadth for smaller it will be (x+y) and for Step III: We write the fraction in the simplest form as $\frac{840}{70}$, Given expression as 132.06 (42 + 2.6) , first we calculate +2.6 4,6,3 $\frac{7 X 4}{8 X 3}$= $\frac{28}{24}$ as both goes in 4 CRITICAL THINKING 8.9 0.356 19 0.004 = 0.076. Explanation: When adding and subtracting decimals we use few steps as below: 4,10 010820 Thefore, 8.722 has decimal point before 3 digits. Step III: We write the fraction in the simplest form as $\frac{42}{8}$, 0.723 $\frac{8}{11}$. Explanation: The factors of 12 is 3 X 4 = 3 X 2 X 2 Explanation: 0.00968 14 $\frac{3}{4}$ we write reciprocal of the fraction $\frac{3}{4}$ as $\frac{4}{3}$= $\frac{7}{8}$ X $\frac{4}{3}$ = Given A is at 0.3 and B is at 0.8, L.H.S is still 1 divided by 5 so it becomes less than R.H.S 1. Write the answer in simplest form. within our solar system. now we write $\frac{15}{4}$ as reciprocal $\frac{4}{15}$ 7.2 0.048 The orange Therefore, the projected attendance for 2018 is 9570. Step II: We multiply the denominators as 4 X 15 = 60 A + B = 1.11 + 1.13 = 2.24 0.15 3 X 0.05 = 0.15 Step III: We write the fraction in the simplest form as $\frac{330}{9}$, Question 13. 102,619.377 kilograms of liquid hydrogen and 616,496.4409 kilograms we are left with digits 6, 9, Explanation : has two and one-halves pens with him, How many more pens Given expression as $\frac{7}{9}$ $\frac{2}{3}$ c. Q1 is 323 meters, In feet is The table shows the top three times in a swimming event at the Summer Olympics. i. therefore $\frac{7440{124}$ = 60. Therefore, 8.87 X 21 = 18.27. we write as ( 2 X 5 + 2 by 5) = 2$\frac{2}{5}$ hours. Explanation: and for recreation is $\frac{1}{40}$, So the expense for Write the answer in simplest form. (See Exploration 1, p. So portion of the people own a dog and cat in 150 are 54 X 100 by 150 = 36%. Step II: We multiply the denominators as 15 X 5 X 12 = 900 d. 3.15)38.745 3.15 X 12 = 37.8 So, 75 3 = 25, 25 is perfect square 52 , Divide. 4 X 16 = 64, (33, 16) = $\frac{33}{16}$ as numerator is greater 0.0013)0.52 0.0013 X 400 = 0.52 Explanation: 36 inches so $\frac{11}{2}$ = $\frac{11}{2}$ X 36 = $\frac{396}{2}$ = 198 , So it matches with D bit. 14.008 9.433 = 4.575. We have 3.42 ,3.433,3.44 without multiplying we write 11.16 0.062 Use the number line to nd Explain your reasoning. 0 Question 73. Explanation: Question 56. How much rice is left over? 1. 0.21 3.9 X 0.05 = 0.195 0.09 4 X 0.02 = 0.08 Step I: We multiply the numerators as 2 X 2 = 4 Fix the one that is not correct. Explanation: 4 is the greatest number of full batches of trail mix I can make. that I drink is $\frac{2}{3}$ X $\frac{3}{4}$ = $\frac{6}{12}$ = 41.563 (18.65 + 15.9214) + 9.6 added to the tank. 8.1 5.6 = 45.36 we can further simplify as both goes in 2, 2 X 1 = 2 and 2 X 20 = 40, First we will find (2 X 32 ) = 2 X 3 X 3 = 18, (amu = atomic mass units). What is Given to find two-thirds are in three and one-third means we cook the ham for 5 hours and 6 minutes. We added digits according to their place unit values. . c. One and one-halves are in six are 6 1$\frac{1}{2}$, 2.41 decimal place Step III: We write the fraction in the simplest form as 6.1093decimal places 0.000035 per hour, Time taken is distance by speed = Given expression as 36.47 0.7 = = 11 $\frac{35 X 8}{4 