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Ordering Six Digit Numbers Numbers have an order or arrangement. The number two is between one and three. Three or more numbers can be placed in order. A number may come before the other numbers or it may come between them or after them. Example: If we start with the numbers 4 and 8, the number 5 would come between them, the number 9 would come after them and the number 2 would come before both of them. The order may be ascending (getting larger in value) or descending (becoming smaller in value). Addition equations with 3 digit numbers An equation is a mathematical statement such that the expression on the left side of the equals sign (=) has the same value as the expression on the right side. An example of an equation is 222 + 222 = 444. One of the terms in an equation may not be known and needs to be determined. The unknown term may be represented by a letter such as x. (e.g. 222 + x = 444). The solution of an equation is finding the value of the unknown x. Use the subtractive equation property to find the value of x. The subtractive equation property states that the two sides of an equation remain equal if the same number is subtracted from each side. Example: 500 + x = 1200 500 + x - 500 = 1200 - 500 0 + x = 700 x = 700 Check the answer by substituting the answer (700) back into the equation. 500 + 700 = 1200 Addition equations with 4 digit numbers An equation is a mathematical statement such that the expression on the left side of the equals sign (=) has the same value as the expression on the right side. An example of an equation is 2222 + 2222 = 4444. One of the terms in an equation may not be known and needs to be determined. The unknown term may be represented by a letter such as x. (e.g. 2222 + x = 4444). The solution of an equation is finding the value of the unknown x. Use the subtractive equation property to find the value of x. The subtractive equation property states that the two sides of an equation remain equal if the same number is subtracted from each side. Example: 5000 + x = 12000 5000 + x - 5000 = 12000 - 5000 0 + x = 7000 x = 7000 Check the answer by substituting the answer (7000) back into the equation. 5000 + 7000 = 12000 Addition equations with 5 digit numbers An equation is a mathematical statement such that the expression on the left side of the equals sign (=) has the same value as the expression on the right side. An example of an equation is 22222 + 22222 = 44444. One of the terms in an equation may not be known and needs to be determined. The unknown term may be represented by a letter such as x. (e.g. 22222 + x = 44444). The solution of an equation is finding the value of the unknown x. Use the subtractive equation property to find the value of x. The subtractive equation property states that the two sides of an equation remain equal if the same number is subtracted from each side. Example: 50000 + x = 120000 50000 + x - 50000 = 120000 - 50000 0 + x = 70000 x = 70000 Check the answer by substituting the answer (70000) back into the equation. 50000 + 70000 = 120000 Addition equations with 6 digit numbers An equation is a mathematical statement such that the expression on the left side of the equals sign (=) has the same value as the expression on the right side. An example of an equation is 222222 + 222222 = 444444. One of the terms in an equation may not be known and needs to be determined. The unknown term may be represented by a letter such as x. (e.g. 222222 + x = 444444). The solution of an equation is finding the value of the unknown x. Use the subtractive equation property to find the value of x. The subtractive equation property states that the two sides of an equation remain equal if the same number is subtracted from each side. Example: 500000 + x = 1200000 500000 + x - 500000 = 1200000 - 500000 0 + x = 700000 x = 700000 Check the answer by substituting the answer (700000) back into the equation. 500000 + 700000 = 1200000 Subtraction equations with 5 digit numbers An equation is a mathematical statement such that the expression on the left side of the equals sign (=) has the same value as the expression on the right side. An example of an equation is 60000 - 40000 = 20000. One of the terms in an equation may not be known and needs to be determined. The unknown term may be represented by a letter such as x. (e.g. 60000 - x = 40000). The solution of an equation is finding the value of the unknown x. Use the additive equation property to find the value of x. The additive equation property states that the two sides of an equation remain equal if the same number is added to each side. Example: x - 50000 = 70000 x - 50000 + 50000 = 70000 + 50000 x - 0 = 120000 x = 120000 Check the answer by substituting the value of x (120000) back into the equation. 120000 - 50000 = 70000 Subtraction equations with 6 digit numbers An equation is a mathematical statement such that the expression on the left side of the equals sign (=) has the same value as the expression on the right side. An example of an equation is 600000 - 400000 = 200000. One of the terms in an equation may not be known and needs to be determined. The unknown term may be represented by a letter such as x. (e.g. 600000 - x = 400000). The solution of an equation is finding the value of the unknown x. Use the additive equation property to find the value of x. The additive equation property states that the two sides of an equation remain equal if the same number is added to each side. Example: x - 500000 = 700000 x - 500000 + 500000 = 700000 + 500000 x - 0 = 1200000 x = 1200000 Check the answer by substituting the value of x (120000) back into the equation. 