b) Multiply 1.45 by 3.5. First, estimate the value of 1.45 × 3.5. 1.45 × 3.5 ≈ 1 × 4 =4 The product should be about 4. 1 2 3 22 11 11 22 22 1.4 5 × 3.5 1.4 5 1 . 4 5 ← 2 decimal places × 3.5 × 3 . 5 ← 1 decimal place 725 725 725 4350 4350 5 . 0 7 5 ← 3 decimal places SCHOLASTIC Since the product is about 4, align the decimal points correctly so that the answer is 5.075, which is close to the estimate. When we multiply two decimals, the number of decimal places in the product is equal to the total number of decimal places in both decimals. Practices20 1. Multiply. a) 0.2 × 0.9 = × b) 0.7 × 0.05 = × == == © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4 43
2. Multiply. a) 0.4 × 0.7 b) 0.8 × 0.03 3. Estimate and then multiply. Multiply Estimate 5.2 SCHOLASTIC 5.2 × 0.8 ≈× × 0.8 = Multiply 4. Estimate and then multiply. 1.6 Estimate × 0.7 a) 1.6 × 0.7 ≈ × = 12.7 × 9.3 b) 12.7 × 9.3 ≈ × = 3.2 9 × 4.6 c) 3.29 × 4.6 ≈ × = 72.0 5 × 5.8 d) 72.05 × 5.8 ≈ × = 44 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4
5. Multiply. b) 3.2 × 8.4 a) 4.1 × 0.9 d) 3.57 × 4.4 f) 83.05 × 6.8 c) 22.8 × 7.3 e) 60.78 × 0.5 SCHOLASTIC Solving word problems Learn 1 3 Jake can run 8.6 kilometers every hour. How far can he run in 2.5 hours? 8.6 × 2.5 8.6 × 2.5 = 21.5 He can run 21.5 kilometers in 2.5 hours. 430 17 2 0 8.6 × 2.5 ≈ 9 × 3 = 27 21.5 0 My answer is close to 27. So, it is reasonable. © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4 45
Practices21 Solve the word problems. Show your work clearly. 1. A rectangular plot of land measures 9.55 kilometers by 4.6 kilometers. What is the area of the plot of land? 9.55 × 4.6 = 9.5 5 × 4.6 SCHOLASTIC 2. Kylie bought a rectangular piece of wrapping paper measuring 0.85 meter by 3.7 meters. What was the area of the wrapping paper? 3. There are 20.98 liters of water in Tank A. Tank B contains 5.4 times as much water as Tank A. What is the volume of water in Tank B? Round the volume to the nearest liter. 46 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4
Lesson 8 Conversion of Measurements Learning Outcomes: • Convert a measurement from a larger unit to a smaller unit or compound units • Convert a measurement from a smaller unit or compound units to a larger unit Converting a measurement from a larger unit to a smaller unit Learn Express 4.25 kilograms in grams. SCHOLASTIC Method 1 4.25 kg = 4 kg + 0.25 kg 0.25 kg = 0.25 of 1 kg = 4000 g + 250 g = 0.25 × 1000 g = 4250 g = 250 g Method 2 1 kg = 1000 g 4.25 kg = 4.25 × 1000 g = 4250 g Converting a measurement from a larger unit to compound units Learn Express 3.5 meters in meters and centimeters. 3.5 m = 3 m + 0.5 m 0.5 m = 0.5 of 1 m = 3 m 50 cm = 0.5 × 100 cm = 50 cm © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4 47
Practices22 Find the equivalent measures. 1. a) 0.6 km = 0.6 × m b) 2.4 L = 2 L + L ml = m = 2 L + ml = 2 L 2. a) 0.05 m = cm b) 0.4 L = ml c) 3.2 kg =SCHOLASTIC g d) 7.06 km = m e) 4.275 km = __________ m f) 5.008 kg = __________ g 3. a) 4.7 kg = kg g b) 2.5 km = km m c) 6.08 m = m cm d) 3.02 km = km m e) 5.087 L = L ml f) 9.001 kg = kg g 48 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4
Converting a measurement from a smaller unit to a larger unit Learn Express 2090 milliliters in liters. Method 1 90 ml = (90 ÷1000) L = 0.09 L 2090 ml = 2000 ml + 90 ml = 2 L + 0.09 L = 2.09 L Method 2 2090 ml = (2090 ÷ 1000) L = 2.09 L SCHOLASTIC 1 L = 1000 ml Practices23 Find the equivalent measures. 1. a) 260 ml = 200 ml + 60 ml b) 3090 g = (3090 ÷ ) kg L = = L+ kg = L 2. a) 2 ml = L b) 50 mm = cm c) 4035 m = km d) 7800 g = kg e) 3002 ml = L f) 6007 cm = m © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4 49
Converting a measurement from compound units to a larger unit Learn Express 4 kilometers 195 meters in kilometers. 4 km 195 m = 4 km + 195 m 195 m = (195 ÷ 1000) km = 0.195 km = 4 km + 0.195 km = 4.195 km Practices24 SCHOLASTIC Find the equivalent measures. 1. a) 3 m 25 cm = 3 m + 25 cm b) 6 kg 30 g = 6 kg + 30 g =3m+ m = 6 kg + kg = m = kg 2. a) 1 km 400 m = km b) 2 cm 9 mm = cm c) 4 L 850 ml = L d) 3 m 5 cm = m e) 6 km 95 m = km f) 5 kg 5 g = kg 50 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4