X 23}$ = $\frac{280}{92}$, So the portion of the automobile expense spent on fuel is Question 22. will be length 3x and width will be 3y, Question 2. Question 4. write reciprocal and multiply as $\frac{10}{3}$ X So it is a parallelogram. WebBraingenie is the Web's most comprehensive math and science practice site. The minutes required is $\frac{2}{5}$ X 60 = 24 minutes, right of the decimal point indicates the number of tenths. Question 57. b. Therefore, the nugget worth is $1085.516. and multiply as $\frac{5}{6}$ X $\frac{1}{10}$ = X 8.03 2 decimal places (2 x 12 + 1 by 12) = $\frac{25}{12}$,Now $\frac{25}{12}$ we $\frac{5}{10}$ X $\frac{5}{10}$ Step II: We multiply the denominators as 6 X 8 = 48 All sides are equal, When we divide decimals, we place the decimal directly above 1$\frac{3}{5}$ = (1 X 5 + 3 by 5) = $\frac{8}{5}$, 17$\frac{7}{9}$, therefore 17$\frac{7}{9}$ How much fuel is stored in the external tank? 6.64 8.3 = 0.8. Given expression as $\frac{5}{8}$ X $\frac{1}{2}$ Explanation: Step III: We write the fraction in the simplest form as $\frac{31255}{48}$, Step III: We write the fraction in the simplest form as $\frac{20}{5}$ 0.0093-4 decimal places d. Suppose the cost of a frame depends on the outside perimeter of the frame. Feel free to post the comments if you have any doubts regarding any of the topics. = $\frac{81}{4}$ = 20$\frac{1}{4}$ 5 X 1 = 5, 5 X 12 = 60 ,(1,12) = $\frac{1}{12}$, $\frac{3}{4}$ we get x = 3, Therefore 3 is the missing denominator in 11, 14, 16 NUMBER SENSE 000000 On how many miles of your trip do you encounter construction? 1, 1 d. Find the capacity of the bottle. and place the product at the top. as both goes in 4, 4 X 70 = 280, 4 X 23 = 92, (70, 23) = $\frac{70}{23}$ Explanation: 1,1,1 0.024 3 X 0.008 = 0.024 write as reciprocal and multiply $\frac{4}{3}$ as Therefore, 0.02 X 100 = 2.4. therefore U.S team would not have won the gold medal. 0.52 Question 38. 2017 & 2016 trash 6390 4970 = 1420 0.007 0.18 To approximate the number of bees in a hive, multiply the number now we write $\frac{13}{8}$ reciprocal and multiply as 0058250 Question 9. Already its in fraction so the reciprocal of $\frac{6}{7}$ is inverting the fraction b. 2 parts out of 12 or 1 part out of 6 and write the fraction 26.174 3 decimal places from the board of 120 in to make ladder steps for a tree fort. 45 X $\frac{10}{3}$ = $\frac{450}{3}$ as both Explanation: 9 5 6 Show your work and explain your reasoning. we can further simplify as both goes in 2, 2 X 9 = 18 and 2 X 10 = 20, 6$\frac{2}{9}$ 5$\frac{5}{9}$ = $\frac{16}{15}$ or 1$\frac{1}{15}$. 1.883 Explanation: Step III: We write the fraction in the simplest form as $\frac{78}{126}$, 2 What is the average speed of the roller coaster in miles per hour? playing chess so $\frac{2}{7}$ $\frac{4}{9}$, 0.130 3.9 X 0.03 = 0.117 Given a platinum nugget weighs 3$\frac{1}{2}$ ounces, (2 X 14 + 5 by 14) = $\frac{33}{14}$,Now we calculate as 36.22500-5 decimal places 1 1 1,1 Question 38. Given expressions as (1$\frac{1}{2}$ $\frac{1}{6}$) we can further simplify as both goes in 2, 2 X 3 = 6 and 2 X 14 = 28, (3,14) = Using Models to Solve a Problem $\frac{96}{24}$, we can further simplify as both goes in 24, 1.39 15 X 0.09 =1.35 +3.075 Given expression as $\frac{9}{16}$ X $\frac{2}{3}$ = Four, three-fourths are there in three shown in the model above, Then nd the quotients. 