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ICEVI –The Nippon Foundation Mathematics Project

One of the concerns of the partners implementing the Nippon Foundation-supported higher education program was that not many students graduating from the school system were successfully enrolling in higher education. One of the significant reasons identified was the limited teacher training in mathematics instruction for students with visual impairment. The resultant lack of confidence and skills of teachers was directly impacting on the students’ access and achievement in mathematics in schools. ICEVI recognized this gap in teacher knowledge and developed a publication titled “Mathematics Made Easy for blind children” in 2005-06 in collaboration with the Overbrook Nippon Network on Educational Technology (ONNET). This publication is available on ICEVI website for free download. The Nippon Foundation came forward to support ICEVI to develop video instructional materials to improve the expertise of teachers to teach mathematics effectively to visually impaired students. The CEO of ICEVI, Dr. M.N.G. Mani, is heading this initiative as his expertise is in the area of Mathematics.

The first set of concept videos were piloted in a workshop in South Africa in 2018 involving teachers of mathematics, teacher educators, and teachers who are visually impaired. The participants worked through the concepts and instructions presented in each of the sample videos, and successfully understood methods of teaching mathematics. The project had a target of preparing at least 100 instructional videos every year on various topics of primary, secondary and senior secondary mathematics. ICEVI has established a dedicated YouTube channel https://www.youtube.com/c/ICEVIMathMadeEasy/ playlists which has 475 instructional videos on teaching concepts in mathematics, including teaching the abacus. ICEVI is pleased to advise that there are currently 3800+ subscribers and the rate of subscription is steadily increasing. The viewership of the instructional videos is also more than 400,000. ICEVI has initiated the process of preparing another 100 demonstration videos on mathematics concepts by teachers from the Philippines and Indonesia in 2023.

ICEVI believes that these open access, online instructional videos are a quality resource for individuals with visual impairments, parents and teachers, and promote children learning and enjoying mathematics.

List of Videos on ICEVI Math Made Easy YouTube Channel

https://www.youtube.com/c/ICEVIMathMadeEasy/videos

Sl. No. Title Playlist
1 ICEVI – Nippon Foundation Introduction General
2 Mathematics Video- teaching tips
3 ICEVI Math Made Easy – Messages
4 Adapting regular teaching aids
5 Math Videos – Present Status and Future Plans
6 Here is how we improvise teaching materials
7 Drawing experience to Visually Impaired Children
8 (a+b) x (a+b) Algebra
9 (a+b) x (a-b)
10 (x+a) x (x+b)
11 (x+a) X (x-b)
12 (x-a) x (x+b)
13 (a + b + c) x (a + b + c)
14 (x-a) x (x-b)
15 (a-b) x (a-b)
16 Expanded Form of a number Basic operations in Mathematics
17 Addition of numbers using Expanded Template
18 Complex addition using Expanded Form Template
19 Simple subtraction of numbers using Expanded Template
20 Complicated subtraction of numbers using Expanded Template
21 Decimal multiplication – Part 1 Decimal
22 Decimal multiplication – Part 2
23 Least Common Multiple Fractions
24 Greatest Common Divisor
25 Fractions – General Concepts
26 Whole to Fractions
27 Proper Fraction
28 Improper Fraction
29 Converting Improper Fraction into Mixed Fractions
30 Like, unlike and equivalent fractions
31 Means extremes property
32 Reducing fraction into lowest terms
33 Multiplicative inverse
34 Comparison of fractions
35 Sum of angles of a quadrilateral equals 360° Geometry
36 Angle formed on a semicircle equals 90°
37 Sum of angles of a triangle is equal to 180°
38 Major Angles – Part 1
39 Sixteen folds and geometrical shapes
40 Major Angles – Part 2
41 Complementary and Supplementary angles
42 Perimeter
43 Exterior angle of a cyclic quadrilateral equals the interior opposite angle
44 Centroid
45 Centroid divides the median in the ratio of 1: 2
46 Incentre
