Lesson 10.1: Number Properties
1.
Draw a rectangle to show that:
a) 7(x + 3) and 7x + 21 are equivalent
b) 2(n + 5) and 2n + 10 are equivalent
2.
Expand.
a) 5(x + 6)
b) 7(5 + e)
c) 8(2n + 4)
d) 3(11y + 7)
e) 2(3x + 4y + 7)
f) 3(9a + 5b + 6)
g) 9(4b + 7c + 10)
3.
Name the number property each statement represents.
a) 4 + x = x + 4
b) b + 0 = b
c) c × 1 = c
d) gh = hg
e) 3(c + 7) = 3c + 21
f) w × 0 = 0
4.
Which expressions in each pair are equivalent? Explain your reasoning.
a) 4x + 60 and 4(x + 15)
b) c + 4 and 4 + c
c) 4 + 2b and 6b
d) 3(a + 5) and 8 + 3a
5.
Expand.
a) a(b + 0)
b) a(0 + b)
c) b(0 + a)
d) b(a + 0)
What do you notice?