Knowing how to multiply rational numbers is essential in simplifying algebraic expressions and solving equations. The multiplication of rational numbers can be modeled by repeated addition.
Find 4 × (–0.2).
4 × (–0.2)
= –0.2 + (–0.2) + (–0.2) + (0.2)
= –0.8
This example illustrates the rule for multiplying two
rational numbers.
Example
Find each product.
1.
2.3(–4)
Alternative Solutions :
2.3(–4) = –9.2 The
factors have different signs. The product is negative.
2.
–3.5(–0.8)
Alternative Solutions :
–3.5(–0.8) = 2.8 The factors have
the same sign. The product is positive.
Example
Sports Link
3. A skydiver jumps from 12,000 feet. Solve the equation h = 12,000 +
(0.5)(–32.1)(576)
to find his height after he free-falls for 24 seconds.
Alternative Solutions :
h = 12,000 + (0.5)( –32.1)(576)
= 12,000 + (–16.05)(576) Multiply 0.5 and –32.1.
= 12,000 + (–9244.8) Multiply –16.05 and 576.
= 2755.2 Add
12,000 and –9244.8.
After 24
seconds, the skydiver’s height is 2755.2 feet.
You can use grid paper to model the multiplication of fractions.
The Hands-On Algebra activity suggests the following rule for
multiplying fractions.
Example
Find each product.
Study these products.
–1(5) = –5 –1
times 5 equals 5.
(–1)(–2.4) = 2.4 –1
times –2.4 equals 2.4.
Notice that multiplying a number by 1 results in the opposite
of the number. This suggests the Multiplicative Property of 1.
You can use what you know about multiplying rational numbers
to simplify algebraic expressions.
Example
7. Simplify –7.2t(5u).
Alternative Solutions :
–7.2t(5u)
= (–7.2)(t)(5)(u) –7.2t = (–7.2)(t) ; (5u) = (5)(u)
=
(–7.2)(5)(t)(u) Commutative
Property
= (–7.2 ⋅ 5)(t ⋅ u)
Associative
Property
= –36tu Simplify.
When you add any two rational numbers, is the sum always a
rational number? What happens when you subtract or multiply rational numbers? In
all three cases, the result is a rational number.
Sumber
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