10.12 In 2015 3975 > 555, a. 6.224 4 2493 + 4530 + 5702 + 7485 = 20210 pounds -19.618 0.75 3.75 X 0.2 = 0.75 (+) 8.229 18.626 13.88 0.051 3 decimal places Decimalsare a shorthand way to write fractions and Temperature. (+)90.99 therefore each piece is of length $\frac{5}{24}$ cm long is each piece. Question 8. Then nd the total. Question 66. 8 11.215 The remaining length of ribbon = 25.00 8.13= 16.87. First we calculate [(14 12) 23] = (14 -12) X (2 X 2 X 2), 1.46 by the degree of difficulty of the dive. Question 20. 1.0 9 X 0.1 = 0.9 Explanation: 0.24 Question 3. 2 Question 3. beverages, with their prices. 0 also as (1 X 14 + 3 by 14), 1$\frac{3}{14}$. = $\frac{66}{5}$ or 13$\frac{1}{5}$. -5.046 in the simplest form as $\frac{3}{24}$. Given expressions as 6.66 0.74 , 66.6 7.4, now power of 10 as 103. +17.009 So x X $\frac{2}{3}$ = $1500, on simplification 2x = 1500 X 3 = 4500, 4 times as 5 X 5 X 5 X 5 = 625. We write 4$\frac{1}{2}$ as (4 X 2 + 1 by 2) = $\frac{9}{2}$ Question 52. So $\frac{2}{5}$ X $\frac{25}{4}$ = Explanation: 002.4003 decimal places Reasonable 45.36 45, Explanation: (+)7.423 Write 1.8 6 as a multiplication problem with a missing factor. 323 X 3.28 = 1059.44 +3.75 30.070 now we multiply $\frac{5}{2}$ X $\frac{39}{5}$, Question 3. 9.41 Step II: We multiply the denominators as 10 X 10 =100 54 people, 36% portion of the people own a dog and a cat. 8.1310 0000000 we can further simplify as both goes in 15, 15 X 16 = 240 and 15 X 1 = 15, (16,1), Given expressions as (3$\frac{1}{3}$ $\frac{5}{6}$) + 19.6 7 X 9 = 25.2. as we know for 1 bowl it is $\frac{7}{8}$ of a pint to glaze, 2 $\frac{1}{6}$ as 2 X 6 + 1 by 6 = $\frac{13}{6}$ and 4 $\frac{2}{5}$ as 4 X 5 + 2 by 5 = $\frac{22}{5}$ Now we multiply We have 4 deciml places so 0.12 X 0.24 = 0.0288. We write reciprocal and multiply as $\frac{5}{2}$ X 36.6900 This entails transposing a number such that 5.448 here the first number 57 is called the dividend b. 0.0132)95.04 0.0132 X 700 = 95.04 Explanation: It is very tough to clear all the math exams without proper preparation. Multiply. 0.07)32.2 0.07 X 460 = 32.2 Explanation: 4.8 1 decimal place 13)37.7 13 X 2 = 26 How many times greater is the increase? and so on, therefore 0.04, 0.02, 0.01, 0.005, . Question 49. and recyclables collected in pounds is less 0.062decimal places 0.984 12.3 we can further simplify as both goes in 5, 5 X 1 = 5 and 5 X 24 = 120, (1,24), Therefore $\frac{2}{9}$ $\frac{2}{3}$ = $\frac{1}{3}$. multiply $\frac{4}{21}$ as $\frac{1}{2}$ X $\frac{4}{21}$ = Explanation: $\frac{25 X 14}{7 X 3}$ = $\frac{350}{21}$, as both goes $\frac{5}{8}$ X $\frac{1}{2}$ = $\frac{5}{16}$. 3 Question 30. MODELING REAL LIFE for United States it will be 52.9725 seconds, 2 Question 33. Due to its uniqueness for every positive integer, the prime factorization provides a foundation for elementary number theory. Step I: We multiply the numerators as 4 X 2 = 8 = 21.84, Given expressions as 10 $\frac{5}{12}$, we write reciprocal because 15 X 0.1 = 1.5, Question 4. 80 = 10 X length, So length = 80 10 = 8, (8 X 10 = 80), PRECISION 8 X $\frac{5}{2}$ = $\frac{8 X5}{1 X 2}$ = We subtract each digit according to their place unit values. 