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3-1 Adding and Subtracting Decimals
DO NOW
Find the sum or difference.
1) -2 + 6
2) -3 + (-4)
3) 7 + (-5)
4) -2 – 2
5) 76 – (-42)
6) -21 – 15
3-1 Adding and Subtracting Decimals
Learn to add and subtract decimals.
3-1 Adding and Subtracting Decimals
• In order to add and subtract decimals, you
must first line up the decimals
• Next, they MUST HAVE the same
decimal length.
• To increase the number of decimal places,
you can add zeros after the decimal.
•If a number does not have a decimal,
put a decimal at the end of the number.
Add zeros to hold the place value
Ex: 23
23.0
3-1 Adding and Subtracting Decimals
Example: Find the sum.
66.8
+ 4.0
70.8
66.8 + 4
Use zero as a placeholder so that
both numbers have the same number
of digits after their decimal points.
Add each column just as you would
add integers.
Line up the decimal points.
3-1 Adding and Subtracting Decimals
Example A
Find the sum.
6.44 + 16
6.44
+ 16.00
22.44
Line up the decimal points.
Use zeros as placeholders.
Add.
3-1 Adding and Subtracting Decimals
Example A
Find the sum.
–8.33 + (–10.972)
8.330
+10.972
19.302
Line up the decimal points.
Use zeros as placeholders.
Add.
–19.302
Use the sign of the two
numbers.
3-1 Adding and Subtracting Decimals
Example A
Find the sum.
3.6 + (–9.65)
9.65
- 3.60
-6.05
Remember: Different signs – Eliminate!
Line up the decimal points.
Subtract. Answer has
sign of ‘bigger number’
3-1 Adding and Subtracting Decimals
• Remember to be careful with your signs.
Even if the operation is addition, if the
signs are different you are going to
subtract and take the sign of the larger
number.
• With subtraction problems, use KCS to
make it an addition problem.
3-1 Adding and Subtracting Decimals
Example B
Find the difference.
5.34 – 2.08
5.34
–2.08
3.26
Line up the decimal points.
Subtract.
3-1 Adding and Subtracting Decimals
Example B
Find the difference.
15.911 - 28
7 9 9 10
28.000
–15.911
-12.089
Use zeros as placeholders.
Line up the decimal points.
Subtract.
3-1 Adding and Subtracting Decimals
Find the difference.
-32.6 – (-15.86)
-32.6 + 15.86
32.60
–15.86
-16.74
KCS
Line up the decimal points.
Subtract.
3-1 Adding and Subtracting Decimals
Extra Example
During one month in the United States, 492.23
million commuter trips were taken on buses,
and 26.331 million commuter trips were taken
on light rail. What was the total number of trips
taken on buses and light rail? Estimate to check
whether your answer is reasonable.
492.230
+26.331
518.561
Use zero as a place holder.
Line up the decimal points.
Add.
The total number of trips was 518.561 million.
3-1 Adding and Subtracting Decimals
Extra Example
In 1999, 143.66 million bushels of corn were
grown in the United States. In 2000, the harvest
yielded 169.831 million bushels. What was the
total production for those two years? Estimate
to check whether your answer is reasonable.
143.660
+169.831
313.491
Use zero as a place holder.
Line up the decimal points.
Add.
The total number of bushels was 313.491 million.
3-1 Adding and Subtracting Decimals
Lesson Quiz
Find the sum.
1. 6.98 + (-14.27)
-7.29
2. –8.46 + (–19.2)
–27.66
Find the difference.
3. -6.72 – (-4.16)
-2.56
4. -24 – 3.8
-27.8
3-1 Adding and Subtracting Decimals
Lesson Quiz
5. Renee finished her first lap in the 200 m freestyle
event in 28.76 seconds. She completed the second
lap in 30.17 seconds. By how much did her time
increase in the second lap? Estimate to check
whether your answer is reasonable.
1.41 seconds
3-1 Adding and Subtracting Decimals
6. Identify the sum and then estimate to
check whether the answer is reasonable.
7.86 + 12.16
A. 20.02; estimate: 8 + 12 = 20
B. 19.16; estimate: 8 + 12 = 20
C. 20.02; estimate: 7 + 12 = 19
D. 19.16; estimate: 7 + 12 = 19
3-1 Adding and Subtracting Decimals
7. Identify the sum and then estimate to
check whether the answer is reasonable.
–9.32 + (–18.1)
A. –8.78; estimate: –9 + (–18) = –9
B. –27.42; estimate: –9 + (–18) = –9
C. –27.42; estimate: –9 + (–18) = –27
D. –8.78; estimate: –9 + (–18) = –27
3-1 Adding and Subtracting Decimals
8. Identify the difference and then estimate
to check whether the answer is reasonable.
7.63 – 3.25
A. 4; estimate: 7 – 3 = 4
B. 4.22; estimate: 7 – 3 = 4
C. 4.32; estimate: 8 – 3 = 5
D. 4.38; estimate: 8 – 3 = 5
3-1 Adding and Subtracting Decimals
9. Identify the difference and then estimate
to check whether the answer is reasonable.
35 – 2.7
A. 32; estimate: 35 – 3 = 32
B. 32.3; estimate: 35 – 3 = 32
C. 33; estimate: 35 – 2 = 33
D. 33.3; estimate: 35 – 2 = 33
3-1 Adding and Subtracting Decimals
10. Margaret took an exam that has two
parts. She completed the first part in 17.55
minutes and the second part in 32.36
minutes. By how much did her time
increase in the second part? Estimate to
check whether the answer is reasonable.
A. 16 min; estimate: 33 – 17 = 16
B. 15.11 min; estimate: 32 – 17 = 15
C. 14.81 min; estimate: 32 – 18 = 14
D. 10 min; estimate: 30 – 20 = 10