Proportional Reasoning
Definition: Ratioa comparison of two numbersa/b or a:b (b cannot equal zero).
A 1 to 2 ratio of males to females means that the number of males is the number of
females or there is 1 male for every 2 females.
EX: Suppose there are 2
Introduction to Decimals
Consider 12.61843
1tens place
2units place
6tenths place
1hundredths place
8thousandths place
4ten-thousandths place
3hundred-thousandths place
Use base 10 blocks:
In General
1 Block = 10 units
1 Flat = 1 unit
1 Long = 1/10 of a u
Multiplication and Division of Rational Numbers
Two types of multiplication problems
1. Whole number times a fraction
4
3
5
1
2
6
1
4
3
2. Fraction times a fraction
My husband has 3/4 of an acre of land and 5/6 of this is planted in trees. What
part of th
Percents
What is Percent?
n%
6%
1%
n
100
6
100
1
.01
100
100%
100
1
100
200%
200
2
100
Do Activity 9What does it mean?
-estimate percentages first
-check with grid
-complete first page
3
n
5 100
3
n 60%
100
5
In general, to convert a number to a perc
?-iSson
r( X>s)
,A^= z f
*
=
t*r*"J
X=
*rrytntilsfi*
= b (Esr*ods
l- ?(v*+)
I - [i,f*-)t
L
trfx=r) +Fr#
*=z)
+F
ti
+ ycfw_x= +)J
= l-lr'lr +"-t6'l
L-A,
TI
= t ;'[ #,.tr
cfw_.# cfw_t
J
;
0,+ls
S 0u*e,.rv f
U
t
Z
3 non+1,ni,c r
oacL acfw_
zAnlrades
Z s,zad*
The Set of Rational Numbers
N = cfw_1, 2, 3, 4, .
W = cfw_0, 1, 2, 3, 4, .
I = cfw_., -4, -3, -2, -1, 0, 1, 2, 3, 4, .
Problem: I have a cake to share equally among 4 people. How much of the cake does
each person get?
Can we use the numbers in N, W, or I
Real Numbers
Irrational numbers
What about a square with area 2?
The side length is now 2 and 2 is not a rational number! The decimal does
not repeat nor does it terminate.
3
.75
4
2
.6
3
2 1.14213562.
3.141592654.
Definition: Irrational Numbersan irrati