Decimals
What is a decimal
A piece of a whole
(think about dollars and cents)
You can add, subtract, multiply and divide decimals.
Multiplying Decimals
• Multiplying decimals is just like multiplying fractions!
• Model the value of your first decimal by shading it in.
• Model the value of your second decimal by drawing diagonal lines.
The Hundreds Grid
• The whole grid represents the whole number 1
1•Each row or column represents one-tenth (0.1) of the whole.
•Each individual unit represents one-hundredth (0.01) of the whole.
Model 0.1 x 0.3
Algorithm
0.1
0.3
0.03
x
The product is determined by the number of units that are overlapping with color (shaded and striped)
Model 0.4 x 0.3
Algorithm
0.4
0.3
0.12
x
The product is determined by the number of units that are overlapping with color (shaded and striped)
Model 0.9 x 0.1
Algorithm
0.9
0.1
0.09
x
The product is determined by the number of units that are overlapping with color (shaded and striped)
Decimals—Let’s take a look!
0.1 0.4 0.9
x 0.3 x 0.3 x 0.1
0.03 0.12 0.09
DecimalsMultiplying• Don’t worry about the decimal• Align the numbers on the right• Count the number of digits AFTER the decimal. In the answer, move the decimal that many places0.74 x 3.2 0. 74
x 3 . 2
2.368
3 digits after the decimal
Move the decimal 3 places
Shoot for the STARS!Kendra created a 5-day study
schedule for her exams. If the pattern continues, how many hours will she study of the fifth day?
The table shows the number of hours she studies in the first three days.
A) 3 B) 4 C) 4.5 D)3.75
Day 1 2 3
Hours 0.75 1.5 2.25
Kendra created a 5-day study schedule for her exams. If the pattern continues, how many hours will she study of the fifth day?
3/5 is between which two fractions?
I made a chart and noticed that she was multiplying each day by 0.75.
On the 5th day, Kendra would study for 3.75 hours on the 5th day.
Studied 1st day for 0.75 hrs2nd day for 1.5 hrs3rd day 2.25 hrs
Day 1 2 3
Hours 0.75 1.5 2.25
1 x 0.75 = 0.75
2 x 0.75 = 1.50
3 x 0.75 = 2.25
4 x 0.75 = 3.00
5 x 0.75 = 3.75
Speed Test
1. Get a speed test, marker, and eraser.
2. Make sure your marker works!
3.You have 1 minute to complete as many problems as you can.
4. Graph your results. Keep the graph in your notebook.
5. We will do this every day.
Assignment
• Measuring Up Pg.
DecimalsDividing• There cannot be any decimals in the number outside the “house” (divisor)• Move the decimals to make it a whole #• If you move the decimals in the divisor, move the decimal in the dividend.• Push the decimal up
9.156 0.4
22.890 4 9 1 5 6. .
Move the decimal one place
Shoot for the STARS!Example 1
A school took in a total of $1,773.75 during the run of its spring musical. The cost per ticket was $2.75. How many tickets were sold?
Dividing Decimals
What is the question asking?
How many tickets were sold.
2 7 5 1 7 7 3 7 5. .
How do we find out how many tickets were sold?
Decimals
= 645
If the cost per ticket is $2.75 and the school made $1,773.75, then there were 645 tickets sold.
2 7 5 1 7 7 3 7 5. .Move the decimals 2 places and push the decimal up.
Decimals
Is our answer reasonable?• Does the answer make sense?• Does the answer
COMPLETELY answer the question?
Dividing DecimalsExample 2
Arnold earned $29.75 in 3.5 hours. How much did he earn per hour?
Decimals
What is the question asking?
How much did he earn per hour.
3 5 2 9 7 5. .
How do we find out how much he earned per hour?
Decimals
= 8.50
Arnold worked 3.5 hours and made $29.75, therefore, he earned $8.50 per hour.
Move the decimals 1 place and push the decimal up.
3 5 2 9 7 5. .
3 5 2 9 7 5.
Decimals
Is our answer reasonable?• Does the answer make sense?• Does the answer
COMPLETELY answer the question?
Shoot for the STARSExample 3
Sarah drove a total of 101.6 miles. She got 25.4 miles per gallon. How many gallons of gas did she use on her trip?
Decimals
= 4
If she drove 101.6 miles, and she got 25.4 miles per gallon, she used 4 gallons of gas.
Move the decimals 1 place and push the decimal up.
2 5 4 1 0 1 6. .
2 5 4 1 0 1 6
What has to happen before we can divide?
Ex 4: 8.7 ÷ 3
Ex 5: 5.8 ÷ 4
Ex 6: 9.81 ÷ 0.3
Ex 7: 0.0132 ÷ 0.22
Class Work
Measuring Up: Pg. 19: 3-13 odd, 15-17
Advanced: Glencoe Pg. 150-151 # 25-39, 49-51, 54, 55
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