1$\frac{3}{5}$) = $\frac{19}{4}$ = 4$\frac{3}{4}$. How many steps can you make? Given expression 9.475 X 8.03 we add as = $\frac{117}{5}$ = 23$\frac{2}{5}$, 1$\frac{3}{10}$ X 18 = $\frac{117}{5}$ = 23$\frac{2}{5}$. $\frac{6}{8}$ now we subtract as $\frac{7}{2}$ therefore approximately I need to wait 9 weeks. 129300 When the simplied fraction has a 1 in the numerator, First we write mixed fraction into fraction 9$\frac{1}{6}$ as 6.105 than 3000 pounds. 1,1,1 But sometimes, A. Question 6. Given to find the number which is prime factor of 572, Check your answer. similar to whole part we do multiplication Therefore, 0.52 0.0013 = 400. Factors of 72 : 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72, Given expressions as 8$\frac{1}{3}$ $\frac{2}{3}$, b. By counting the blocks in the area model found Example : If we have numerator as 1 in the simplified fraction like 1,1 0.55 X 60 = 33 miles per hour. First we calculate 6.85 X 2 as Given $\frac{3}{8}$ $\frac{3}{4}$ we write reciprocal of the fraction $\frac{3}{4}$ as $\frac{4}{3}$ and multiply as $\frac{3}{8}$ X Therefore 5$\frac{5}{8}$ 3 = 1$\frac{7}{8}$. Question 6. 4.87 7.23 = 35.2101. Step II: We multiply the denominators as 7 X 7 = 49 do you have left? 1, 0.6, 0.36, 0.216, 0.1296, 0.07776, 0.046656 . the reciprocal of the number as $\frac{1}{10}$ and multiply as $\frac{2}{3}$ X $\frac{1}{10}$ Step I: We multiply the numerators as 2 X 1 = 2 Question 54. $\frac{6 X 2}{1 X 3}$ =$\frac{12}{3}$ = 4, The table shows the portions of a family budget that are spent on several expenses. +11.81 Opposites sides are equal. (the numbers on the bottom). numerator is greater we write as (12 X 24 + 13 by 24) = 34930 that is represented by the model is $\frac{4}{5}$ X $\frac{1}{3}$ = $\frac{4}{15}$. Step 6 : The purple area came through overlapping which is the product as 0.459 7.442 first we write mixed number 3$\frac{3}{4}$ as 3 X 4 + 3 by 4 = $\frac{15}{4}$ now we multiply $\frac{15}{2}$ X $\frac{2}{5}$, Question 20. 0028425 When is the reciprocal of a fraction a whole number? So the LCM of 2,5,7 is 70. Explanation: The volume of the rectangular prism is 240 yd3. Given expression as 6$\frac{1}{2}$ ($\frac{7}{8}$ 5$\frac{11}{16}$), First we write mixed fraction into fraction as 5$\frac{11}{16}$ = 33.6 gallons of water is in the tank when it is $\frac{1}{2}$ full. Step II: We multiply the denominators as 10 X 10 =100 1 0.629[81 (10 2.7)] = 1.887, Explanation: $\frac{3}{7}$ 1 = $\frac{3}{7}$ 4 X 3$\frac{7}{10}$ = 14$\frac{8}{10}$ 12$\frac{7}{10}$, No friend is incorrect. 11.7 13 X 0.9 = 11.7 So, $\frac{7059}{301}$ = 23$\frac{136}{301}$ which matches with H. Question 8. 1.36 248 X 0.005 = 1.24 we write mixed fraction as ( 2 X 7 + 6 by 7) = $\frac{20}{7}$, $\frac{9}{4}$ now we write reciprocal of the fraction Therefore, 38.79 9 = 4.31. a. Explanation: 0.009)2.16 0.009 X 240 = 2.16 numerator is greater and 12 X 109 = 1308 2 to the power of 4 means we multiply 2 by Step II: We multiply the denominators as 7 X 8 = 56 Given expression as $\frac{4}{7}$ $\frac{13}{28}$, Question 37. X7.5-1 decimal place We write reciprocal and multiply as $\frac{3}{2}$ X that are greater than one that are multiplied together end up 7.52(6.084 5.44) perimeter of the frame, not on the material used. iii. 11.15 One way is to list the multiples of each number, then choose the common multiples, Explanation: I can make 5 steps and $\frac{35}{41}$-inch piece Question 6. Self-Assessment for Problem Solving Complete each multiplication expression so that it has the same value as the division expression above it. first we evaluate 62 = 6 X 6 = 36, then 0.28 Given expression as $\frac{3}{7}$ X $\frac{1}{4}$ 2$\frac{1}{2}$ 3$\frac{1}{2}$ $11067.5. 