Year4_Term1_Week1_Homework

Yimin Math Centre Year 4 Term 1 Homework Student Name: Grade: Date: Score: Table of contents 1 Year 4 Term 1 Week 1 Homework 1 1.1 Whole Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1 Roman Numerals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.2 Place Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.3 Four Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.1.4 Rounding Off . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.1.5 The Four Operations (+,−,× and ÷) . . . . . . . . . . . . . . . . . . . . . . 6 1.2 Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2.1 Place Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2.2 Ordering Decimal Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3 Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3.1 Equivalent Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3.2 Simplifying Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.4 Across Downs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.5 Quiz 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Page: 12 13 14 15 Total Marks: 27 25 18 30 100 Score: This edition was printed on January 4, 2011. Camera ready copy was prepared with the LATEX2e typesetting system. Copyright © 2000 - 2011 Yimin Math Centre (www.yiminmathcentre.com) Year 4 Term 1 Homework Year 4 Term 1 Week 1 Homework Page 1 of 15 1 Year 4 Term 1 Week 1 Homework 1.1 Whole Numbers 1.1.1 Roman Numerals Roman Numerals were very popular about 2000 years ago. The Roman number system is based on the idea of addition and subtraction. • When a smaller numeral appears before a large one, it is subtracted from the large one: IV means 5 - 1 = 4 XL means 50 - 10 = 40 • When a smaller numeral appears after the larger one, it is added to the large one. VI means 5 + 1 = 6 LX means 50 + 10 = 60 • By repeating a numeral, its value is repeated. XX = 10 + 10 = 20 XXX = 10 + 10 + 10 = 30 • By placing a bar over the numeral, its value is increased by 1000 times (M = 1000). V = 5000 X = 10,000 L = 50,000 C = 100,000 D = 500,000 M = 1,000,000 Example 1.1.1 1. Change the Roman numerals into our own numerals: (a) XXXIV = 10 + 10 + 10 + 4 = 34 (b) CCXXVII = 100 + 100 + 10 + 10 + 7 = 227 2. Change these Hindu-Arabic numerals into Roman numerals: (a) 1256 = MCCLVI (b) 214 = CCXIV (c) 2008 = MMVIII Copyright © 2000 - 2011 Yimin Math Centre (www.yiminmathcentre.com) Year 4 Term 1 Week 1 Homework Page 2 of 15 The table below gives more details of the Roman numeral system: I II III IV V VI VII VIII IX 1 2 3 4 5 6 7 8 9 X XX XXX XL L LX LXX LXXX XC 10 20 30 40 50 60 70 80 90 C CC CCC CD D DC DCC DCCC CM 100 200 300 400 500 600 700 800 900 M 1000 Exercise 1.1.1 1. Change the Roman numerals into our own numerals: (a) XXVII = (b) LXXIV = (c) CCLXXXVII = (d) DLIV = (e) MDXLIV = (f) CMXCIX = 2. Change these Hindu-Arabic numerals into Roman numerals: (a) 94 = (b) 372 = (c) 926 = (d) 409 = (e) 1007 = (f) 2468 = Copyright © 2000 - 2011 Yimin Math Centre (www.yiminmathcentre.com) Year 4 Term 1 Week 1 Homework Page 3 of 15 1.1.2 Place Value Our number system today is based on the Hindu-Arabic system where the value of a number is deter- mined by its place in a particular column as shown in the example below. Example 1.1.2 What is the value of 2 and 6 in the numeral 3,250,698? • The place value of 2 is 200,000 or two hundred thousand. • The place value of 6 is 600 or six hundred. Exercise 1.1.2 What is the value of 3 in the following numbers? 