47 Circumcentre
48 Perimeter of a Semicircle
49 Angles on Minor and Major segments
50 Angle subtended at the centre
51 Concentric Circles
52 Area of a right angle triangle
53 Circles touching internally
54 Area of a Quadrilateral
55 All about Triangles
56 Forming all Types of Triangles
57 Rectangular Pathways – Part 1
58 Incircle of a right angle triangle
59 Rectangular Pathways – Part 2
60 Orthocentre
61 Pi and r – Relationship between the Radius and the Circumference
62 Plane, Side and Vertex
63 Inequalities – Additive property Inequalities
64 Inequalities – Multiplicative property
65 Inequalities – commutative and associative properties
66 Functions Characteristics
67 One-to-One Function
68 Many-to-One Function
69 Transversal – Part 2 – Vertically Opposite Angles through paper folding Lines
70 Transversal – Part 1 – Angles
71 Transversal – Part 5 – Explanation through Paper folding
72 Transversal – Part 4 – Perpendicular Transversal
73 Transversal – Part 3 – Parallel Lines
74 Intersecting and non-intersecting circles
75 Line Segments
76 Skew lines
77 Intersection and bisection
78 Horizontal and vertical
79 Collinear and non-collinear points
80 Equidistance and Concurrent lines
81 Matrices Introduction Matrices
82 Types of Matrices
83 Matrix addition
84 Scalar Matrix
85 Transpose of a Matrix
86 Negative of a Matrix
87 Symmetric Matrix
88 Matrix addition is commutative
89 Matrix Subtraction
90 Matrix subtraction is not commutative
91 Matrix Multiplication – General Concepts part 1
92 Matrix Multiplication – General Concepts part 2
93 Matrix Multiplication – General Concepts part 3
94 Matrix Multiplication – General Concepts part 4
95 Placement of elements in Matrix Multiplication part 1
96 Placement of elements in Matrix Multiplication part 2
97 Placement of elements in Matrix Multiplication part 3
98 Multiplication of 3X2 and 2X2 Matrix
99 Multiplication of 2X2 and 2X3 Matrix
100 Matrix multiplication involving negative numbers
101 Matrix multiplication (2X2) and (2X4) with negative numbers
102 Scalar Multiplication
103 Multiplication with an Identity matrix
104 Unit or Identity matrix
105 Multiplication of single digit numbers 8 and 5 Multiplication of Numbers
106 Multiplication of a single digit number 3
107 Multiplication of a double digit number
108 Multiplier, multiplicand, Dividend, Divisor and Quotient
109 Multiplication of three digit number
110 Multiplication involving a four digit number
111 Multiplication of a 3 digit multiplier and 2 digit multiplicand
112 Multiplication of a 4 digit multiplier with a 4 digit multiplicand
113 Multiplication of a 3 digit multiplier and 3 digit multiplicand
114 Multiplication of a 4 digit multiplier with 3 digit multiplicand
115 Ascending and Descending order Numbers
116 Number Line
117 Twin primes
118 Perfect Numbers
119 Cardinal and Ordinal Numbers
120 Odd and Even numbers
121 Prime Numbers
122 Composite Numbers
123 Predecessor and Successor
124 Natural numbers, whole numbers and integers
125 A Intersection B – Demonstration with Objects Set Theory
126 A Union B – Demonstration with Objects
127 Types of Sets
128 An Identity in Set Language
129 De Morgan’s Law on Set Difference – Part 1 – A– (B Ո C) = (A-B) U (A-C) – Through Shapes
130 De Morgan’s Law on Set Difference – Part 2 – A– (B U C) = (A-B) Ո(A-C) – Through Numbers
131 Equal and Equivalent Sets
132 A Union B – Demonstration with Numbers
133 A Intersection B – Demonstration with Numbers
134 De Morgan’s Law on Set Difference – Part 2 – A–(B Ո C) = (A-B) U (A-C) – Through Numbers
135 De Morgan’s Law on Set Difference – Part 1 – A–(B U C) = (A-B) Ո (A-C) – Through Shapes
136 A Union B – Demonstration with Tactile Materials
137 A Intersection B – Demonstration with Tactile Materials
138 Cartesian Product
139 Power Set
140 Roster Form and Set Builder Form
141 Set difference and Symmetric difference
142 Subset, proper and improper subsets
143 De Morgan’s Law on Complementation (A Ո B)C = AC U BC – Through Shapes
144 Test of divisibility for number 2 Tests of divisibility
145 Tests of divisibility for numbers 5 and 10
146 Test of divisibility for number 4
147 Test of divisibility for number 3
148 Test of divisibility for number 6