2. we further simplify as both goes in 2, 2 X 6 = 12, 2 X 5 = 10,(6,5), Factors of 50 : 1, 2, 5,10, 25, and 50, 0.030 4 X 0.007 = 0.028 d. $\frac{5}{4}$ $\frac{3}{2}$ we write reciprocal of the fraction $\frac{3}{2}$ as $\frac{2}{3}$ and multiply as $\frac{5}{4}$ X and friend costs are $15.10, and for 4 friends it is Question 2. 111.2875 First part is $\frac{2}{5}$ and second part is $\frac{2}{3}$ f. Gran Torre Santiago is 300 meters, Now in feet is b. 8$\frac{3}{4}$ 2$\frac{1}{2}$, First we write Explanation : 11.59 multiplying mixed numbers: 1, Step I: We multiply the numerators as 5 X 10 = 50 (+)3.209 Question 19. a. 10 X 14 = 140 square feet, First we write mixed fraction into fraction 7$\frac{1}{5}$ as Therefore, 0.007 X 0.03 = 0.00021. first we write mixed numbers 2$\frac{5}{12}$ as 12 X 2 + 5 by 12 = $\frac{29}{12}$ and 2$\frac{2}{3}$ as 3 X 2 + 2 by 3 = $\frac{8}{3}$ Given vehicles must weigh no more than 10.75 tons to cross a bridge. $\frac{3 X 4}{7}$ = $\frac{12}{7}$ 4)2.44 is the one which is incorrect. Given I make 30 equal payments for the go-kart. If we see the area model the purple color blocks show The LCM of 2,5,7 is 70. Given expression as 1$\frac{1}{15}$ X 5$\frac{2}{5}$ X 4$\frac{7}{12}$,first we write mixed numbers 1$\frac{1}{15}$ as 1 X 15 + 1 by 15 = $\frac{16}{15}$, 5$\frac{2}{5}$ as 5 X 5 + 2 by 5 = $\frac{27}{5}$, Explanation: Explanation: I. Explanation: Your friend nds the quotient. 0.216 Therefore (1$\frac{1}{2}$ $\frac{1}{6}$) as $\frac{3}{8}$ and multiply as $\frac{32}{3}$ X costs $0.85, So number of snacks I did buyed is $\frac{36}{12}$ as both goes in 12, 12 X 3 = 36, Evaluating the expression to solve the problem, Given a cyclist is 7$\frac{3}{4}$ kilometers from the nish line of a race, 6.3 1 decimal place (-)11.7300 X 0.51 decimal place So I spent 4 hours for riding waterslides. From 600 we can make 600 38 = Explanation: Question 29. 0.5 Question 42. and 1$\frac{1}{6}$ mixed fraction as (1 X 6 + 1 by 6)= $\frac{7}{6}$. = $\frac{125}{7}$ = 17$\frac{6}{7}$. The statement is 3 X $\frac{1}{3}$ = 1. iii. 27.900 f. How many three and one-halves are in two and one-half? Question 15. = $\frac{2}{3}$ Explanation: 2 X 8 = 16, Now 82 16 = (8X 8) 16 = 64 16 = 4 (16 x 4 =64), first we calculate $\frac{3}{8}$ 9,now we write 9 reciprocal and multiply as $\frac{3}{8}$ X $\frac{1}{9}$ = $\frac{3 X 1}{8 X 9}$ =$\frac{3}{72}$ we can simplify as both goes in 3, in 10, 10 X 450 = 4500, 10 X 8 = 80, (450 , 8) = $\frac{450}{8}$ 1740 A platinum nugget weighs 3$\frac{1}{2}$ ounces. X 9 4)37.72 4 X 9 = 36 0.99 Write the answer in simplest form. 8.3)6.64 8.3 X 0.8 = 6.64 = $\frac{1}{20}$, 3999 129 is greater. 2. 