1. 12743 2. 25327 3. 23708 4. 302984 5. 9232901 6. 3200987 7. 234508 8. 120039 Copyright © 2000 - 2011 Yimin Math Centre (www.yiminmathcentre.com) Year 4 Term 1 Week 1 Homework Page 4 of 15 1.1.3 Four Notations There are four ways or notations of describing a whole number: 1. As an ordinary numeral: 3,250,698. 2. In words: Three million, two hundred and fifty thousand, six hundred and ninety eight. 3. In expanded notation: (3× 1, 000, 000) + (2× 100, 000) + (5× 10, 000) + (6× 100) + (9× 10) + (8× 1) 4. In exponential notation: (3× 106) + (2× 105) + (5× 104) + (6× 102) + (9× 101) + (8× 100) Exercise 1.1.3 1. Write the following numbers in words: (a) 1,234 (b) 10,609 (c) 20,359 (d) 537,209 2. Write the following numbers in expanded notation. (a) 2,345 = (b) 10,483 = (c) 200,482 = (d) 6,200,345 = 3. Write the following numbers in exponential notation: (a) 3,124 = (b) 62,389 = (c) 12,034 = (d) 430,156 = Copyright © 2000 - 2011 Yimin Math Centre (www.yiminmathcentre.com) Year 4 Term 1 Week 1 Homework Page 5 of 15 1.1.4 Rounding Off Exercise 1.1.4 1. Round off the following numbers to the nearest 10: (a) 1234 = (b) 3405 = (c) 1004 = (d) 1996 = 2. Round off the following numbers to the nearest 100: (a) 1898 = (b) 1054 = (c) 1009 = (d) 8946 = 3. Round off the following numbers to the nearest 1000: (a) 1369 = (b) 2456 = (c) 1898 = (d) 1098 = 4. Evaluate the following expressions and round off to the nearest 100: (a) 234 + 18 + 1096 + 208 = (b) 2974 + 102− 37 + 604 = (c) 1028 + 64 + 120− 102 = (d) 325× 12 + 207 = Copyright © 2000 - 2011 Yimin Math Centre (www.yiminmathcentre.com) Year 4 Term 1 Week 1 Homework Page 6 of 15 1.1.5 The Four Operations (+,−,× and ÷) Exercise 1.1.5 1. Evaluate the following additions: (a) 1234 + 405 + 20456 = (b) 7213 + 68 + 856 + 4 + 1305 = (c) 8012 + 23 + 305 + 18 = (d) 327 + 96 + 409 + 1003 = 2. Evaluate the following subtractions: (a) 6000− 2369 = (b) 3406− 1097 = (c) 1203− 394 = (d) 3914− 1825 = 3. Evaluate the following multiplications: (a) 102× 35 = (b) 145× 17 = (c) 490× 18 = (d) 209× 103 = 4. Evaluate the following divisions: (a) 817÷ 19 = (b) 1140÷ 15 = (c) 486÷ 18 = (d) 1008÷ 14 = Copyright © 2000 - 2011 Yimin Math Centre (www.yiminmathcentre.com) Year 4 Term 1 Week 1 Homework Page 7 of 15 1.2 Decimals 1.2.1 Place Value The numbers to the left of the decimal point have exactly the same place values as in the set of whole numbers. While the numbers to the right of the decimal point have special place value shown below: Example 1.2.1What is the place value of each digit to the right of the decimal point in the number 7952.348? • The place value of 3 is 3 lots of 1 10 = 3× 1 10 = 3 10 or 3 tenths. • The place value of 4 is 4 lots of 1 100 = 4× 1 100 = 4 100 or 4 hundredths. • The place value of 8 is 8 lots of 1 1000 = 8× 1 1000 = 8 1000 or 8 thousandths. Exercise 1.2.1 What is the place value of 5 in each of these numbers? 1. 23.957 2. 