SECTION 4-3 Arithmetic in the Hindu-Arabic System Slide 4-3-1.
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Transcript of SECTION 4-3 Arithmetic in the Hindu-Arabic System Slide 4-3-1.
![Page 1: SECTION 4-3 Arithmetic in the Hindu-Arabic System Slide 4-3-1.](https://reader035.fdocuments.net/reader035/viewer/2022070402/56649f265503460f94c3cad4/html5/thumbnails/1.jpg)
SECTION 4-3
• Arithmetic in the Hindu-Arabic System
Slide 4-3-1
![Page 2: SECTION 4-3 Arithmetic in the Hindu-Arabic System Slide 4-3-1.](https://reader035.fdocuments.net/reader035/viewer/2022070402/56649f265503460f94c3cad4/html5/thumbnails/2.jpg)
ARITHMETIC IN THE HINDU-ARABIC SYSTEM
• Expanded Form• Historical Calculation Devices
Slide 4-3-2
![Page 3: SECTION 4-3 Arithmetic in the Hindu-Arabic System Slide 4-3-1.](https://reader035.fdocuments.net/reader035/viewer/2022070402/56649f265503460f94c3cad4/html5/thumbnails/3.jpg)
EXPANDED FORM
Slide 4-3-3
By using exponents, numbers can be written in expanded form in which the value of the digit in each position is made clear.
![Page 4: SECTION 4-3 Arithmetic in the Hindu-Arabic System Slide 4-3-1.](https://reader035.fdocuments.net/reader035/viewer/2022070402/56649f265503460f94c3cad4/html5/thumbnails/4.jpg)
EXAMPLE: EXPANDED FORM
Slide 4-3-4
Write the number 23,671 in expanded form.
Solution
4 3 2 1 02 10 3 10 6 10 7 10 1 10
![Page 5: SECTION 4-3 Arithmetic in the Hindu-Arabic System Slide 4-3-1.](https://reader035.fdocuments.net/reader035/viewer/2022070402/56649f265503460f94c3cad4/html5/thumbnails/5.jpg)
DISTRIBUTIVE PROPERTY
Slide 4-3-5
For all real numbers a, b, and c,
For example,
.b a c a b c a
4 4 4
4
3 10 2 10 3 2 10
5 10 .
![Page 6: SECTION 4-3 Arithmetic in the Hindu-Arabic System Slide 4-3-1.](https://reader035.fdocuments.net/reader035/viewer/2022070402/56649f265503460f94c3cad4/html5/thumbnails/6.jpg)
EXAMPLE: EXPANDED FORM
Slide 4-3-6
Use expanded notation to add 34 and 45.
1 0
1 0
1 0
34 3 10 4 10
45 4 10 5 10
7 10 9 10 79
Solution
![Page 7: SECTION 4-3 Arithmetic in the Hindu-Arabic System Slide 4-3-1.](https://reader035.fdocuments.net/reader035/viewer/2022070402/56649f265503460f94c3cad4/html5/thumbnails/7.jpg)
DECIMAL SYSTEM
Slide 4-3-7
Because our numeration system is based on powers of ten, it is called the decimal system, from the Latin word decem, meaning ten.
![Page 8: SECTION 4-3 Arithmetic in the Hindu-Arabic System Slide 4-3-1.](https://reader035.fdocuments.net/reader035/viewer/2022070402/56649f265503460f94c3cad4/html5/thumbnails/8.jpg)
HISTORICAL CALCULATION DEVICES
Slide 4-3-8
One of the oldest devices used in calculations is the abacus. It has a series of rods with sliding beads and a dividing bar. The abacus is pictured on the next slide.
![Page 9: SECTION 4-3 Arithmetic in the Hindu-Arabic System Slide 4-3-1.](https://reader035.fdocuments.net/reader035/viewer/2022070402/56649f265503460f94c3cad4/html5/thumbnails/9.jpg)
ABACUS
Slide 4-3-9
Reading from right to left, the rods have values of 1, 10, 100, 1000, and so on. The bead above the bar has five times the value of those below. Beads moved towards the bar are in “active” position.
![Page 10: SECTION 4-3 Arithmetic in the Hindu-Arabic System Slide 4-3-1.](https://reader035.fdocuments.net/reader035/viewer/2022070402/56649f265503460f94c3cad4/html5/thumbnails/10.jpg)
EXAMPLE: ABACUS
Slide 4-3-10
Which number is shown below?
Solution1000 + (500 + 200) + 0 + (5 + 1) = 1706
![Page 11: SECTION 4-3 Arithmetic in the Hindu-Arabic System Slide 4-3-1.](https://reader035.fdocuments.net/reader035/viewer/2022070402/56649f265503460f94c3cad4/html5/thumbnails/11.jpg)
LATTICE METHOD
Slide 4-3-11
The Lattice Method was an early form of a paper-and-pencil method of calculation. This method arranged products of single digits into a diagonalized lattice.
The method is shown in the next example.
![Page 12: SECTION 4-3 Arithmetic in the Hindu-Arabic System Slide 4-3-1.](https://reader035.fdocuments.net/reader035/viewer/2022070402/56649f265503460f94c3cad4/html5/thumbnails/12.jpg)
EXAMPLE: LATTICE METHOD
Slide 4-3-12
Find the product by the lattice method.38 794
7 9 4
3
8
SolutionSet up the grid to the right.
![Page 13: SECTION 4-3 Arithmetic in the Hindu-Arabic System Slide 4-3-1.](https://reader035.fdocuments.net/reader035/viewer/2022070402/56649f265503460f94c3cad4/html5/thumbnails/13.jpg)
EXAMPLE: LATTICE METHOD
Slide 4-3-13
Fill in products
2 1
2 7
1 2
5 6
7 2
3 2
7 9 4
3
8
![Page 14: SECTION 4-3 Arithmetic in the Hindu-Arabic System Slide 4-3-1.](https://reader035.fdocuments.net/reader035/viewer/2022070402/56649f265503460f94c3cad4/html5/thumbnails/14.jpg)
EXAMPLE: LATTICE METHOD
Slide 4-3-14
Add diagonally right to left and carry as necessary to the next diagonal.
2 1
2 7
1 2
5 6
7 2
3 2
1 7 2
0
21
3
![Page 15: SECTION 4-3 Arithmetic in the Hindu-Arabic System Slide 4-3-1.](https://reader035.fdocuments.net/reader035/viewer/2022070402/56649f265503460f94c3cad4/html5/thumbnails/15.jpg)
EXAMPLE: LATTICE METHOD
Slide 4-3-15
Answer: 30,172
2 1
2 7
1 2
5 6
7 2
3 2
1 7 2
0
21
3
![Page 16: SECTION 4-3 Arithmetic in the Hindu-Arabic System Slide 4-3-1.](https://reader035.fdocuments.net/reader035/viewer/2022070402/56649f265503460f94c3cad4/html5/thumbnails/16.jpg)
EXAMPLE: NINES COMPLEMENT METHOD
Slide 4-3-16
Use the nines complement method to subtract 2803 – 647.
Solution
2803 2803 2803 2155
647 0647 +9352 1
12,155 2156
Step 1 Step 2 Step 3 Step 4