MTAP DepEd Saturday Mathematics Program Grade 5 Session 4

I. A The first part of the session is on decimals. Stress that decimals are just another way of writing a fraction with a power of 10 as denominator. That is the reason why 0.3 and 3/10 or 0.23 and 23/100 are read in the same way. The number of zeros in the power of 10 determines the number of decimal places. This can be a whole class work one pupil after another going to the board to write one.

B. Expand the place value chart that they had in S1. Explain that for decimals, the place values are tenths, hundredths, thousandths, etc. in the opposite direction to those of whole numbers. The “decimal point: is read as “and”.

C-D. Explain that operations on decimals is exactly like that for whole numbers except for the placing of the decimal point. Go back to fractions to except for the placing of the decimal point. In addition and subtraction, there is no change in the number of decimal places since when we add 23/100 + 45/100, we get 68/100. So, 0.23 + 0.45 = 0.68. 0.67 – 0.23 = 0.44.

E-F. Since 2/10 x 21/100 = 42/1000, 0.2 x 0.21 = 0.042. The number of decimal places in the factors. Thus, in #1, there are 3 decimal places. For a few of the of the numbers, ask the pupils to show on the board the reason behind the number of decimal places. 5. 2.406 x 0.077 = 2 406/1000 x 77/1000. So, there will be 6 decimal places in the product.

G. For division, since we know how to divide by whole numbers, we change the divisor to a whole number by multiplying both dividend and divisor by a power of 10 that will make the divisor a whole number. We know that multiplying 5 by n/n = 1 does not change since we get 5n/n and the n can be cancelled.

H. Analyze by asking questions leading to an understanding of the problem.

1. a. How many hours a day does Greg work.b. How many hours does it take him to finish a piece of work.c. If he wants to finish in 12 days instead of 16 days, how many hours a day must he work?

Answer: (16 x 8)/12 = 32/3 or 10 2/3 hours a day.

2. 5.4 ha is 0.3 of his land. So, originally, he had 5.4/0.3 = 18 ha.

3. He sold 0.2 x 180 = 36 to a friend and 0.9 x (180 – 36) 130 (round up). 14 remained for his family.

4. 150/2.8 = 53.57. So, 53 pieces each 2.8 dm long can be cut from 15m

5. The average speed is 7.5/2/3 = 11 ¼ km/h.

6. It takes the salesman 48 min or 4/5 h to reach the place. His average speed is 40/0.8 = 50 km/h.

II A. Explain that a ratio is the comparison of two things of the same kind and in the same unit by division. This is the reason why a ratio has no unit. Thus, 12cm:6 cm = 2:1. When what are compared are not of the same kind, usually we use the term “rate”. Thus, a clerk encodes at the “rate” of 90 words a minute.

B. Explain the principle “The product of the means equals the product of the extremes. “However, if they can easily see how one number is obtained as in 3:4 = 9:N, since 9 = 3x 3, then N = 3 x 4 = 12.

C. 1. Rice:sugar = 125:45 = 55:9; rice:corn = 125:60 = 55:12

2. a. 3:5 = 21: N.N = 35 b. 3:5 = 27:N, N = 45

3. Let n be the GCF used to reduce the ratio to lowest terms. Thus, the sales of one boy is 3n and the others is 5n. 3n + 5n = 8n = 376, n = 376/8 = 47. One boy sold 3 x 47 = 141 and the other sold 5 x 47 = 235 newspapers. Do b and c in the same way.

4. The cost of 25 cavans of rice was 25 x 11,600/8 = 25 x 1450 = P 36,350.

5. a. right:wrong = 40:10 = 4:1b. for every wrong answer, there were 4 correct answers.

6. Let n be the GCF used in reducing the ratio to lowest terms. Then the age of the son is 2n and that of the father is 7n. So, 2n+7n = 9n = 45, n = 5. The son is 2x5 = 10 years old and the father is 7 x 5 = 35 years old.

Challenge!!!

1. (5+5)/(7+5) = 10/12 = 5/6. 5/6 – 5/7 = 35/42 – 30/42 = 5/42. The fraction increased by 5/42.

2. 1/3 of P 1,2000,000 = P 400,000. If one brother owned Pn of the P 400,000, the other owned (3/7)n. 10n/7 = 400,000. N = P 280,000. The amount owned by one brother and the other owned (3/7) (280,000) = P 120,000 of the value of the store.

3. The cement is 2/9 of the mixture. In 10 cubic meters of the mixture, the amount of cement is (2/9) (10) = 20/9 or 2 2/9 m3

4. If the ratio is 3:5 and the difference between the two numbers is 38, then since 5 – 3 = 2, one unit of ratio is equivalent to 38/2 = 19. The smaller number is 3 x 19 = 57 and the bigger is 5 x 19 = 95.

5. Make the pupils try not only 3, 4, 6, 7 but other numbers. Ask them to try to find any set of 4 numbers for which the difference will never become the same. They could also find a set for which fewest number of subtraction is possible. For 5, 8, 7, 3, there are 3 subtractions before the differences were the same.

6. The number is the LCM(4, 6, 7) + 3 which is 87 which is greater than 60 but less than 100.

7. If 4 mynahs ate 300 g of grains in 5 days, 1 mynah ate 300/(4x5) = 15 g of grain in one day, 1 canary ate 300/12 = 25g in one day and 1 parrots ate 300/10 = 30 g in one day. The parrots are the greatest eater.

