Download Grade 7 General Math Family Letter Chapter 1A [8/26/2014]

CHAPTER
1
Family Letter
1A Patterns and Relationships
Dear Family,
The student is learning to identify and extend number
patterns. He or she is also learning to represent numbers by
using exponents. Just as multiplication is valuable when you
are representing repeated addition, exponents are valuable
when you are representing repeated multiplication. An
exponent is a part of a power. It is a number that tells how
many times the base is to be multiplied by itself. A power with
base 3 and exponent 4 is written 34. The example below
shows how the student will find the value of a number with an
exponent.
Find the value of 34.
34 = 3 • 3 • 3 • 3 = 81
Multiply the base 3 by itself
4 times.
The student will use powers of ten when expressing numbers
with scientific notation. To multiply by a power of ten with
positive exponents, move the decimal point to the right the
same number of places as the value of the exponent.
4
Multiply 258 • 10 .
Remember: 258 = 258.0 = 258.0000
258 • 104 =
= 2,580,000
Move the decimal point 4
places to the right. Add
4 zeros as placeholders.
Write 45,250,000 in scientific notation.
Move the decimal point left
to form a number that is
greater than or equal to one
but less than 10.
107
Since the decimal point was
moved 7 places to the left,
the power of ten is 7.
4.525 × 107
Write the number in scientific
notation.
Note that 4.525 > 1 but < 10.
As the student works with more complex numbers, he or she
will continue to explore the use of scientific notation.
Vocabulary
These are the math
words we are learning:
Associative Property
property that states that
when you add or multiply,
you can group numbers
in any combination
base when a number is
written in exponential
form, the number that is
used as a factor is the
base
Commutative Property
property that states that
when you add or
multiply, you can do so
in any order
conjecture a statement
believed to be true
Distributive Property
property that states that
a number times a sum
equals the sum of the
products of that number
and each addend
exponent a number that
tells how many times to
use the base as a factor
Identity Property
property that states that
the product of 1 and a
number and the sum of 0
and a number is that
number
numerical expression
an expression made up
of numbers and
operations
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
1
Holt McDougal Mathematics
CHAPTER
1
Family Letter
1A Patterns and Relationships continued
The student will follow the order of operations, a set of rules
that standardize how to simplify expressions.
Order of Operations
1. Perform operations within grouping symbols.
order of operations
the rules that must be
followed when
simplifying expressions
power a number
written as a base and
an exponent
2. Evaluate powers.
3. Multiply and divide in order from left to right.
scientific notation a
type of shorthand for
writing numbers
4. Add and subtract in order from left to right.
Here is how the student will simplify an expression using the
order of operations.
Simplify 32 • 6 + 4.
32 • 6 + 4
9•6+4
54 + 4
58
There are no parentheses so evaluate the power.
Multiply.
Add.
The following properties will also help the student simplify
expressions. These properties apply to all numbers.
Property
Words
Algebra
a+b=b+a
k•m=m•k
Commutative
Property
You can add or multiply
numbers in any order.
Associative
Property
When you add or multiply, you
can group the numbers
together in any combination.
Identity
Property
The sum of 0 and any number
is the number. The product of
1 and any number is the
number.
Distributive
Property
A multiplier outside the
parentheses of another
operation can be applied to
each number inside the
parentheses before the
operation is performed.
(p + s) + t
= p + (s + t)
(x • y) • z
= x • (y • z)
x+0=x
x•1=x
d(e + f)
= d(e) + d(f)
Sincerely,
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
2
Holt McDougal Mathematics