Lesson 9 Problem Solving Word problems Learn Mrs. Torres had some flour. She used the flour to make 19 cupcakes and had 100 grams of flour left. If she used 20.15 grams of flour for each cupcake, how much flour did Mrs. Torres have at first? 1 Understand Mrs. Torres made 19 cupcakes. the problem. She used 20.15 grams of flour for each cupcake. She had 100 grams of flour left. I need to find how much flour Mrs. Torres had at first. SCHOLASTIC 2 Plan First, I find the total amount of flour used in what to do. 19 cupcakes. Then, I add that amount to the amount she had left. 3 Work out the 19 × 20.15 = 382.85 Answer. The total amount of flour used in 19 cupcakes was 382.85 grams. 382.85 + 100 = 482.85 Mrs. Torres had 482.85 grams of flour at first. 4 Check 19 × 20.15 ≈ 20 × 20 if your answer = 400 is reasonable. 400 + 100 = 500 My answer is close to 500 grams. So, it is reasonable. 1. Understand 2. Plan 3. Answer 4. Check © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4 51
Practices25 Solve the word problems. Show your work clearly. 1. Understand 2. Plan 3. Answer 4. Check 1. Nicole had 48 meters of cloth. She used the cloth to make 23 curtains of length 1.85 meters each. What length of cloth did she have left? First, find the total length of cloth she used to make 23 curtains. SCHOLASTIC 2. The height of Mount Everest is 8.848 kilometers. The height of Mount Kilimanjaro is 2953 meters shorter than that of Mount Everest. Find their total height in kilometers. 52 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4
3. A farmer used 28 kilograms of fertilizer on his vegetable plantation. He used 12.55 kilograms of fertilizer on his tomato crop. Then, he used the remaining fertilizer on 3 similar-sized plots of land used to grow carrots. How much fertilizer did the farmer use on each of these plots of land? 4. Mr. Walter wants to paint a rectangular wall measuring 4.8 meters by 2.5 meters. The cost of painting each square meter of the wall is P460. If Mr. Walter has P5600, how much will he have left after paying for the painting of the entire wall? SCHOLASTIC © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4 53
Percent Lesson 1 Percent Learning Outcomes: • Read and interpret the percentage of a whole • Express fractions with denominator 100 or 10 as percents • Express decimals as percents and vice versa • Express percents as fractions in their simplest form • Express percents as ratios in their simplest form Understanding percent Learn a) There are 100 unit cubes in a hundred-square. 48 of the unit cubes are blue. 48 out of 100 unit cubes are blue. 48 percent of the unit cubes are blue. We write 48 percent as 48%. SCHOLASTIC b) The square is divided into 100 equal parts. 70 out of 100 parts are green. 70% of the whole is green. 30 out of 100 parts are white. 70 + 30 = 100 30% of the whole is white. 70% + 30% = 100% Expressing fractions as percents Learn 35 out of 100 equal parts are shaded. a) 35 of the whole is shaded. 100 35% of the whole is shaded. 35 = 35% 100 54 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4
b) 8 out of 10 equal parts are shaded. × 10 8 = 80 = 80% 10 100 × 10 80% of the whole is shaded. Practices1 1. Write each of the following as a percent. a) b) SCHOLASTIC 9 out of 100 90 out of 100 % % 2. Write each of the following as a percent. a) 18 out of 100 b) 60 out of 100 % % c) 1 out of 100 d) 100 out of 100 % % 3. Express each fraction as a percent. b) a) 72 = % 5 = 100 = % 100 10 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4 55
4. Express each fraction as a percent. a) 1 b) 6 100 100 c) 24 d) 30 100 100 e) 4 f) 10 10 10 5. Fill in the missing numerator or denominator.SCHOLASTIC a) 2% = 100 b) 83% = 100 c) 20% = 100 d) 60% = 100 e) 7% = 7 f) 95% = 95 Expressing decimals as percents Learn a) Express 0.45 as a percent. 0.45 = 45 = 45% Express the decimal 100 as a fraction with a denominator of 100 first. b) Express 0.1 as a percent. 0.1 = 1 = 10 = 10% 10 100 56 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4