92.503 3. 28.125 4. 25.102 5. 10.205 6. 52.203 7. 125.18 8. 12.252 Copyright © 2000 - 2011 Yimin Math Centre (www.yiminmathcentre.com) Year 4 Term 1 Week 1 Homework Page 8 of 15 1.2.2 Ordering Decimal Numbers Example 1.2.2 1. Order the following numbers from greatest to least: 13.3, 13.03, 13, and 13.33 Solution: 13.3 = 13.30 = 13 + 30 100 13.03 = 13 + 3 100 13 = 13.00 = 13 + 0 100 13.33 = 13 + 33 100 Therefore the order from greatest to least is: 13.33, 13.3, 13.03, 13. 2. Five boys ran in a final of 100 m school sprint and recorded the following times in seconds: 13.27, 13.07, 12.95 13.73 and 13.7. order the times from the least to the greatest. Solution: 13.27 = 13 + 27 100 13.07 = 13 + 7 100 12.95 = 12 + 95 100 13.73 = 13 + 73 100 13.7 = 13 + 70 100 Therefore the order from least (fastest) to greatest (slowest) is: 12.95, 13.07, 13.27, 13.7, 13.73 Exercise 1.2.2 1. Order the following numbers from greatest to least: (a) 1.02, 1.022, 1.202 and 1.002 (b) 10.01, 10.11, 10.1 and 10.02 2. Order the following numbers from least to greatest: (a) 4.2, 4.02, 4.22 and 4.12 (b) 0.25, 0.4, 0.125 and 0.215 Copyright © 2000 - 2011 Yimin Math Centre (www.yiminmathcentre.com) Year 4 Term 1 Week 1 Homework Page 9 of 15 1.3 Fractions 1.3.1 Equivalent Fractions = 4 64 2 8 = 1 Score: 2 2 4 32= 8 = 3 4 8 56= 32 = 4 1 2 12= 2 = 5 4 7 16 = 42= 6 2 5 50= 18 = 7 6 8 60 = 24= 8 1 6 10 = 54= 9 4 5 20= 28 = 10 2 3 10 = 18= 11 1 5 40= 4 = 12 2 7 18 = 56= 13 1 3 3 = 27= 14 5 6 25 = 48= 15 1 4 32= 3 = 16 4 6 24 = 12= 17 3 5 15= 12 = 18 2 6 16 = 54= 19 3 8 15 = 64= 20 6 7 60 = 63= Copyright © 2000 - 2011 Yimin Math Centre (www.yiminmathcentre.com) Year 4 Term 1 Week 1 Homework Page 10 of 15 1.3.2 Simplifying Fractions 3 9 = 1 Score: 2 2 4 = 3 30 50 = 4 27 36 = 5 8 32 = 6 10 50 = 7 12 18 = 8 12 24 = 9 40 50 = 10 10 20 = 11 35 42 = 12 16 24 = 13 8 24 = 14 6 15 = 15 24 48 = 16 5 30 = 17 16 24 = 18 3 6 = 19 6 12 = 20 9 18 = Copyright © 2000 - 2011 Yimin Math Centre (www.yiminmathcentre.com) Year 4 Term 1 Week 1 Homework Page 11 of 15 1.4 Across Downs 2421 19 401 + - - - 15 13 6 10 + - + + 5 7 18 16 = = = = + - - - + - + + + - - - + - + + 8 18 6 10 + - + + 13 1 4 30 + - - - 14 4 9 6 = = = = + - + + + - - - + - + + + - + + 24 5 12 11 + - - - 5 3 1 1 + - + + 9 1 27 27 = = = = = = = = = = = = = = = = = = = = + - + + + - + + = = = = 2 3 4 Copyright © 2000 - 2011 Yimin Math Centre (www.yiminmathcentre.com) Year 4 Term 1 Week 1 Homework Page 12 of 15 1.5 Quiz 1 Question 1. Write the following in Hindu-Arabic numerals: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (3 points) (a) [1]DXVII = (b) [1]CCCLXII = (c) [1]CDXLIX = Question 2. Write in Roman numerals: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (3 points) (a) [1]920 = (b) [1]704 = (c) [1]1205 = Question 3. What is the place value of 3 in the following numbers: . . . . . . . . . . . . . . . . . . . . . (3 points) (a) [1]2345 = (b) [1]2003 = (c) [1]3690 = Question 4. Write the following numbers in expanded notation: . . . . . . . . . . . . . . . . . . . . . . . . (6 points) (a) [2]723 = (b) [2]3412 = (c) [2]4927 = Question 5. Write the following in exponential notation: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (12 