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Addition and Subtraction using the Number Line
Addition and Subtraction using the Number Line
To add or subtract two numbers, start on number line at the first number, then:
To add a positive number, move the number of spaces of the second number to the right along the number line --> 1 + 3 = 4
To subtract a positive number, move the number of spaces of the second number to the left along the number line <-- 1 - 2 = -1
To add a negative number, move the number of spaces of the second number to the left along the number line. <-- Adding a negative number is the same as subtracting a positive number. -3 + (-2) = -5
To subtract a negative number, move the number of spaces of the second number to the right along the number line. --> A negative of a negative is a positive, so subtracting a negative is like adding a positive. 9 - (-3) = 12
By definition, numbers to the right are larger than numbers to the left, so -3 is smaller than +2. -3 < 2 You could also say that 2 is greater than -3. 2 > -3
Follow the links for more practice using the number line and a running game.
Whole Number Place Values
Whole Number Place Values
Single Numbers have different values depending on their position in the whole.
Starting at the right:
Each single block represents one. Ten single blocks make a row of 10 and will carry over to the next position to the left.
In the second position, the number represents a row of 10 units.
Ten tens make 100.
Numbers in the third position to the left represent a square of 100 units. Ten square hundreds blocks make a cube of 1000.
Each number to the right is worth a tenth what it would be if you shifted it by one place to the left.
The blocks above represent 1,257
One thousand plus 2 hundreds plus 5 tens plus 7 ones.
Decimal Place Values
Decimal Place Values
If you looked really closely at a single unit and divided it into a 10 x 10 grid,
A tenth would be one row. This is the place right next to the decimal point.
A hundredth would be one square. This is the place one removed to the right of the decimal point.
Ten tenths make One.
Ten hundredths make 1 tenth. Also, 100 hundredths make one.
The blocks above on the right represent 0.14 or 14 hundredths. This is the same as 1 tenth plus 4 hundredths.
Just like the whole number places, the numbers to the right are worth one tenth of the value it would have if it were shifted one place to the left. (Numbers to the right are always smaller than numbers to the left.)
So 0.11 is one tenth plus one hundredth, which is greater than 0.103, which is one tenth plus 3 thousandths. 0.11 > 0.103
Practice Adding and Subtracting Decimals.
Practice Evaluating Decimals.
Money Place Values
Money Place Values
Money is counted using place values, but the tenths have a special name, dimes, and the hundredths are counted in pennies.
For example:
$20 + $10 in the tens place plus
$5 + $1 in the ones place plus
2 dimes in the tenths place plus
3 pennies in the hundredths place
Equals 36 dollars and 23 cents
$36.23
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