Expressing percents as decimals Learn Express 67% as a decimal. 67% = 67 = 0.67 Express the percentage 100 as a fraction with a denominator of 100 first. Practices2 1. Express each decimal as a percent. a) 0.16 = 100 = % b) 0.3 = = = % SCHOLASTIC 2. Express each decimal as a percent. b) 0.75 a) 0.49 c) 0.03 d) 0.05 e) 0.2 f) 0.8 3. Express each percent as a decimal. a) 23% = 100 = b) 9% = 100 = 4. Express each percent as a decimal. b) 34% a) 48% c) 5% d) 7% e) 50% f) 70% © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4 57
Expressing percents as fractions Learn Express 60% as a fraction in its simplest form. 60% = 60 = 3 Write 60 in its simplest form. 100 5 100 SCHOLASTIC Practices3 1. Express each percent as a fraction in its simplest form. a) 30% = 100 = b) 42% = 100 = 2. Express each percent as a fraction in its simplest form. a) 10% b) 55% c) 60% d) 45% e) 6% f) 4% 58 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4
Expressing percents as ratios Learn Express 40% as a ratio in its simplest form. 40 40% is 40 out of 100. We 40 : 100 40% = 100 can write 40% or 40 as ÷ 20 ÷ 20 = 40 : 100 =2:5 100 2:5 the ratio 40 : 100. We then simplify this ratio. SCHOLASTIC Practices4 1. Express each percent as a ratio in its simplest form. a) 90% = 100 b) 75% = = : 100 = : = : : 10 = 2. Express each percent as a ratio in its simplest form. a) 70% b) 19% c) 50% d) 45% e) 64% f) 42% © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4 59
Lesson 2 Expressing Fractions as Percents Learning Outcomes: • Relate 1 whole to 100% • Express fractions as percents • Express a part of a whole as a percent • Solve word problems Relating 1 whole to 100% Learn 0 10% 20% 30% 40% 50% 60% 70% 80% 90%100% ← 10% + 90% = 100% ← 20% + 80% = 100% ← 30% + 70% = 100% ← 40% + 60% = 100% ← 50% + 50% = 100% ← 60% + 40% = 100% ← 70% + 30% = 100% ← 80% + 20% = 100% ← 90% + 10% = 100% 1 whole = 100% SCHOLASTIC Expressing fractions with denominators smaller than 100 as percents Learn Express 1 as a percent. 4 Method 1 60 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4
× 25 1 = 25 = 25% Express 1 as a fraction with 4 100 4 a denominator of 100 first. × 25 Method 2 14 = 1 × 100% 1 whole = 100% 4 1 1 = 25% 4 of 1 whole = 4 × 100% Expressing parts of a whole as percentsSCHOLASTIC Learn Express 8 out of 20 as a percent. Method 1 Method 2 ×5 280 = 8 8 out of 20 20 8 40 × 100% = 8 20 100 20 = = 40% = 40% ×5 Practices5 1. Express 3 as a percent. 5 Method 1 3 = 100 5 = % Method 2 3 = 3 × 100% 5 5 = % © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4 61
2. Express each fraction as a percent. a) 3 b) 6 4 12 c) 12 d) 18 20 25 e) 26 f) 60 40 75 3. Express 4 out of 25 as a percent. Method 1 SCHOLASTIC Method 2 245 = 100 245 = 4 × 100% = 25 % = % 4. Write each of the following as a percent. a) 1 out of 5 b) 3 out of 12 c) 12 out of 25 d) 45 out of 60 Solve the word problems. Show your work clearly. 5. Gabriel bought 16 pens. 12 of the pens were blue pens. What percentage of the pens were blue pens? 62 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4
6. There are 75 animals on a farm. 48 of them are sheep. What percentage of the animals are sheep? Expressing fractions with denominators greater than 100 as percents Learn Express 120 out of 200 as a percent. Method 1 SCHOLASTIC ÷2 120 = 60 = 60% Express 120 as a fraction with 200 100 200 a denominator of 100 first. ÷2 Method 2 120 = 120 × 100% 200 200 = 60% © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4 63
Practices6 1. Express 18 as a percent. 300 Method 1 Method 2 31080 = 100 31080 = 18 × 100% = 300 % = % 2. Write each of the following as a percent. a) 60 out of 400 b) 245 out of 700 SCHOLASTIC c) 135 out of 500 d) 560 out of 2000 Solve the word problems. Show your work clearly. 3. There were 200 pages in a book. Alan read 84 of the pages. What percentage of the book did Alan read? 64 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4
4. 600 runners took part in a charity race. 420 of the runners were women. What percentage of the runners were women? 5. Eileen bought 3000 grams of nuts. 540 grams of the nuts were cashew nuts. What percentage of the nuts were cashew nuts? SCHOLASTIC Solving 2-step word problems Learn 2 of the members of a fitness club are women. 5 a) What percentage of the members are women? b) What percentage of the members are men? a) 2 = 52 × 100% = 40% 5 40% of the members are women. b) 100% – 40% = 60% 60% of the members are men. © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4 65
