Multiplication in Q
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ScribdTranslationsBolivarian Republic of Venezuela
Ministry of Popular Power for Education
U.E Colegio San Pedro
Barquisimeto State. Lara
Rational Numbers
Multiplication and Division in Q
Mariam Rodríguez
C.I: 31.930.357
1st "A"
Professor: Pastor Silva
Mathematics
Barquisimeto, April 2020
Multiplication in Q
a c
The product of two rational numbers y is another rational number, whose
b d
the numerator is the product of the numerators and the denominator is the product of
the denominators. Then it is necessary to simplify the resulting fraction.
For example:
1 4 1.4 4 2
a) 10 . =5 10.5 =50 25
=
16 36 16.36 576 48
b) 14 . 102 = 14.102 1428
= =
119
Multiplication of an integer by a fraction
To carry out the product of an integer and a fractional number, one proceeds
to rewrite the integer as a fraction, placing as the denominator the
number 1, and then the previous procedure is performed, that is, numerator by
numerator and denominator by denominator. For example:
3 3 5 3.5 15
a) .5= . = =
4 4 1 4.1 4
8 5 8 5.8 40 4
b) 5 . = . = = = =4
10 1 101.10 10 1
Multiplication with negative fractions
To multiply fractions with negative numbers we must take into account
count the rule of signs, among which we have:
Any number multiplied by a negative number will result in a
negative number.
When multiplying two negative numbers, the result will always be a number.
positive.
Any number, whether negative or positive, multiplied by zero always
will result in zero.
With these rules in mind, multiplication is performed in the same way.
according to the procedure explained above. For example:
−9−12 108 27
( )
a) 4 . 7 = 28 = 7
−21 4 −84 3
b) .= =
8 35 280 10
Multiplication of three or more fractions
The procedure is similar to having two fractions, the multiplication is
line up, numerator with numerator and denominator with denominator.
example:
5 4 3 5.4.3 60 15
a) . =. = =
4 8 2 4.8.2 64 16
1 4 2 8 1.4.2.8 64 8
b) . .= . = =
3 9 8 3 3.9.8.3 648 81
Properties of Multiplication in Q
1. Commutative Property: the order of rational numbers can vary in
a c c a
the multiplication and the result will be the same. That is to say, .=. .For
b d d b
example:
3−1−1 3 −3−3
a) 2 . 5 = 5 . 2 =
10 10
5 4 4 5 20 20 5 5
b) 8 . =6 . 6 8 =
48 48
=
12 12
2. Associative Property: regardless of how the numbers are grouped
a c e a c e
the result will be the same. That is to say,
( b . d=) .f. b . d ( f )For
example:
1 3 1 1 3 1 3 1 1 3 3 3
( )
a) 2 . 4=.5. 2. 4 5( ) .=.
8 5 2 20
=
40 40
9 5 1 9 5 1 45 1 9 5 45 45
( )
b) 2 . 2 =.4. 2 . 2 4 ( ) .=.
4 4 2 8
=
16 16
3. Distributive Property: when combining sums and multiplications, the result
is equal to the sum of the factors multiplied by each of the
a c e a e c e
addends. That is,
( )
+.=.+.
b d f b f d f
For example:
5 2 1 5 2 35+6 41
( )
a) 3 + 7. = 6 +18 =42 126 126
=
1 1 2 33 3 6 45+15−54 6 1
b) ( 3 + 9 − 5. =) 8 +24 −72 =40 360
= =
360 60
a
4. Neutral Element: the product of a rationalb number for 1 it is the same
rational number. For example:
3 3 36 36
a) 2 . 1 = 2 b) 1 . 5 = 5
5. Inverse Element: the inverse of a rational number in multiplication,
it will result in the number one. For example:
3 8 9 5
a) 8 . =1
3
b) 5 . =1
9
Division in Q
The division of two rational numbers is another rational number that has,
by numerator the product of the extremes and by denominator the product of the
means; or it can also be defined as the product of the first by the inverse of
a c a.d
second. That is, := different from zero. For example:
b d b.c
−6 8−6 . 9 −54−27
a) ( 5 ): ( 9) = 5 . 8 = 40 = 20
9 15 9.15 135 3
b) ( 10( ) : )9 = 10.9 90
=
2
=
Combined Operations
When combined operations are present, the order must be respected.
order of operations. Where:
1. Operations that are inside parentheses are resolved first.
grouping signs (parentheses, brackets, ...).
2. The powers are solved according to their order of appearance, from
left to right.
3. Multiplications and divisions are solved.
4. The additions and subtractions are resolved.
For example:
{ [
−7 8 1−5 4 3 2 4
(
a) 4 − 3+ 3+ 2 − 3+ :2 5 ) ( ) 5−2 ]+
7
} =
4 { [
−7812504 7
− + − −
3 3 4
+
6
−
4
+
5 ] }
=¿
2
−S H A Y T O D G
− − + + − + − =¿
4 3 3 46 4 5 2
−105−160−20+375+200−225+48−210−720+623−97
= =
60 60 60
b) (
1 3 −2
−:
2 4)( )3 { [
3 1 1
− + +.−
4 3 3 (
5
2 )]
4 1
+ =¿
3 4 }
{ [
−3 9 3 1 5 4 1
+ − + + − + =¿
4 84 3 6 94 ] }
{ }
−3 9 3 1 5 4 1
+ − + + − + =¿
4 84 3 6 9 4
−3 9 3 1 5 4 1
+ − − − + − =¿
4 8 4 3 6 9 4
−54+81−54−24−60+32−18−210+113 97
= =
72 72 72