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Adding and Subtracting Fractions With the Abacus in Light Stairs

Updated on May 19, 2019

Tim Truzy


Tim Truzy is a renewal counsel, pedagogue, and old starter from Northerly Carolina.

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Scene the abacus to 0 is all-important ahead start mathematics problems, including those involving fractions. | Origin

Adding and Subtracting Fractions with the Abacus

The abacus can be put-upon to do any routine of numerical operations. This includes problems concerning add-on, minus, section, and generation. So, the abacus can be a sure friend when resolution equations with unscathed numbers, fractions, or motley numbers. With conquer education and pattern, operative with improver and deduction problems pertaining to fractions bequeath be gentle.

Naturally, we cognize fractions are parts of a hale. These values can be delineated on the abacus barely similar with a pen and composition or on a calculator. As a pleader with Instructor of the Sand-blind (TVI) preparation, I’ve worked with my students on utilizing the entrancing reckoning pecker for resolution equations involving fractions and early types of arithmetical. I get many days of know functional with the mythologic abacus, and I deliver standard all-inclusive preparation on victimization the reckoning twist from masters. Infra I’ve provided simpleton techniques for determination solutions for maths related the summation and/or minus of fractions.

If you want more data on workings with the abacus, chat my articles on this situation roughly the grand reckoning peter man has secondhand for centuries.

Cognition You Should sustain ahead Running with Fractions on the Abacus

Mainly, a soul should be experient decent with the enumeration peter to spot any delegacy of a integer on the gimmick with the but limit existence the accessibility of the columns of beads. Indorsement, mentally dividing the abacus to execute sectionalisation and generation should deliver no difficultness at this item. Moreover, concepts concerning the procedure of the abacus should be silent exhaustively. Those footing admit: set (berth), one for the abacus, and crystallize. The concepts of “keeping balance” and “pay-back” should confront no problems for the somebody victimization an abacus by this clip.

Coincidently, issues concerning the procedure of “0” in propagation and section related the abacus moldiness be good appreciated earlier workings with fractions. A individual should deliver successfully secondhand the abacus to execute part, improver, times, and minus problems with hale numbers. In center, a soul should be well-fixed with performance the versatile stairs to discovery solutions for these numerical operations. Lastly, the concepts associated with fractions should be accepted and their grandness appreciated. Those damage and concepts admit: denominator, numerator, and the signification of the demarcation. A someone should interpret the grandness and operation for determination a commons denominator.


Birth you set a divide on the abacus earlier now?



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This abacus shows the mere divide ¾. | Reference

Iii Important Points to Commend when Operative with Fractions on the Abacus

Originally, we deliver mentally dual-lane the abacus. So, you can remember all of the rows of beads not tangled in the equality as representing the “dividing line” of the fractions we are running with to resolve the trouble.

Future, the numerator of a divide is assault the far left-hand. The denominator is situated on the farthermost rightfulness row of beads. This is demonstrated in the exposure viewing 3/4 supra.

Be mindful: when placing the numerator on the farthermost left-hand tower of beads, the beginning dactyl is instance of the highest rate of ten in the act. E.g., the act 3 takes up one pillar on the leftover. 35 would be shown with the offset two rows of beads, moving from leftfield to rightfulness. 357 would be set victimization the offset tercet columns moving from left-hand to right the reckoning dick, etcetera. Now, let’s execute an accession trouble victimisation mere fractions.

Let’s resolve an Gain Equivalence involving Fractions

Since we already suffer the divide 3/4 attack the abacus, we can get with it for this equating. Our par is: ¾ + 1/5.

Incur a vernacular denominator for these fractions. That turn is 20.

We live: 5 multiplication the denominator 4 in the divide ¾ = 20. Thus, we manifold 5 multiplication the numerator 3 in ¾ to get the solution of 15/20.

You may regard to spot this divide on the abacus: 15/20.

Now, we recognize fourfold the denominator 5 in the divide 1/5 = 20. So, we breed the numerator 1 by 4 for the response of 4.

Add the numerators: 4 + 15. The result is 19 in the numerator, and we besides bear 20 as a denominator.

Set 19 on the left-hand english of the numeration gimmick.

The root is 19/20.

Fundamentally: you should get 19 on the tens and ones columns on the left face; you should be exhibit 20 on the right slope of the count cock.

It should feel similar the picture downstairs.

Astern you get examined the resultant, play the abacus to relaxation. Let’s try subtracting uncomplicated fractions.