Learn John won P250 in a contest. He donated P120 and saved the rest. What percentage of the money did he save? Method 1 120 = 120 × 100% = 48% First, find the percentage 250 250 John donated. Then, find the percentage he saved. John donated 48% of the money. 100% – 48% = 52% He saved 52% of the money. Method 2 SCHOLASTIC P250 – P120 = P130 First, find the amount of John saved P130. money John saved. Then, express it as a percentage. 130 130 250 = 250 × 100% = 52% He saved 52% of the money. Practices7 Solve the word problems. Show your work clearly. 1. 3 of the movies shown at a movie hall are in English. What percentage of 4 the movies are not in English? First, find the percentage of movies that are in English. Then, find the percentage of movies that are not in English. Another way is to find the fraction of movies that are not in English first. Then, express the fraction as a percentage. 66 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4
2. Rachel has 75 books. 18 of the books are comic books. The rest of the books are novels. a) What percentage of her books are comic books? b) What percentage of her books are novels? 3. There are 480 seats on an airplane. 120 of them are first class seats. The rest of the seats are economy class seats. What percentage of the seats are economy class seats? SCHOLASTIC © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4 67
Lesson 3 Percentage of a Quantity Learning Outcomes: • Identify the base, rate and percentage • Find the value of a percentage of a quantity • Solve word problems Identifying the base, rate and percentage Learn a) There are 45 apples in a box. 20% of the apples are rotten. How many apples are rotten? The base is the whole from which we are finding a percentage. Base = Total number of apples = 45 The rate is the percent of a whole (base). Rate = Percent of rotten apples = 20% The percentage is a part or amount in relation to a whole (base). We multiply the rate and the base to get the percentage. Percentage = Number of rotten apples = 20% of 45 = 12000 × 45 = 9 There are 9 rotten apples. SCHOLASTIC b) What is 35% of 200? The base is the total or whole, which is 200. The rate is the percent of the whole, which is 35%. Percentage = Rate × Base = 35% of 200 = 35 × 200 100 = 70 68 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4
Finding the value of a percentage of a quantity Learn a) Find the value of 40% of 300. 0 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 300 ? Method 1 Method 2 SCHOLASTIC 100% → 300 40% of 300 = 40% × 300 Base = 300 Rate = 40% 1% → 300 = 3 = 40 × 3 Percentage = 40% of 300 100 1100 = 120 300 40% → 40 × 3 = 120 = 120 b) Mr. Castillo bought a bag that cost P700. He had to pay 10% sales tax on top of the cost of the bag. How much was the sales tax? 0 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% P 700 ? Method 2 Method 1 10% of P700 = 10% × P700 7 100% → P700 = 10 × 1% → P 710000 = P7 1100 P 700 10% → 10 × P7 = P70 The sales tax was P70. = P70 The sales tax was P70. © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4 69
Practices8 1. Find the value of 65% of 800 grams. 65% of 800 g = 100 × g = g 2. Find the value of each of the following. a) 6% of 500 b) 70% of 950 c) 35% of 24 kgSCHOLASTIC d) 84% of 55 km Solve the word problems. Show your work clearly. 3. Mr. Reyes bought 240 meters of cloth. He used 45% of the cloth to make some shirts. How much cloth did he use to make shirts? 4. Lydia collected 875 milliliters of rainwater in a pail. She used 20% of the rainwater to water her plants. How much rainwater did she use to water her plants? 70 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4