1200000 - 500000 = 700000 Multiplying a two digit number by a one digit number How to multiply a two digit number by a one digit number (for example 59 + 7). Place one number above the other so that the ones place digits are lined up. Draw a line under the bottom number. 59 7 Multiply the two ones place digits. (9 * 7 = 63). This number is larger than 10, so place the six above the tens place column and place the three below the line in the ones place column. 6 59 7 3 Multiply the digit in the tens place column (5) by the digit in the ones place of the second number (7). The result is 5 * 7 = 35. Add the 6 to the 35 (35 + 6 = 41) and place the answer below the line and to the left of the other number below the line. 59 7 413 Multiplying a three digit number by a one digit number How to multiply a three digit number by a one digit number (for example 159 * 7). Place one number above the other so that the ones place digits are lined up. Draw a line under the bottom number. 159 7 Multiply the two ones place digits. (9 * 7 = 63). This number is larger than 10, so place the six above the tens place column and place the three below the line in the ones place column. 6 159 7 3 Multiply the digit in the tens place column (5) by the digit in the ones place of the second number (7). The result is 5 * 7 = 35. Add the 6 to the 35 (35 + 6 = 41). Place the one below the line and to the left of the other number. Place the 4 above the hundreds column. 46 159 7 13 Multiply the digit in the hundreds place column (1) by the digit in the ones place of the second number (7). The result is 1 * 7 = 7. Add the 4 to the 7 (4 + 7 = 11). Place this below the line and to the left of the other number. 46 159 7 1113 Multiplication of Two and Three Digit Numbers Multiplying a three digit number by a two digit number (for example 529 * 67) with paper and pencil involves several steps. Place one number above the other so that the hundred's, ten's and one's places are lined up. Draw a line under the bottom number. 529 67 Multiply the two numbers in the ones places. (9 * 7 = 63). This number is larger than 10 so place a six above the tens place column and place three below the line in the one's place column. 6 529 67 3 Muliply the digit in the top ten's place column (2) by the digit in the lower one's place column (7). The answer (2*7=14) is added to the 6 above the top ten's place column to give an answer of 20. The 0 of 20 is place below the line and the 2 of the 20 is placed above the hundred's place column. 26 529 67 03 The hundreds place of the top number (5) is multiplied by the one's place of the multiplier (5*7=35). The two that was previously carried to the hundreds place is added and the 37 is placed below the line. 26 529 67 3703 After 529 has been multiplied by 7 as shown above, 529 is multiplied by the tens place of the multiplier which is 6. The number is moved one place to the left because we are multiplying by a ten's place number. The result would be 3174: 15 529 67 3703 3174 A line is drawn under the lower product (3174) and the products are added together to get the final answer of 35443. 15 529 67 3703 3174 35443 Division Dividing a three digit number by a one digit number (for example 413 7) with paper and pencil involves several steps. Place the divisor before the division bracket and place the dividend (413) under it. 7)413 Examine the first digit of the dividend(4). It is smaller than 7 so can't be divided by 7 to produce a whole number. Next take the first two digits of the dividend (41) and determine how many 7's it contains. In this case 41 holds five sevens (5*7=35) but not six (6*7=42). Place the 5 above the division bracket. 5 7)413 Multiply the 5 by 7 and place the result (35) below the 41 of the dividend. 5 7)413 35 Draw a line under the 35 and subtract it from 41 (41-35=6). Bring down the 3 from the 413 and place it to the right of the 6. 5 7)413 35 63 Divide 63 by 7 and place that answer above the division bracket to the right of the five. 59 7)413 35 63 Multiply the 9 of the quotient by the divisor (7) to get 63 and place this below the 63 under the dividend. Subtract 63 from 63 to give an answer of 0. This indicates that there is nothing left over and 7 can be evenly divided into 413 to produce a quotient of 59. 59 7)413 35 63 63 0 Division Dividing a three digit number by a one digit number (for example 416 7) involves several steps. Place the divisor before the division bracket and place the dividend (416) under it. 7)416 Examine the first digit of the dividend(4). It is smaller than 7 so can't be divided by 7 to produce a whole number. Next take the first two digits of the dividend (41) and determine how many 7's it contains. In this case 41 holds five sevens (5*7=35) but not six (6*7=42). Place the 5 above the division bracket. 5 7)416 Multiply the 5 by 7 and place the result (35) below the 41 of the dividend. 5 7)416 35 Draw a line under the 35 and subtract it from 41 (41-35=6). Bring down the 6 from the 416 and place it to the right of the other 6. 5 7)416 35 66 Divide 66 by 7 and place that answer above the division bracket to the right of the five. 59 7)416 35 66 Multiply the 9 of the quotient by the divisor (7) to get 63 and place this below the 66. Subtract 63 from 66 to give an answer of 3. The number 3 is called the remainder and indicates that there were three left over. 59 R 3 7)416 35 66 63 3 See this website for more information: http://www.aaamath.com/B/grade7.htm