149 Test of divisibility for number 9
150 Tests of divisibility for number 11
151 Test of divisibility for number 12
152 Test of divisibility by number 15
153 Test of divisibility by 8
154 Pythagoras Theorem Trigonometry
155 Trigonometry – Introduction
156 Trigonometric Ratios – Part 1
157 Trigonometric Ratios – Part 2
158 Trigonometric Ratios of Angle 30 Degrees
159 Trigonometric Ratios of Angle 0 Degree
160 Trigonometric Ratios of Angle 45 Degrees
161 Trigonometric Ratios of Angle 60 Degrees
162 Trigonometric Ratios of Angle 90 Degrees
163 Cot Ө = Cos Ө / Sin Ө
164 Sin square theta + Cos square theta =1
165 1+ tan square theta = sec square theta
166 1+ cot square theta = Cosec square theta
167 Sec (90- Ө) = Cosec Ө and Cosec (90- Ө) = Sec Ө
168 Trigonometric identities :– Sin Ө x Cosec Ө = 1
169 Tan (90- Ө) = Cot Ө and Cot (90- Ө) = Tan Ө
170 Trigonometric identities :- Tan Ө x Cot Ө = 1
171 Tan Ө = Sin Ө / Cos Ө
172 Trigonometric identities :- Cos Ө x Sec Ө = 1
173 Sin (90 – Ө) and Cos (90 – Ө) when Ө is 30 and 60 degrees
174 Sec (90 – Ө) and Cosec (90 – Ө) when Ө is 45 degrees
175 Tan (90 – Ө) and Cot (90 – Ө) when Ө is 30 and 60 degrees

ABACUS

176 Instructional Videos for Learning Abacus General Videos
177 Introduction to Abacus
178 Terminology pertaining to Beads in the Abacus
179 Essential skills for learning abacus
180 Values of numbers in abacus
181 Concepts of clearing and setting abacus
182 Complement of a number
183 Dots in the Separating Bar
184 Abacus addition – General Rules Abacus Addition
185 Addition of Single Digit Numbers
186 Addition of Double Digit Numbers
187 Addition of double digit number with a single digit number example 63+9
188 Addition of Triple Digit Numbers
189 Addition of Triple Digit Numbers involving Zero
190 Addition of 4 Digit Numbers
191 Addition of a 4 Digit Number with a 2 digit number
192 Addition of a 4 Digit Number with a 3 digit number
193 Addition of a 2 digit number with a 4 digit number
194 Addition of a 5 Digit Number with a 4 digit number
195 Addition of a 5 Digit Number with a 4 digit number involving many zeros
196 Example of a mathematical operation in the same column of the abacus
197 Complicated additions made simple in Abacus
198 Abacus addition involving three numbers
199 Addition of three numbers involving variable digits.
200 Column wise abacus addition of three digit numbers
201 Random selection of columns for abacus addition
202 Column wise addition of numbers in abacus
203 Abacus Subtraction – General guidelines Abacus – Subtraction
204 Abacus Subtraction – Example: 43-32
205 Abacus Subtraction – Example: 82-19
206 Abacus Subtraction – Example: 378 – 179
207 Abacus Subtraction – Example: 984-234
208 Abacus Subtraction – Example: 842-599
209 Abacus Subtraction involving Zero
210 Abacus Subtraction involving Zero and multiple digits
211 Abacus Subtraction: Example 5804-4971
212 Abacus Subtraction giving many zeros in the result
213 Abacus subtraction involving zeros: Example 5001-408
214 Abacus subtraction – Example 20003-322
215 Abacus subtraction – Example 1111-999
216 Abacus Subtraction involving larger digits: Example: 105711-4305
217 Abacus Subtraction involving larger digits: Example: 77777-8888
218 Abacus subtraction – example 41123-9008
219 Abacus Subtraction involving larger digits: Example: 232824-99821
220 Abacus Subtraction involving larger digits: Example: 172844-81234
221 Abacus multiplication – General guidelines Abacus – Multiplication
222 Setting of Multiplier, Multiplicand and Result
223 Multiplication process using Abacus
224 Need for the knowledge of multiplication tables for single digit numbers
225 Multiplication of Single Digit Numbers using Abacus
226 Multiplication of Single Digit Numbers where result is also a single digit number
227 Multiplication of double digit numbers
228 Multiplication of Double Digit numbers – Example: 38×29
229 Multiplication of double digit numbers – Example: 23×45
230 Multiplication of double digit numbers – Example: 49×51
231 Multiplication of double digit numbers – Example: 21×34
232 Multiplication of double digit numbers – Example: 47×39
233 Multiplication of double digit numbers – Example: 66×77
234 Place values of multiplied numbers using double digit multiplier and multiplicand
