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Adding, Subtracting, and
Multiplying Decimals
Topic 1.1
Review: Place Values
Thousands
Hundreds
Tens
Ones
Decimal
Tenths
Hundredths
Thousandths
Ten-Thousandths
0 0 0 0 . 0 0 0 0
3 4 2 2 . 1 2 3 4Example:
Review: Place Values as Fractions
Thousands
Hundreds
Tens
Ones
Decimal
Tenths
Hundredths
Thousandths
Ten-Thousandths
0 0 0 0 . 0 0 0 0
1 . 1/10
Decimal Grids + Fractions
This grid is a 10 x 10
grid which means it
has ____ squares
1 2 3 4 5 6 7 8 9 10
12345678910
If I shade in all of the squares I’ll have ______ shaded squares
If I shade in half of the squares I’ll have _______ shaded squares
One fully shaded square is equal to one whole
Decimal Grids + Fractions
1 2 3 4 5 6 7 8 9 10
12345678910
= 1
1 2 3 4 5 6 7 8 9 10
12345678910
= 0.5
Because all 100 squares are filled in Because half of the 100 squares are filled in
Decimal Grids + Fractions
1 2 3 4 5 6 7 8 9 10
12345678910
= 0.2
1 2 3 4 5 6 7 8 9 10
12345678910
= 0.7
Because 20 out of 100 squares are filled in Because 70 out of 100 squares are filled in
Decimal Grids + Fractions
1 2 3 4 5 6 7 8 9 10
12345678910
Now, lets model 0.8 on the grid
0.8 = 8/10
8/10 of 100 is 80
So, how many squares should I fill in?
Adding on Decimal Grids (To the tenths place)
1 2 3 4 5 6 7 8 9 10
12345678910
Let’s take it a step further…. Consider the following equation:
0.4 + 0.5 = ?
Let’s shade in 0.4 first…
Now, let’s add 0.5 (or 50 squares)
How many squares are filled in now?
What would that be as a decimal?
Adding on Decimal Grids (To the hundredths place)
1 2 3 4 5 6 7 8 9 10
12345678910
Let’s take it a step further…. Consider the following equation:
0.42 + 0.54 = ?
Let’s shade in 0.42 first…
Now, let’s add 0.54 (or 54 squares)
How many squares are filled in now?
What would that be as a decimal?
At your tables…
1.Solve: 0.5 + 0.4
2.Solve: 0.32 + 0.26
3.Solve: 0.8 + 0.4
Subtracting on Decimal Grids (To the tenths
place)1 2 3 4 5 6 7 8 9 10
12345678910
Let’s take it a step further…. Consider the following equation:
0.5 - 0.4 = ?
Let’s shade in 0.5 first…
Now, take away 0.4 (or 40 squares)
How many squares are filled in now?
What would that be as a decimal?
At your tables…
1.Solve: 0.6 - 0.5
2.Solve: 0.55 - 0.28
3.Solve: 1 - 0.4
Multiplying on Decimal Grids
(To the tenths place)
1 2 3 4 5 6 7 8 9 10
12345678910
Let’s try multiplying 0.4 x 0.3
Fill in 0.4 first (vertically)
Then fill in 0.3 (horizontally)
Now, find where they overlap
There are 12 squares covered which means our answer is…
0.12
At your tables…
1.Solve: 0.5 x 0.2
2.Solve: 0.3 x 0.1
3.Solve: 0.2 x 0.6

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Topic 1.1

  • 3. Review: Place Values as Fractions Thousands Hundreds Tens Ones Decimal Tenths Hundredths Thousandths Ten-Thousandths 0 0 0 0 . 0 0 0 0 1 . 1/10
  • 4. Decimal Grids + Fractions This grid is a 10 x 10 grid which means it has ____ squares 1 2 3 4 5 6 7 8 9 10 12345678910 If I shade in all of the squares I’ll have ______ shaded squares If I shade in half of the squares I’ll have _______ shaded squares One fully shaded square is equal to one whole
  • 5. Decimal Grids + Fractions 1 2 3 4 5 6 7 8 9 10 12345678910 = 1 1 2 3 4 5 6 7 8 9 10 12345678910 = 0.5 Because all 100 squares are filled in Because half of the 100 squares are filled in
  • 6. Decimal Grids + Fractions 1 2 3 4 5 6 7 8 9 10 12345678910 = 0.2 1 2 3 4 5 6 7 8 9 10 12345678910 = 0.7 Because 20 out of 100 squares are filled in Because 70 out of 100 squares are filled in
  • 7. Decimal Grids + Fractions 1 2 3 4 5 6 7 8 9 10 12345678910 Now, lets model 0.8 on the grid 0.8 = 8/10 8/10 of 100 is 80 So, how many squares should I fill in?
  • 8. Adding on Decimal Grids (To the tenths place) 1 2 3 4 5 6 7 8 9 10 12345678910 Let’s take it a step further…. Consider the following equation: 0.4 + 0.5 = ? Let’s shade in 0.4 first… Now, let’s add 0.5 (or 50 squares) How many squares are filled in now? What would that be as a decimal?
  • 9. Adding on Decimal Grids (To the hundredths place) 1 2 3 4 5 6 7 8 9 10 12345678910 Let’s take it a step further…. Consider the following equation: 0.42 + 0.54 = ? Let’s shade in 0.42 first… Now, let’s add 0.54 (or 54 squares) How many squares are filled in now? What would that be as a decimal?
  • 10. At your tables… 1.Solve: 0.5 + 0.4 2.Solve: 0.32 + 0.26 3.Solve: 0.8 + 0.4
  • 11. Subtracting on Decimal Grids (To the tenths place)1 2 3 4 5 6 7 8 9 10 12345678910 Let’s take it a step further…. Consider the following equation: 0.5 - 0.4 = ? Let’s shade in 0.5 first… Now, take away 0.4 (or 40 squares) How many squares are filled in now? What would that be as a decimal?
  • 12. At your tables… 1.Solve: 0.6 - 0.5 2.Solve: 0.55 - 0.28 3.Solve: 1 - 0.4
  • 13. Multiplying on Decimal Grids (To the tenths place) 1 2 3 4 5 6 7 8 9 10 12345678910 Let’s try multiplying 0.4 x 0.3 Fill in 0.4 first (vertically) Then fill in 0.3 (horizontally) Now, find where they overlap There are 12 squares covered which means our answer is… 0.12
  • 14. At your tables… 1.Solve: 0.5 x 0.2 2.Solve: 0.3 x 0.1 3.Solve: 0.2 x 0.6