Download 03-30 7.1 Decimals, 7.2 Adding and Subtracting Decimals

§7.1 Decimals
3/30/17
Today We’ll Discuss
How do we read and write decimals?
How do we convert decimals and
fractions?
How do we recognize when a decimal
terminates?
How do we order terminating decimals?
What are Decimals?
Definitions: A decimal represents a
fraction whose denominator is a power of
10. Instead of writing the fraction, digits
are placed after a decimal point to
represent the fraction.
Fractional part
For example:
Whole-number part
What are Decimals?
Just like before, each digit represents a
different place value.
However, now each digit after the
decimal represents how many of each
“10-power fraction” we have.
The book differentiates between each
form using the terms fraction form and
decimal form
Notation:
When starting out, stress writing decimals
that are less than one using a leading
zero.
0.25 instead of .25.
Examples
Base-Ten Block Model for
DECIMALS
The main point of the base-ten blocks is
that each piece (cube, rod, flat,...) is 10
times the size of the last.
Since each place value in a decimal is still
10 times the next, we can use base-ten
blocks, but in a different way.
New Values
Example
Use base-ten blocks to model
a) 2.34
Example
Use base-ten blocks to model
a) 2.34
b) 1.59
Example
Use base-ten blocks to model
a) 2.34
b) 1.59
c) .15
Terminating vs. NonTerminating Decimals
There are three main kinds of decimals:
1) Terminating
2) Non-Terminating, Repeating
3) Non Terminating, Non-Repeating
Terminating Decimals
Fact: A fraction in simplest form can be
written as a terminating decimal if and
only if the prime factorization of the
denominator contains no other primes
other than 2 or 5.
Terminating Decimals
There are 2 ways to write these fractions
as terminating decimals.
A) Rewrite the fraction so that its
denominator is a power of 10
B) Divide the numerator by the
denominator (mostly saved for §7.3)
Example
Determine whether each fraction can be
written as a terminating decimal. If so, write
the terminating decimal.
Ordering Terminating Decimals
As with many of the numbers we order, we use a
number line to order decimals.
1) Draw a number line including all decimals to
be ordered.
2) Graph each decimal on the number line.
3) Read the decimals from left to right to order
from least to greatest.
Example
Order the following from least to greatest.
a) 0.34, 0.4, 0.21, and 0.58
b) 0.3, 0.209, 0.25, and 0.2003
Example
You are marking distances on a map from your home
to several locations. Use a number line to decide
which location is closest to your home.
Example
The results of the men’s 100 meter dash final at the
2012 Summer Olympics are shown below. Who won
the gold, silver, and bronze medals?
§7.2 Adding and
Subtracting Decimals
3/30/17
Today We’ll Discuss
How do we add and subtract decimals
using models and algorithms?
How do we add and subtract decimals
using mental math?
How do we round decimals?
Base-Ten Block
Addition/Subtraction (Decimals)
We’ve already discussed the reasoning
and method for base-ten blocks as a
model for usual addition and subtraction.
We can take all of that and transfer those
skills directly to our new decimal values
for base-ten blocks.
Vertical Algorithm for Adding
and Subtracting Decimals
To add or subtract decimals:
1) Write the numbers vertically, lining up the
decimal points.
2) Place the missing “invisible zeros.”
3) Add or subtract with your favorite old algorithm
keeping the decimal throughout.
4) Carry down the decimal point into your final
answer.
Example
Use the vertical algorithm to find
a) 2.405 + 13.01 + 7.2
b) 5.3 − 1.255
c) 3.042 − 1.0322
Example
The first and second place winning times
for the women’s downhill Alpine skiing at a
recent Winter Olympics were 1 minute,
44.19 seconds and 104.75 seconds,
respectively. How much faster is the first
place skier?
Example
Find the balance after each transaction.
Example - Answer
Find the balance after each transaction.
Mental Math with Decimals
Recall that we can use compatible
numbers to make addition or subtraction
easier mentally.
The same concept still applies for
decimals.
Examples
Compensation Strategy with
Adding and Subtracting Decimals
Also recall that compensation is a technique
we used to change numbers in an addition or
subtraction problem to compatible numbers.
The key was:
Addition → Add/Subtract oppositely
Subtraction → Add/Subtract the same
Example
Use compensation to add or subtract the
following.
a) 2.8 + 2.3
b) 8.1 − 2.9
Example
You purchase 5 packs of batteries online.
The prices are $9.97, $11.97, $5.97, $6.97,
and $18.72. You pay using the $75 gift
card. How much credit is left on the gift
card?
Rounding Decimals
All previous rounding rules still hold. We
just need to be careful to round to the
correct value.
Examples
Examples
Rewrite each statement by rounding the
decimal to a number that is reasonable in
the real-life context.
a) A typical weight of an adult Percheron
horse is 1873.4 pounds.
b) Adult giraffes generally stand between
4.572 and 6.096 meters tall.
Homework #17
§7.1 - Pages 252-255
#4, 6, 8, 12, 18, 24, 40
§7.2 - Pages 262-265
#7, 10, 16