235 Multiplication of Double Digit Multiplier and a single digit Multiplicand
236 Multiplication of Double Digit Multiplier and a single digit Multiplicand – Example: 36×2
237 Multiplication of Double Digit Multiplier and a single digit Multiplicand – Example: 34×2
238 Multiplication of double digit multiplier and single digit multiplicand – Example: 45×9
239 Multiplication of double digit multiplier and single digit multiplicand – Example: 45×8
240 Multiplication of triple digit multiplier and single digit multiplicand – Example: 123×4
241 Multiplication of a single digit multiplier and three digits multiplicand – Example: 4×123
242 Multiplication of four digit multiplier and single digit multiplicand – Example: 1324×6
243 Multiplication of a single digit multiplier and four digits multiplicand – Example: 6×1324
244 Flexible procedures in setting digits of results in Abacus multiplication
245 Flexible procedures in setting digits of results in Abacus multiplication – Example: 84×73
246 Abacus multiplication involving zero – Example: 405×307
247 Abacus multiplication involving zero – Example: 428×505
248 Abacus multiplication involving zero – Example: 4502×3006
249 Alternate modes of Multiplication: Example 24×32
250 Alternate modes of Multiplication: Example 325×46
251 Alternate modes of Multiplication: Example 305×46
252 Abacus Division – General Concepts part 1 Abacus – Division
253 Abacus Division – General Concepts continuation
254 Abacus Division – Setting Quotient
255 Link between Quotient setting and Remainder values
256 Abacus Division – Beauty of the Quotient setting Rule
257 Abacus Division – How important the quotient sitting rule is
258 Short division: Example – 912÷4
259 Abacus Short Division – Example – 384÷6
260 Abacus Division of small digits – Example: 283÷9
261 Abacus Division – treating every stage of division as a fresh division: Example: 714÷5
262 Abacus Division – treating every stage of division as a fresh division: Example: 666÷3
263 Abacus Division – treating every stage of division as a fresh division: Example: 123÷5
264 Abacus Division – Triple digit dividend and a single digit divisor
265 Abacus Division – Triple digit dividend and a single digit divisor
266 Abacus Division of small digits – Example: 238÷3
267 Abacus Division of small digits – Example: 837÷7
268 Abacus Division – Numbers involving zeros
269 Abacus Division – Dividend having same numbers
270 Abacus Division – four digit dividend and one digit divisor – Example: 9098÷3
271 Abacus Division – four digit dividend and one digit divisor – Example: 3612÷4
272 Abacus Division – four digit dividend and one digit divisor – Example: 4001÷9
273 Abacus Division – four digit dividend involving many zeros – Example: 3070÷4
274 Abacus Division – four digit dividend involving many zeros – Example: 4500÷3
275 Abacus Division – four digit dividend involving many zeros – Example: 6100÷7
276 Abacus Division example 51515÷6
277 Abacus Division – Concept of assumed quotient – Method 1
278 Abacus Division – Demonstration of assumed quotient – Method 1
279 Division of two digit dividend by two digit divisor – Example 84÷23
280 Division of two digit dividend by two digit divisor – Example 91÷25
281 Division of two digit dividend by two digit divisor – Example 91÷15
282 Division of two digit dividend by two digit divisor – Revising Assumed Quotient – Example 91÷15
283 Abacus Division – Concept of assumed quotient – Method 2
284 Abacus Division – Demonstration of assumed quotient Method 2
285 Abacus Division – Adjustment of the assumed quotient – Method 2
286 Abacus Division – what happens when the assumed quotient is larger than the real quotient – Example: 3588÷46
287 Exemption to the assumed quotient rule – Example: 219÷20
288 Exemption and Adoption of the assumed quotient rule in the same problem – Example: 336÷21
289 Application of the assumed quotient exemption rule multiple times in the same problem – Example: 3333÷33
290 Abacus Division – three digit dividend and two digit divisor – Example: 650÷25
291 Abacus division-three digit dividend and two digit divisor with the highest digits of the dividend and divisor being the same