6.85 2 10 = 137. $\frac{2}{10}$, So,$\frac{16}{100}$ = $\frac{6 X 2}{10 X 10}$. $125.75 15 = X 4 and the second number 12 is called the divisor. = 6.9 + (10 1.467) -0.3, 6.980 Explanation: 0.95)11.6 0.95 X 12 = 11.4 The multiplication expression of whole part is shelf 1-22, shelf 2- 22, shelf 3-19, shelf 4-0, shelf 5 -0 books. so $\frac{26}{9}$= 2$\frac{8}{9}$. We subtract each digit according to their place unit values. Therefore, the average amount of money earned by each theater is 9$\frac{1}{2}$ X 8$\frac{3}{4}$ X 7$\frac{5}{6}$ = 651$\frac{7}{48}$ Given expressions as $\frac{14}{27}$ 7, Explanation: We write the reciprocal of a number, rst write the number as a fraction. $\frac{1}{2}$, $\frac{5}{2}$ + $\frac{1}{2}$ as 23)391 23 X 1 = 23 Step III: We write the fraction in the simplest form as b. Opposite sides are parallel. NUMBER SENSE Given expression as $\frac{3}{14}$ X $\frac{2}{5}$ We have collected information of data 0.008 14.008 9.433 (1 X 4 + 3 by 4) = 1$\frac{3}{4}$, Therefore $\frac{5}{6}$ So, 0.629[81 (10 2.7)] = 1.887, Question 66. To multiply fractions : Question 33. we can further simplify as both goes in 15, 15 X 11 = 165 and 15 X 10 = 150, as both have same 24 denominators now we can subtract $\frac{1 X 15}{60 X 1}$ = $\frac{15}{60}$ Question 9. Explanation: c. $\frac{1}{4}$ portion of the automobile 7)43.4 7 X 6 = 42 So in 5 gallons we have 5 X 128 = 640 fluid ounces water Step I: We multiply the numerators as 7 X 27 = 189 as 99 is less than 110 miles no, I cannot make it to destination, = $\frac{33}{16}$ = 2$\frac{1}{16}$. 2,4 $\frac{3 X 5}{1 X 6}$ = $\frac{15}{6}$,as both goes in 3, Estimation is reasonable. Therefore, 12.501 4.63 = 2.7. 5$\frac{5}{7}$ 1$\frac{3}{5}$X 4$\frac{2}{3}$ = Step III: We write the fraction in the simplest form as $\frac{3}{28}$, e. How many one and one-fths are in ve? Now we multiply 0.9 with 166.870 as How many U.S dollars do you receive? Given I have 3.4 gigabytes available on my tablet. 2.686 13.43 X 0.2 = 2.686 to calculate greatest possible product as and its perimeter is 289.76 meters. 5 X $\frac{5}{4}$, Step I: We multiply the numerators as 5 X 5 = 25 3.2 X 2.975 = 9.52 square feet, ii. How many three-fourths are in three? -34.5714 write as reciprocal and multiply $\frac{7}{4}$ as Question 26. Explanation: YOU BE THE TEACHER Given length as 10 yd, width as 8 yd and height as 3 yd, Part A : Step I: We multiply the numerators as 1 X 2 = 2 We have total attendance at the food festival from to being correct. 6)0.498 6 X 0.08 = 0.48 (4 X 7 + 4 by 7) = $\frac{32}{7}$, Now $\frac{4}{7}$ we PRECISION 1.5 3 X 0.5 = 1.5 Question 67. How many books are on each shelf of the How many bowls can you completely glaze? b. b. (1,20)=$\frac{1}{20}$. 8 X 5 = 40, (9,5) = $\frac{9}{5}$, now we multiply $\frac{1}{6}$ of the bottle. Explanation: 0 as (1 X 5 + 3 by 5) = $\frac{8}{5}$ now we write reciprocal of the fraction Explanation: I walk $\frac{7}{8}$ of the path, How far did I walk? X5.9 1 decimal place = 4 now we write $\frac{3}{4}$ as reciprocal and 45.9848 -4 decimal places Question 71. a. Now 3.76 X 12.23 = $\frac{55}{8}$ X $\frac{1}{30}$ = $\frac{55 X 1}{8 X 30}$ = 0.36 X 0.6 = 0.216, Given expressions as $\frac{5}{6}$ $\frac{2}{7}$, 0.020 0.6 X 0.03 = 0.018 Squares, Rectangles , Trapezoids and Rhombuses. A. [3 X (8-5)] = 3 X 3 = 9 23 0.6)0.8 0.6 X 1 = 75.825 number of decimal places multiplied by powers. We get a whole number. Given to find two fractions whose quotient is $\frac{28}{45}$, So $\frac{2}{3}$ X $\frac{3}{4}$ = $\frac{6}{12}$, $\frac{1}{2}$ X $\frac{2}{3}$ = $\frac{2}{6}$, Explanation: A + B = 1.1 and B A = 0.5 Your friends camera can take 36 pictures in 4.5 seconds. 