Negating a variable does not automatically mean that the quantity will be negative: –x means ‘‘the opposite’’ of x. We cannot conclude that –x is a negative number unless we have reason to believe x itself is a positive number. If x is a negative number, –x is a positive number. (Although in practice we verbally say ‘‘negative x’’ for ‘‘–x’’ when we really mean ‘‘the opposite of x’’).
The same rules apply when
multiplying ‘‘negative’’ variables.
Examples
–3(5x) = –15x 5(–x) = – 5x
–12(–4x) = 48x –x (–y)
= xy
–2x(3y) = –6xy x(–y) =
– xy
–16x(–4y) = 64xy 4(–1.83x)(2.36y) = – 17.2752xy
–3(–x) = 3x
Practice
1.
18(–3x)
=
2.
–4(2x)(–9y)
=
3.
28(–3x)
=
4.
–5x(–7x) =
5.
–1(–6)( –7x) =
6.
1.1x(2.5y)
=
7.
– 8.3(4.62x)
=
8.
– 2.6(–13.14(–6x) =
9.
0.36(–8.1x)(
–1.6y) =
10. 4(–7)(2.1x)y =
Solutions
1.
18(–3x)
= –54x
2.
–4(2x)(–9y)
= 72xy
3.
28(–3x)
= –84x
4.
–5x(–7x) = 35xy
5.
–1(–6)( –7x) = –42x
6.
1.1x(2.5y)
= 2.75xy
7.
– 8.3(4.62x)
= –38.346x
8.
– 2.6(–13.14(–6x) = –204.984x
9.
0.36(–8.1x)(
–1.6y) = 4.6656xy
10. 4(–7)(2.1x)y = –58.8xy
Thanks for reading Multiplication and Division with Negative Numbers - 1. Please share...!