292 Adjustment in the assumed quotient
293 Assumed quotient is the Real Quotient with a single digit remainder
294 Assumed quotient is the Real Quotient with a double digit remainder
295 Getting quotient involving zero in the division problem example 2542/36
296 Adjustment of assumed quotient in every division process.
297 Same digits quotient and remainder involving zero
298 Getting a quotient involving zero in the division problem example 4263 ÷ 21
299 Getting a quotient involving zero at the end of the quotient
300 Double digit divisor and 4 digit number with 3 zeros
301 Double digit divisor and 5 digit Dividend
302 Double digit divisor and 5 digit Dividend – Example: 30,001÷44
303 Double digit divisor and 5 digit Dividend – Example: 11111÷55
304 Double digit divisor and 5 digit Dividend – Example: 55555÷44
305 Triple digit divisor and Triple Digit Dividend – Example: 965÷324 which gives a three digit remainder
306 Triple digit divisor and Triple Digit Dividend – Example: 794÷246 which gives a two digit remainder
307 Triple digit divisor and Triple Digit Dividend – Example: 875÷289 which gives a single digit remainder
308 Triple digit divisor and Triple Digit Dividend – Example: 926÷123 where adjustment in assumed quotient is necessary
309 Triple digit divisor and Triple Digit Dividend – Example: 926÷123 where a safe method is adopted in selecting the assumed quotient
310 Triple digit divisor and Four Digit Dividend – Example: 4567÷296
311 Assumed quotient of higher digit divisors – Erring on the lower side is safe
312 Assumed quotient – Erring on the lower side for safety – Example: 1716÷217
313 Assumed quotient – Erring on the lower side for safety – Example: 1716÷296
314 Four digit dividend and three digit divisor division– Example: 8888÷777
315 Use of two abacuses for higher level operations
316 Division involving four digit dividend and three digit divisor – example: 1758÷324
317 Division involving four digit dividend and three digit divisor – example: 8436÷267
318 Four digit dividend and three digit divisor with zero giving zero as a part of the quotient too: Example: 6747÷330
319 Division involving four digit dividend and three digit divisor – example: 2222÷444
320 Four digit dividend and three digit divisor involving higher digits – Example: 9999÷888
321 Four digit dividend and three digit divisor involving zeros in dividend and divisor – example: 9100÷606
322 Division involving five digit dividend and three digit divisor – example: 78142÷236 – Part 1
323 Division involving five digit dividend and three digit divisor – example: 78142÷236 – Part 2
324 Division involving five digit dividend and four digit divisor – Example: 51902÷4235
325 Division involving five digit dividend and four digit divisor – Example: 51902÷4325
326 Abacus Decimal Operations Abacus decimal addition
327 Conversion of Decimal Numbers to whole numbers
328 Dealing with the addition of parts of Decimal Numbers
329 Using two Abacuses for Decimal Addition
330 Using a single Abacus for Decimal Addition
331 Separate addition processes of whole number and decimal parts – Example: 49.86+75.356
332 Separate addition processes of whole number and decimal parts – Example : 756.212+32.989
333 Separate addition processes of whole number and decimal parts – Example : 756.878+329.989
334 Separate addition processes and using the abacus for reference
335 Making single digit adjustments in the decimal parts
336 Making double digit adjustments in the decimal points
337 Making triple digit adjustments in the decimal portions
338 Making triple digit adjustment in one decimal number
339 Making varied digit adjustments in the decimal parts – Part 1
340 Making varied digit adjustments in the decimal parts – Part 2
341 Which method is most suitable for decimal addition
342 Decimal addition – Example – 78.4 + 257.4237
343 Decimal addition – Example – 438.5678 + 65.42378
344 Abacus decimal subtraction – General guidelines Abacus decimal Subtraction
345 Decimals subtraction – example 83.674-56.256
346 Decimals subtraction – example 183.67-5.256
347 Decimal subtraction – example 83.256-56.674