MTAP DepEd Saturday Mathematics Program Grade 5 Session 4

I. A. Write each fraction or mixed number as a decimal.

1. 78/100 = __________ 2. 6 5/10 = __________ 3. 17 624/1000 = _________4. 5 9/100 = _________ 5. 874/1000 = ________ 6. 23 235/10 000 = ________7. 693/1000 = ________ 8. 75 62/100 = ________ 9. 65 275/1000 = __________

B. a. Read each number b. Give the place value and c. Give the value of the underlined digit.

1.) 42.72 2.) 7.4557 3.) 9.1375 4.) 0.684 5.) 7.85 6.) 5.79287.) 5.204 8.) 50.8735 9.) 3.783 10.) 8.065 11.) 7.8394 12.) 81.479

C. Add: 1.) 5.74 2.) 3.67 3.) 7.85 4.) 9.84 5.) 26.8 1.47 2.18 1.52 5.7 9.15

D. Subtract: 1.) 9.84 2.) 1.564 3.) 8.92 4.) 9.5 5) 8.643 3.52 0.228 3.68 2.167 2.075

E. Multiply: 1.) 5.23 2.) 6.15 3.) 4.32 4.) 3.06 5.) 7.48 x 2.5 x 60 x .35 x 4.6 x 6.6

F. How many decimal places are there in the product of each of the following? Do not multiply. Give reasons for your answer.

1.) 45.5 x 0.46 2.) 23.08 x 0.295 3.) 23.5 x 6.035 4.) 62.03 x 6.88

5.) 2.406 x 0.077 6.) 5.75 x 2.57 7.) 82.4 x 3.0256 8.) 9.618 x 56.8

G. Divide: 1.) 2.5 / 90.75 2.) 0.8 / 54.72 3.) 0.023 / 0.14375

H. Analyze and then solve each problem.

1.) Greg working 8 hours a day can finish a piece of work in 16 days. How many hours per day must he work to complete it in 12 days?

2.) A man sold 0.7 of his land, and then he had 5.4 hectares left. How much land had he at first?

3.) A farmer had 180 chickens. He sold 0.2 of them to a friend, and 0.9 of the remainder to a supermarket. The rest he kept for his family. How many chickens remained for his family?

4.) How many pieces of ribbon each 2.8 dm long can be cut from a spool of ribbon 15 m long?

5.) Joy bicycles 7.5 km in 40 minutes: find her average in km per hour.

6.) A salesman leaves his house at 8:15 a.m. and reaches a town 40 km away at 9:03 a.m. Find his average speed in km per hour.

7.) The perimeter of a triangle is 18 cm and the lengths of two of its sides are 5.47 and 6.68 cm. Find the length of the third side.

II. A. Find the ratio of:

1.) 12 cm to 6 dm 4.) 350 gm to kg 7.) 45 days to 10 wk2.) 750 m to 1.25 km 5.) 21 boys to 28 girls 8.) 48 min to 2 2/5 hr3.) 45 cm to 7.5 dm 6.) 15 days to 3 wk 9.) 750 gm to 1.75 kg

B. Find N in each of the following:

1.) 3:4 = 9:N 2.) 5:6 = 20:N 3.) 5:N = 30:42 4.) N:15 = 5:3

5.) N:25 = 3:5 6.) 7:4 = N:16 7.) 7:N = 21:36 8.) 3:8 = N:56

C. Analyze each problem and then solve it.

1.) Daily, a store sells 125 kg of rice, 45 kg of sugar and 60 kg of ground corn. Find the ratio of the rice to sugar sold daily; the ratio of rice to corn; the ratio of corn to sugar.

2.) Two numbers are in the ratio of 3:5. What is the larger number if the smaller number:

a.) 21 b.) 27 c.) 54 d.) 90 e.) 69?

3.) The daily sales of two newspaper boys are in the ratio of 3:5. Find the daily sales of each of the boys if together they sell.

a.) 376 b.) 416 c.) 328

4.) If a farmer sold 8 cavans of rice for P 11,600 how much would he get for 25 cavans?

5.) A student did 40 out of 50 problems correctly.

a.) What is the ratio of the number right to the number wrong?b.) For every wrong answer, how many were right?

6.) The ratio of a father’s age to his son’s age is 7:2. If the sum their ages is 45, how old is the father?

Challenge!!!

1.) If 5 is added to the numerator and denominator of the fraction 5/7, will the value increase or decrease? By how much?

2.) Two brothers together owned 1/3 of a store valued at P 1,200,000. One brother owned 3/7 as much as the other. What is the value of each brother’s share?

3.) If the ratio of cement, sand and crushed stone for making the concrete needed for a sidewalk is 2:3:4, how many cubic meters of cement is needed to make 10 cubic meters of concrete?

4.) Two numbers are in the ratio 3:5 and their difference is 38. Find the two numbers.

5.) Choose any four numbers like 5, 8, 7, 3. Arrange them in any order around a circle as shown. Subtract each number from any larger number next to it. Place the answer on a bigger circle. Repeat until all the numbers are the same. Complete the given until the same differences are obtained. Try 3, 4, 6, 7.

6.) I am a number between 60 and 100. If you divide me by 4, 6 or 7, I will always have a remainder of 3. What number am I?

7.) A pet shop kept 3 different breeds of birds. The shop owner kept a record of the food the birds ate as follows: 4 mynahs ate 300 g of grains in 5 days, 3 canaries ate 300 g of grains in 4 days and 5 parrots ate 300 g in 2 days. Which breed of bird is the greatest eater?