Solving 2-step word problems Learn Amelia had P850. She spent 20% of the money on stationery, 32% on a book and the rest of the money on food. a) What percentage of the money was spent on food? b) How much did she spend on food? a) P 850 20% 32% ? 100% – 20% – 32% = 48% 48% of the money was spent on food. SCHOLASTIC b) P 850 20% 32% 48% ? 48% × P 850 = 48 × P 850 = P 408 50% of P850 = P425 100 48% is close to 50%. P408 is close to P425. She spent P408 on food. My answer is reasonable. Learn There are 600 students in a school. 15% of the students are Grade 5 students. How many students are not in Grade 5? 600 15% ? Method 1 Method 2 100% – 15% = 85% 15% × 600 = 15 × 600 = 90 100 85% of the students are not in Grade 5. 90 students are in Grade 5. 85 85% × 600 = 100 × 600 = 510 600 – 90 = 510 510 students are not in Grade 5. 510 students are not in Grade 5. 85% is close to 90%. 90% of 600 = 540 510 is close to 540. My answer is reasonable. © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4 71
Practices9 Solve the word problems. Show your work clearly. 1. There are 90 customers in a shop. 30% of them are men and the rest are women. How many women are there in the shop? First, find the percentage of women in the shop. Then, find the number of women in the shop. Another way is to find the number of men in the shop first. Then, find the number of women in the shop. 2. Lynn had P750. She spent 16% of the money on food and used 30% to pay for a drink. How much money did she have left? 3. A plot of farm land has an area of 1400 square meters. 63% of the land area is used to grow radishes and the rest to grow turnips. What is the area used to grow turnips? SCHOLASTIC 72 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4
Learn a) Mia deposits P3500 in a savings account with a bank. The bank pays her 2% interest each year. How much money will she have in the savings account after 1 year? 2% of P3500 = 2% × P3500 2% of P3500 ≈ 2% × P4000 = P80 = 2 × P 3500 P70 is close to P80. 100 My answer is reasonable. = P70 The bank pays Mia an interest of P70 after 1 year. P3500 + P70 = P3570 She will have P3570 in the savings account after 1 year. SCHOLASTIC b) Ian bought a pen at a discount of 15% during a sale. The usual price of the pen was P24. How much did he pay for the pen? Discount = Usual price – Selling price Method 1 Method 2 15% of P24 = 15% × P24 100% – 15% = 85% = 15 × P 24 Ian paid 85% of the usual price of 100 the pen. = P3.60 Ian was given a discount of P3.60. 85% of P24 = 85% × P24 P24 – P3.60 = P20.40 = 85 × P 24 100 He paid P20.40 for the pen. = P20.40 He paid P20.40 for the pen. 85% of P24 ≈ 90% × P20 = P18 P20.40 is close to P18. My answer is reasonable. © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4 73
Practices10 Solve the word problems. Show your work clearly. 1. Mary wants to buy a box of color pencils that costs P360. She has to pay an additional 12% sales tax on the color pencils. How much does Mary have to pay for the color pencils? First, find the amount of sales tax. Then, add that amount to the cost of the color pencils. 2. Carl saves P1200 in a savings account with a bank. The bank pays 3% interest per year. a) How much interest will he earn after 1 year? b) How much money will he have in the account after 1 year? 3. The usual price of a tablet was P2800. At a roadshow, it was sold at a discount of 30%. What was the selling price of the tablet? SCHOLASTIC 74 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4
Learn There were 1700 members in a club in 2016. The number of members increased by 9% in 2017. How many members were in the club in 2017? 9% of 1700 = 9% × 1700 9% is close to 10%. 10% of 1700 = 170 = 9 × 1700 153 is close to 170. 100 My answer is reasonable. = 153 The club had 153 more members in 2017. 1700 + 153 = 1853 There were 1853 members in 2017. SCHOLASTIC Practices11 Solve the word problems. Show your work clearly. 1. 4100 babies were born in a hospital last year. The number of babies born in the hospital decreased by 6% this year. How many babies were born this year? First, find the decrease in the number of babies. Then, subtract that number from the number of babies born last year. 2. At Station X, there were 850 passengers on a train. At Station Y, some passengers got on the train and the number of passengers increased by 12%. How many passengers were there when the train left Station Y? © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4 75
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