348 Subtracting whole numbers and decimal numbers separately – Example – 83.256-56.674
349 Subtracting whole numbers and decimal numbers separately Example – 183.25-56.674
350 Decimal Multiplication process using Abacus Abacus decimal Multiplication
351 Multiplication of Decimal numbers – Example: 3.8×2.9
352 Multiplication of Decimal numbers – Example: 2.3×4.5
353 Multiplication of Decimal numbers – Example: 4.9×5.1
354 Multiplication of Decimal numbers – Example: 2.1×3.4
355 Multiplication of Decimal numbers – Example: 13.24×0.6
356 Multiplication of Decimal numbers – Example: 4×1.23
357 Multiplication of Decimal numbers – Example: 6×132.4
358 Multiplication of Decimal numbers – Example: 4.7×3.9
359 Multiplication of Decimal numbers – Example: 6.6×7.7
360 Multiplication of Decimal numbers – Example: 8.4×7.3
361 Multiplication of Decimal numbers – Example: 40.5×3.07
362 Multiplication of Decimal numbers – Example: 4.28×5.05
363 Multiplication of Decimal numbers – Example: 45.02×30.06
364 Division of Decimal numbers – General Guidelines Abacus decimal Division
365 Decimal Division – Example: 175.6÷2.3
366 Decimal Division – Example: 254.2÷3.6
367 Getting Decimal Number in the Divisor
368 Decimal division – Example: 21.9÷2
369 Decimal division – Example : 27.92÷0.42
370 Decimal division – Example : 6.5÷0.25
371 Decimal division – Example : 67.47÷3.3
372 Decimal division – Example : 40÷0.54
373 Addition of fractions in Abacus – General Rules Abacus Fraction Addition
374 Addition of Fractions : Example : 2/7 + 3/5
375 Addition of Fractions : Example : 6/7 + 4/5
376 Addition of Fractions : Example : 5 6/7 + 7 4/5
377 Addition of Fractions : Example : 12 7/9+14 2/7
378 Addition of Fractions : Example : 24 13/16+27 1/4
379 Addition of Fractions : Example : 24 11/16+27 1/4
380 Addition of Fractions : Example : 14/15+ 4/5
381 Addition of Fractions : Example: 135 3/4+98 6/7
382 Addition of Fractions : Example : 44 11/15+45 19/20
383 Addition of Fractions : Example: 156 11/12 +76 7/8
384 Addition of Fractions : Example: 76 10/13+18 20/39
385 Addition of Fractions : Example: 1190 1/9+124 7/11
386 Addition of Fractions : Example: 15/16+ 14/15
387 Addition of Fractions : Example: 5/16+4/15
388 Addition of Fractions : Example: 45 9/12+51 7/11
389 Addition of Fractions : Adjustment of values at the end: Example: 1/4 + 3/8
390 Addition of Fractions : Adjustment of values at the end: Example: 3/4 + 5/8
391 Abacus – Fraction Subtraction – General Guidelines Abacus Fraction Subtraction
392 Abacus – Fraction Subtraction – 7/9 – 1/3
393 Abacus – Fraction Subtraction – 9 5/8 – 6 1/12
394 Abacus – Fraction Subtraction – 9 5/8 – 6 11/12
395 Abacus – Fraction Subtraction – 64 6/7– 13 20/21
396 Abacus – Fraction Subtraction – 54 7/9 – 45 9/10
397 Abacus – Fraction Subtraction – 325 4/9 – 9 11/18
398 Abacus – Fraction Subtraction – 4333 23/30 – 101 39/45
399 Abacus – Fraction Subtraction – 524 12/13 – 453 9/11
400 Abacus – Fraction Subtraction – 546 5/11 – 417 7/17
401 Abacus – Fraction Subtraction – 546 3/11 – 417 7/17
402 Abacus – Fraction Subtraction – 43 3/5 – 21 4/111
403 Abacus – Fraction Subtraction – 1 3/5 – 80/111
404 Abacus Multiplication – Simple fractions Abacus Fraction Multiplication
405 Abacus Multiplication – Cancellation Principle – Example: 2/3 x 9/10
406 Abacus Multiplication – Cancellation principle – Example: 3/4 x 4/9
407 Abacus Multiplication – Cancellation- Example: 6/7 x 8/9
408 Abacus Multiplication, Addition and Subtraction – Key difference – Example 1
409 Abacus Multiplication, Addition and Subtraction – Key difference – Example 2
410 Abacus Multiplication – General Rules for mixed fractions
411 Abacus Multiplication involving one digit fractions : principles
412 Abacus Multiplication : Example 7 2/3 X 11 1/4
413 Abacus Multiplication : Example 4 2/9 X 7 1/4
414 Abacus Multiplication : Example: 12 3/10 x 1 1/3
415 Abacus Multiplication : Example: 13 1/5 x 15 2/5
416 Abacus Multiplication : Example: 85 3/5 x 126 1/4
417 Abacus Multiplication : Example: 50 5/8 x 61 2/5
418 Fraction Division – General Guidelines Abacus Fraction Division
419 Fraction Division : Single digit examples
420 Fraction Division : Cancellation before division