points) (a) [2]6× 6× 6 = (b) [2]2× 2× 2× 2 = (c) [2]10000 = (d) [2]3000 = (e) [2]20463 = (f) [2]532089 = Copyright © 2000 - 2011 Yimin Math Centre (www.yiminmathcentre.com) Year 4 Term 1 Week 1 Homework Page 13 of 15 Question 6. Round off the following numbers to the nearest 10: . . . . . . . . . . . . . . . . . . . . . . . . (5 points) (a) [1]1045 = (b) [1]2395 = (c) [1]1950 = (d) [1]39095 = (e) [1]12305 = Question 7. Round off the following numbers to the nearest 100: . . . . . . . . . . . . . . . . . . . . . . . (5 points) (a) [1]2345 = (b) [1]3456 = (c) [1]2905 = (d) [1]20973 = (e) [1]97654 = Question 8. Round off the following number to the nearest 1000: . . . . . . . . . . . . . . . . . . . . . . . (5 points) (a) [1]971 = (b) [1]3406 = (c) [1]2544 = (d) [1]39256 = (e) [1]38947 = Question 9. Evaluate the following expressions: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (10 points) (a) [2]12 + 8÷ 2 + 6− 9 = (b) [2](12− 4)÷ (7− 5) = (c) [2](6 + 4)× (6− 4) = (d) [2]8× 7− (18− 8÷ 2) = (e) [2]98− (15÷ 3) + (45÷ 9)× 2 = Copyright © 2000 - 2011 Yimin Math Centre (www.yiminmathcentre.com) Year 4 Term 1 Week 1 Homework Page 14 of 15 Question 10. Find the answers to the following: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (18 points) (a) [2]The quotient of a number and four is 5. Find the number. (b) [2]Decrease the quotient of 18 and 3 by 4. (c) [2]Increase the product of 15 and 7 by 7. (d) [2]The product of 7 and 9 is decreased by the quotient of 6 and 3. (e) [2]6 times the square of 2 is increased by the difference of 7 and 2. (f) [2]The average of 3 numbers is 6. A fourth number is added to the total, and the new average is 8. What is the fourth number? (g) [2]Decrease 13.73 by 5.7. (h) [2]The product of 8.25 and 5. (i) [2]Increase 16.8 by 6.4 and subtract the result from 28. Copyright © 2000 - 2011 Yimin Math Centre (www.yiminmathcentre.com) Year 4 Term 1 Week 1 Homework Page 15 of 15 Question 11. Simplifying the following fractions: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (12 points) (a) [2]24 36 = (b) [2]7 84 = (c) [2]9 108 = (d) [2]128 256 = (e) [2]24 168 = (f) [2]124 12 = Question 12. Find the Equivalent Fractions of the following: . . . . . . . . . . . . . . . . . . . . . . . . . . (12 points) (a) [2]12 48 = ? 12 = (b) [2]27 45 = ? 5 = (c) [2]6 10 = ? 30 = (d) [2]10 25 = 2 ? = (e) [2]7 12 = ? 24 = (f) [2]32 36 = 8 ? = Question 13. Problem solving: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (6 points) (a) [2]A movie started at 6:15 pm and finished at 8:38 pm. Find the running time for the movie. (b) [2]At the school’s athletic carnival, Mike and John entered the high jump competition. Mike jumped 1.03 m, while John jumped 5 cm lower. What height did John jump? (c) [2]The 28 students in our class read an average of three books in a month. How many books were read in total in a year? Copyright © 2000 - 2011 Yimin Math Centre (www.yiminmathcentre.com) Year 4 Term 1 Week 1 Homework Whole Numbers Roman Numerals Place Value Four Notations Rounding Off The Four Operations (+, -, and ) Decimals Place Value Ordering Decimal Numbers Fractions Equivalent Fractions Simplifying Fractions Across Downs Quiz 1