Transcript Addition and Subtraction of Decimals

Adding and Subtracting
Decimals
Today’s Learning Goals
 We will continue to use estimation as a way to
determine the reasonableness of our exact answers
with problems involving decimals.
 We will think about how to solve addition and
subtraction problems involving decimals with
fractions.
 We will think about how to solve addition and
subtraction problems involving decimals using our
knowledge of how to add and subtract whole
numbers.
Decimal Addition



Consider the following problem:
A jogger ran for 2.84 miles and then stopped to get a
drink of water. She started up again and ran for 3.69
more miles. How many miles did she run altogether?
What would you do to solve this problem?
Exactly…add 2.84 and 3.69 together.
What would be a good estimate to the answer?
Great…6.5 is a good estimate if you said that
2.84  3 and 3.69  3.5. So the problem
becomes close to 3 + 3.5 = 6.5!
Decimal Addition

How would you add 2.84 and 3.69 using single
fractions for each number?
Yes…
284
100
369
3.69 
100
2.84 
653
 6.53
100

Notice how the exact answer of 6.53 is close to our
estimate of 6.5!
Decimal Addition
How would you add 2.84 and 3.69 using decimals?
Correct…line up the decimal points and add as if they
were whole numbers. So, we have

1 1
2.84
+3.69
6.5 3

So, the jogger ran 6.53 miles
total. This is close to our
estimate of 6.5 miles!
Notice how we added as if they were whole numbers
because the single fractions numerators are those
whole numbers!
Decimal Subtraction
Consider the following problem:
A science lab had 15.34 grams of sulfuric acid. A scientist
used 6.78 grams of sulfuric acid for a chemistry experiment.
How many grams of sulfuric acid was left in the science lab?
 What would you do to solve this problem?
Exactly…subtract 6.78 from 15.34.


What would be a good estimate to the answer?
Great…8 is a good estimate if you said that 6.78  7
and 15.34  15. So the problem becomes close to
15 – 7 = 8!
Decimal Subtraction

How would you subtract 6.78 from 15.34 using
single fractions for each number?
Yes…
1534
100
678
6.78 
100
15.34 
856
 8.56
100

Notice how the exact answer of 8.56 is close to our
estimate of 8! You should always use your estimate
as a way to check the reasonableness of your exact
answer!
Decimal Subtraction
How would you subtract 6.78 from 15.34 using
decimals?
Correct…line up the decimal points and subtract as if they
were whole numbers. So, we have

14 12
1
15.34
– 6.78
8.5 6

So, the science lab has 8.56
grams of sulfuric acid left.
Again, this is close to our
estimate of 8!
Notice how we subtracted as if they were whole
numbers because the single fractions numerators are
those whole numbers!
Partner Work

You have 20 minutes to work on the following
problems with your partner.
For those that finish early
Samuel buys the following at the grocery store:
2 dozen eggs at $0.75 per dozen
1 pound of butter at $1.39
1 5-pound bag of sugar for $1.79
2 5-pound bags of flour at $1.19 each
1 8-ounce package of unsweetened chocolate for $1.64
1. What was the total bill for his groceries?
2. Suppose he didn’t have enough money to pay for
everything. So, he decided to buy just 1 bag of sugar
and 1 bag of flour. How much would his total bill be
then?
Big Idea from Today’s Lesson



We can change decimals to single fractions and then
add and subtract the fractions because we already
know how to do that.
When we add and subtract decimals, we want to add
and subtract things of the same-sized pieces (just
like we did with fractions). This is why we line up
decimal points.
We can add and subtract decimals just like they were
whole numbers because these are the whole
numbers in the numerators for the single fractions.
Homework


Complete Homework Worksheet.
Pgs. 118 – 119 (8, 9, 11, 14 – 19)