Download Decimals Adding and Subtracting

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Decimals Adding and Subtracting
Decimals are a group of digits, which express numbers or measurements in units, tens, and
multiples of 10. The digits for units and multiples of 10 are followed by a decimal point and then
by the digits for tenths, hundredths etc.
1. ADDING MORE THAN TWO POSITIVE DECIMAL NUMBERS
When adding more than two positive decimal numbers, the sum is positive. Align the
decimal points.
Decimals must always be lined up. Add the decimals as if they are whole numbers.
To add decimal numbers:
1. Put the numbers in a vertical column aligning the decimal points.
1. Add each column of digits, starting on the right and working left. If the sum of a
column is more than 10, "carry" digits to the next column on the left.
2. Place the decimal point in the answer directly below the decimal points in the
terms.
Example:
12.45
10.2
15.22
8.654
46.524
2. ADDING TWO NEGATIVE DECIMAL NUMBERS
When adding two negative decimal numbers, the sum will be negative and smaller than
either of the decimal numbers.
Example (- 0.37) + (-0.29) = (- 0.66)
3. ADDING MORE THAN TWO NEGATIVE DECIMAL NUMBERS
If you add more than two negative decimal numbers, the sum will be negative and smaller
than each of the decimal numbers. Again, the order in which they are added does not
matter.
Example (-0.3) + (-0.8) + (-0.2) + (-0.7) + (-0.4) = ( -2.4)
4. ADDITION WITH DECIMAL NUMBERS WITH MIXED SIGNS
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If you add decimal numbers with both positive and negative signs, the sign of the larger of
the positive or negative sum will determine the sign.
Example (0.5) + (-0.8) + (0.2) = (-0.1)
Because
0.5 + 0.2 = 0.7 and 0.7 and 0.7 + (-0.8) = (-0.1)
5. READING DECIMAL NUMBERS ON A NUMBER LINE
As with other numbers, decimal numbers can be read on a number line.
The line here indicates that this number is (+1.3).
This number line shows that decimal numbers can be negative or positive.
Decimals Multiplying
1. MULTIPLYING TWO POSITIVE DECIMAL NUMBERS
When multiplying two positive decimal numbers, the product is always positive and
larger than either factor.
Example (+ 0.5) x + (0.8) = (+ 0.40)
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2. MULTIPLYING MORE THAN TWO POSITIVE DECIMAL NUMBERS
When multiplying more than two decimal numbers, the product is always positive and
larger than each of the factors.
Example 0.9 x 0.5 x 0.2
= 0.45 x 0.2
= 0.090
← Three decimal places.
← Three decimal places.
← Three decimal places.
The number of decimal places in the product should be the total number of decimal
places in the factors. 0.9 has one decimal place, 0.5 has one decimal place and 0.2 has
one decimal place. The product must have three decimal places.
3. MULTIPLYING TWO NEGATIVE DECIMAL FACTORS
When you multiply two negative decimal numbers, the product is always positive and
larger than either of the factors.
Example (-0.7) x (–0.3) = (+0.21)
4. MULTIPLYING MORE THAN TWO NEGATIVE DECIMAL NUMBERS
When you multiply more than two negative decimal numbers, the product is always
negative if there is an odd number of factors. The product is positive if there is an even
number of factors.
Example (-0.3) x (–0.2) x (–0.5) = (- 0.030)
There are three factors and 3 is an odd number
(-0.3) x (–0.2) x (–0.5) x (-0.4) = (+ 0.0120)
There are four factors and 4 is an even number.
5. MULTIPLYING DECIMAL NUMBERS WITH MIXED SIGNS
When multiplying a series of decimal numbers, the product is negative if the number of
negative factors is odd. The product is positive if the number of negative factors is even.
Example (-0.6) x (+1.3) x (–2.33) x (+52.1) = (+94.68654)
There are two negative factors and 2 is an even number.
6. REVIEW
To multiply decimal numbers, follow these steps:
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1) Multiply the numbers just as if they were whole numbers.
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Line up the numbers on the right - do not align the decimal points.
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Starting on the right, multiply each digit in the top number by each digit in the
bottom number, just as with whole numbers.
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Add the products.
2) Place the decimal point in the answer by starting at the right and moving a number of
places equal to the sum of the decimal places in both numbers multiplied.
Decimals Dividing
1. DIVIDING DECIMAL NUMBERS
When dividing decimal numbers, write the numbers in standard division form.
Move the decimal point over the same number of places in the divisor and in the
dividend. Remember these steps:
1) If the divisor is not a whole number, move the decimal point to right to make it a
whole number and move the decimal point in the dividend the same number of
places.
2) Divide as usual. Keep dividing until the answer terminates or repeats.
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3) Put decimal point directly above decimal point in the dividend.
4) Check your answer. Multiply quotient by divisor. Does it equal the dividend?
Example
3. 552.
← Decimal has moved in the divisor and in the dividend.
Then divide as you would with whole numbers.
Answer: 184
2. DIVIDING TWO POSITIVE DECIMAL NUMBERS
When dividing one positive decimal number by another positive decimal number, the
answer or the quotient is positive.
Example (+0.56) ÷ (+0.4) = (+1.4)
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3. DIVIDING TWO NEGATIVE DECIMAL NUMBERS
When you divide one negative decimal number by another negative decimal number, the
answer or quotient is positive.
Example (-6.7) ÷ (-0.32) = (+7.02)
4. Dividing Decimal Numbers with Mixed Signs
When dividing one decimal number by another, if one is positive and the other is
negative, the answer or quotient is negative.
Example (+0.85) ÷ (-0.05) = (-17)
A thermometer is like a vertical number line. The reading
on this thermometer would be (+.7) degrees Celsius.
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The reading on this thermometer would be (-.7) degrees Celsius.
6. SUBTRACTING TWO POSITIVE DECIMAL NUMBERS
When you subtract two positive decimal numbers, the sign following the subtraction sign,
must be changed.
Example (+0.57) – (+0.17) = 0.57 – 0.17 = 0.40
The + sign in front of the 0.17 was changed to a – sign.
7. SUBTRACTING TWO NEGATIVE DECIMAL NUMBERS
When you subtract two negative decimal numbers, the sign following the subtraction
sign must be changed.
Example (-0.89) -(-0.59) = (- 0.89) + (+0.59) = (-0.30)
The sign in front of the 0.59 was changed to a + sign.
8. SUBTRACTING TWO DECIMAL NUMBERS WITH MIXED SIGNS
When you subtract two decimal numbers with mixed signs, the sign
following the subtraction sign must be changed.
Example (-0.97) – (+ 0.61) = (-0.97) + (-0.61) = (-1.58)
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