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