The abacus shows the solution of ¾ + 1/5 = 19/20 | Root

This abacus shows the uncomplicated divide: 2/3. | Beginning

Let’s Execute a Minus Trouble Exploitation the Abacus for Fractions

Our minus job is: 2/3 – 2/5.

Starting by determination the plebeian denominator for these fractions. Therein suit, we recognize that numeral is 15.

Now, billet the divide 2/3 on the abacus.

We acknowledge: 5 x 3 = 15. Thence, we procreate the numerator by 5 for the reply of 10.

Now, set 10/15 on the abacus. This is the issue we bequeath be subtracting 2/5 from aft we commute it to a divide with a vernacular denominator.

We experience: 3 x 5 = 15. Thence, we manifold the numerator by 3 for the intersection of 6.

Our fractions now suffer green denominators. We can resolve the equality.

Deduct: 10 – 6 on the left english of the abacus.

Your resolve is 4.

Our resultant is: 4/15.

Astern you get reviewed the response to the equivalence, work the abacus to repose.

The abacus shows the termination of 2/3 – 2/5. The reply is 4/15. | Germ

Adding and Subtracting Motley Numbers and Composite Fractions on the Abacus

Not just can you use the abacus for resolution equations involving bare fractions, but the awesome count twist is utile for workings with composite fractions also as interracial numbers. A composite divide is one in which the numerator, the denominator, or both dwell of a divide. Commute these fractions to dim-witted fractions by determination park denominators and simplifying them. This treat may be essential when adding or subtracting sundry numbers during an par, edubirdie review too.

A miscellaneous turn is an integer with a right divide. To do plus and/or deduction on the abacus, we mustiness exchange a motley issue into an unlawful divide. An unlawful divide is one in which the numerator is greater than the denominator, such as in 7/6.

Formerly the wrong divide is set on the numeration dick, you can keep with resolution a minus or plus equivalence. Let’s do this with the motley numeral: 3 ½.

Converting a Assorted Bit into an Unlawful Divide

Commence by multiplying the integer and the denominator: 3 x 2, for the ware: 6.

Future, add the numerator and the merchandise: 6 + 1. This leave dedicate you the result of 7.

Situation the 7 on the far leftover of the abacus. This is your new numerator.

Office the denominator, 2, on the far rightfulness. Your reply should flavor similar the exposure beneath.

Now, you leave be capable to workplace with an add-on or minus trouble involving the wrong divide: 7/2.

Later you deliver studied the answer, work your abacus to repose.

Extolment. You birth victimized the abacus to execute minus and add-on for fractions.

This abacus shows the wrong divide: 7/2. | Beginning


Which of these tasks is easiest for you on the abacus when functional with fractions?

Scene the divide

Adding the numerators

subtracting fractions

Mentally dividing the enumeration gimmick


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How to Use the Abacus to Inclose Children to Fractions

Although the Latin password abacus way “flat open,” the count instrument has many forms. It may be ill-used horizontally, alike the Cranmer abacus shown altogether of the photos therein clause. Yet, approximately abaci may stall vertically. Thither are digital abaci too. The account of the reckoning dick is disputable, but many researchers evoke the abacus was kickoff put-upon in Chinaware or Babylon. Disregardless of the invention or extraction of the count cock, the abacus can be helpful in assisting new children who are quieten development mathematical concepts and agreement approximately fractions. Under is a elementary way to insert children to fractions with the abacus:

Low, severalize the shaver you testament be exploring what fractions are. Explicate what fractions are in footing the tiddler can perceive.

Future, birth the minor counting the act of columns of beads on the abacus. In the cause of the abacus victimised therein clause, the figure would be 13 columns of beads.

Now, excuse the xiii columns of beads typify one finish set. Let the tiddler ask questions at this period.

Now, sustain the nipper back a few rows with his men. Excuse this represents contribution of the solid.

E.g., if the younker covers two rows of beads, excuse that 2 out of 13 columns of beads let been covered.

Raise inclusion by victimization unlike examples. E.g., try the like matter with money, i.e., foursome quarters shuffling a buck etcetera. The nipper moldiness grow the skills to pertain the cognition of fractions to respective situations.

Resolve your elementary example by explaining how this is the introductory rudimentary construct of fractions. Yet and with rehearse, the younker volition be capable to implement his/her noesis to workings with fractions on the awesome abacus.