10.260 1,1 Explanation: 0 $\frac{4 X 7}{9 X 5}$ = $\frac{28}{45}$, $\frac{2}{5}$,therefore $\frac{6}{5}$ 3 = $\frac{2}{5}$. Explanation: that there is no glaze left over? as $\frac{3}{1}$ and multiply as $\frac{11}{3}$ X Explanation: 19 We write 6$\frac{7}{8}$ as (6 X 8 + 7 by 8) = $\frac{55}{8}$, so 24 minutes for each pound, Now we multiply minutes by pounds So $\frac{1}{2}$ X $\frac{3}{5}$ X $\frac{4}{9}$ = $\frac{2}{15}$. Given 3$\frac{3}{4}$ X $\frac{2}{5}$ so Explanation: Answer the question using a model. Step II: We multiply the denominators as 6 X 3 =18 05.611 We subtract each digit according to their place unit values. Is there enough food to last 3 weeks? Explanation: Explanation: $0.109, so on comparing $0.109< $0.133 jar is the better buy. 1.1575 4.63 X 0.25 = 1.1575 PROBLEM SOLVING 2.02 spent $\frac{1}{5}$ of that time writing a blog. $\frac{6}{7}$ 4 as the number 4 is whole number we convert $\frac{169}{26}$ $\frac{4}{26}$as denominators are same we Therefore $\frac{3}{4}$ 2$\frac{1}{2}$ = $\frac{3}{10}$. 0.12 X 3 16.1)35.903 16.1 X 2 = 32.2 d. Perimeter will be 2 times more in large rectangle and How many total points do the three players score? Given expression as 4.32(3.7 + 1.65), first we calculate now we will find height in feet as Question 13. 3 X 7 X $\frac{7}{3}$ = $\frac{3 X 7 X 7}{3}$ = $\frac{147}{3}$, A day-care center is building a new outdoor play area. 4)6.224 4 X 1 = 4 now we write as reciprocal and multiply $\frac{25}{3}$ X $\frac{3}{2}$ = Explanation: 32 + 6 X 5 3 is equivalent to a perfect square. we write mixed fraction as ( 5 X 8 + 5 by 8) = $\frac{45}{8}$, 20.35) = 150.183. 31.5 1 decimal place food than for recreation is $\frac{4}{9}$ $\frac{1}{40}$ = $\frac{11}{2}$ or 5$\frac{1}{2}$ Question 69. divided by 2 as 0.04 2 = 0.02, Draw a model to justify your answer. Let us take the amount be x and a band earns $\frac{2}{3}$ of their prot from selling concert tickets and makes a prot of $1500 from selling concert tickets, Area of the banner is 7 square feet Explanation: (23,18)=$\frac{23}{18}$ as numerator is greater therefore 34.995 meters fencing is needed to enclose the play area. You are saving money to buy a new bicycle that costs $155.75. $\frac{35}{4}$ X $\frac{2}{5}$= $\frac{35 X 2}{4 X 5}$= $\frac{70}{20}$ as both goes in 10 as 10 X 7 = 70, 10 X 2= 20,(7, 2), MULTIPLYING DECIMALS AND WHOLE NUMBERS Therefore (7.12 8.22) 100 = 5852.64. 15,13 Step I: We multiply the numerators as 7 X 23 = 161 6 bowls I can completely glaze, 10 plates I can completely glaze, Explanation: 13.061 +549000 0.0000726 decimal places we know 1.8 6 = 0.3 means , So 1.8 = 6 X 0.3, Concepts, Skills, & Problem Solving $\frac{9 X 4}{2 X 3}$ = $\frac{36}{6}$ Given expression as 82 [(14 12) 23] DIVIDING DECIMALS BY WHOLE NUMBERS Question 49. $\frac{1}{3}$ = $\frac{6 X 1}{5 X 3}$ = $\frac{6}{15}$, therefore the distance from the start to the rst checkpoint is 4 miles. Find both answers. The nugget worth is $1085.516. Given expression as 44.2 3.25 = = $\frac{2}{10}$ or $\frac{16}{100}$ $\frac{8}{10}$ = 95.04 0.0132 = 7,200. 12.29 6.15 Question 32. Your friend rewrites the problem. 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