421 Fraction Division: Example – 103 3/5 ÷ 1 3/4
422 Fraction Division: Conversion through decimals – Example: 254 1/5÷3 3/5
423 Fraction Division: Conversion through decimals – Example: 67 47/100 ÷ 3 3/10
424 Fraction Division: Without conversion into decimals – Example: 67 47/100 ÷ 3 3/10
425 Fraction Division: Without conversion into decimals – Example: 23 7/12 ÷ 11 8/9
426 Fraction Division: With conversion into decimals – Example: 23 7/12÷ 11 8/9
427 Fraction Division: Without conversion into decimals – Example: 455 11/18 ÷ 32 7/9
428 Fraction Division: Without conversion into decimals – Example: 2201 7/8624 3/4
429 Fraction Division: Fractions involving zero – Example: 6 91/105 ÷ 3 61/70
430 Fraction Division: Fractions involving zero, Doing Cancellations at the beginning – Example: 6 91/105 ÷ 3 67/70
431 Fraction Division: Fractions involving zero – Example: 101 7/10 ÷ 10 1/70
432 Fraction Division: Fractions involving zero – Example: 6 121/1001 ÷ 2 1/10
433 Fraction Division: Fractions involving higher digit whole numbers – Example: 612 1/9 ÷ 34 1/10
434 Abacus – Square Roots – General Guidelines Abacus Square Roots
435 Finding the Square root of a Perfect Square – Example : 324
436 Finding the Square root of a Perfect Square – Example : 576
437 Finding the Square root of a Perfect Square – Example : 576 with the application of assumed quotient rule
438 Finding the Square root of a Perfect Square – Example : 1296 with the application of assumed quotient rule
439 Finding the Square root of a Perfect Square – Example : 4225
440 Square root of Multiple digit numbers – Example : 103041
441 Square root of Multiple digit numbers – Example : 186624
442 Square root of odd digit numbers – Example : 55225
443 Square root of odd digit numbers – Example : 96721
444 Square root with Zero – Example : 91,809
445 Square root of a number with two zeros as the lowest digits – Example : 96,100
446 Square root of a number with two zeros as the lowest digits – Example : 53600
447 Square root of a number with one zero as the lowest digit – Example : 96,120
448 An even digit number with many zeros at the end can never be a perfect square
449 An even digit number with many zeros at the end can never be a perfect square – Example 4000
450 Square root of odd digit numbers – Reducing the Groups : Example : 15129
451 Square root of odd digit numbers – Reducing the Groups : Example : 24649
452 Square root of Imperfect Square : 24697
453 Square root of Imperfect Square : 46369
454 Square root of an Imperfect Square : 84697
455 Square root of an Imperfect Square with 3 decimal digits: Example: 84693
456 Square root of six digit numbers – with 3 decimal digits: Example : 186834
457 Square root of six digit numbers involving zeros as lower digits – Example : 117000
458 Square root of six digit numbers involving four zeros as lower digits – Example : 120000
459 Square root of numbers involving zeros at the end
460 Square root of six digit numbers involving four zeros as lower digits – Example : 200000
461 Square root of seven digit number involving six zeros as lower digits – Example : 5000000
462 Square root of seven digit numbers involving many zeros – Example : 6000057
463 Square root of seven digit numbers involving alternate sets of zeros – Example : 4006500
464 Square root of eight digit numbers involving four zeros as lower digits – Example : 12100000
465 Problems dealing with Percentage – General Guidelines Abacus Percentage
466 Problems dealing with Percentage – Example 2.3% of 45
467 Problems dealing with Percentage – Example 5.2% of 176
468 Problems dealing with Percentage – Example 6% of 13.24
469 Problems dealing with Percentage – Example 4.28% of 505
470 Percentage – conversion to fractions – Example 25% of 624
471 Percentage – conversion to fractions – Example 2.5% of 624
472 Percentage – conversion to fractions – Example 25% of 6249
473 Percentage – conversion to fractions – Example 25% of 6249 – Alternate method – Extempore
474 Percentage – conversion to fractions – Example 31% of 8357
475 The Amazing Abacus
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