Download Multiplication and division of Integers

Multiplication and Division of Positive and Negative Integers, including Fractions
Multiplication and division of Integers
Sign of the
Operation Sign of the
Number
Number
Page 1
Result Sign of the
Number
A Positive
Positive
Multiplied Positive
or Divided
Equals Number
Positive
Multiplied Negative
or Divided
Equals Number
Negative
Multiplied Positive
or Divided
Equals Number
A Negative
A Negative
Negative
Multiplied Negative
or Divided
A Positive
Equals Number
Multiply fractions: numerator * numerator and denominator * denominator
Multiplication
Fractions
3*3=9
1/3 * 1/3 = 1/9
3 * -3 = -9
1/3 * -1/3 = -1/9
-3 * 3 = -9
-1/3 * 1/3 = -1/9
-3 * -3 = 9
-1/3 * -1/3 = 1/9
-------------------------------------------------------------------------------Remember the rules for dividing fractions. We change the division sign to
multiplication and use the inverse of the second fraction. You can remember this
as “Keep – Change – Flip” Keep the first fraction as it is, Change the division sign
to multiplication, and Flip the second fraction over
Division
Fractions
9/3=3
1/3
1/3 = 1/3 * 3/1 = 3
9 / -3 = -3
1/3
-1/3 = 1/3 * -3/1 = -3
-9 / 3 = -3
-1/3
1/3 = -1/3 * 3/1 = -3
-9 / -3 =3
-1/3
-1/3 = -1/3 * -3/1 = 3
Multiplication and Division of Positive and Negative Integers, including Fractions
The rules for Multiplying Fractions are as follows:




Change any mixed numbers to improper fractions.
Cancel any factors common to both the numerator and denominator.
Multiply the remaining terms in the numerator and in the denominator.
Write the answer either as an proper fraction or as a mixed number as appropriate
Here is an example:
First we change it to an improper fraction, which gives us.
8
3
12
5
Can we can reduce this fraction? Yes, 3 is a common factor to
both the numerator and denominator. We rewrite the fraction as:
8
1
4
5
Now multiply the numerators 8*4 and denominators and 1*5
32
5
The result is an improper fraction and we can simplify it into a
mixed number.
The rules for Dividing Fractions are as follows:



Change mixed numbers into improper fractions.
Multiply the first fraction by the reciprocal of the second fraction.
Follow the rules for multiplication.
Here is an example:
Again, we simplify the mixed number into an improper fraction
8
3
4
3
Now we will follow the rule and change the division sign to
multiplication and invert (or flip) the second fraction.
8
3
3
4
Reduce the fraction before you multiply by dividing by or
cancelling common factors. Cancel the 3’s and 4 is a common factor
2
1
1
1
Now multiply the numerators 2*1 and denominators and 1*1
2
1
Is your final answer and it can be reduced to 2
Page 2
Multiplication and Division of Positive and Negative Integers, including Fractions
Page 3
A Quick Review of Multiplying Decimals:
1. Multiply the numbers just as if they were whole numbers:



Line up the numbers on the right--do not align the decimal points.
Starting on the right, multiply each digit in the top number by each digit in the
bottom number, just as with whole numbers.
Add the products.
2. Place the decimal point in the answer by starting at the right and moving the point
the number of places equal to the sum of the decimal places in both numbers
multiplied.
Example
37.7 x 2.8 = ? --->
37.7
x 2.8
3016
+754
105.56
( 1 decimal place )
( 1 decimal place )
( 2 decimal places, move point 2 places left )
A Quick Review of Dividing Decimals
Dividing decimals is almost the same as dividing whole numbers, except you use the
position of the decimal point in the dividend to determine the decimal places in the result.
To divide decimal numbers:
1. If the divisor is not a whole number:


Move the decimal point in the divisor all the way to the right (to make it a whole
number).
Move the decimal point in the dividend the same number of places.
2. Divide as usual. If the divisor doesn't go into the dividend evenly, add zeroes to the
3.
4.
right of the last digit in the dividend and keep dividing until it comes out evenly or a
repeating pattern shows up.
Position the decimal point in the result directly above the decimal point in the
dividend.
Check your answer: Use the calculator and multiply the quotient by the divisor. Does
it equal the dividend?
Find this quotient:
First show the division like this:
Multiplication and Division of Positive and Negative Integers, including Fractions
Page 4
Now move the decimal point one place to the right, which makes the divisor a whole
number. Also move the decimal point in the dividend one place to the right:
Divide as whole numbers. 65 goes into 169 two times with 39 left over:
To continue dividing, add a zero to the right of the decimal point in the dividend. Then bring
down the zero, and add it to the end of 39, making it 390
65 goes into 390 six times. We write a 6 above the zero in the quotient and put the decimal
point just above the decimal point in the dividend:
Definitions from this Lesson:
Reciprocal: The reciprocal of a fraction is obtained by interchanging the numerator and the
denominator. This is also called inverting the fraction, and we’ll use the term ‘flip’ in class.
Improper Fraction: If the numerator is greater than the denominator, then the fraction is called
an improper fraction. 25 11
Are examples of an improper fraction.
13
9
Mixed Number: A mixed number has a whole number followed by a fraction. Examples below.
Multiplication and Division of Decimals is provided by Math.com
All contents copyright � 2000-2007 Math.com. All rights reserved.