Improve math skills of your kids - Learn step-by-step arithmetic from Math games

Math: Unknown - Step-by-step math calculation game for iOS.

Math: Unknown is much more than a math game. It is a step-by-step math calculation game which will teach users how to calculate in the correct order rather than just asking only the final calculated results.

The app consists of four basic arithmetic operations which are addition, subtraction, multiplication and division. In order to get started, users who are new to arithmetic can learn from animated calculation guides showing step-by-step procedures of solving each type of operation. It is also helpful for experienced users as a quick reference.

Generally, addition and subtraction may be difficult for users who just start learning math especially when questions require carrying or borrowing (also called regrouping). The app helps users to visualize the process of carrying and borrowing in the way it will be done on paper. Once users understand how these operations work, they are ready to learn multiplication and division.

For most students, division is considered as the most difficult arithmetic operation to solve. It is a common area of struggle since it requires prior knowledge of both multiplication and subtraction. To help users understand division, the app uses long division to teach all calculation procedures. Relevant multiplication table will be shown beside the question. Users will have to pick a number from the table which go into the dividend. Multiplication of selected number and divisor is automatically calculated, but the users have to do subtraction and drop down the next digit themselves. Learning whole calculation processes will make them master it in no time.

Math: Unknown is a helpful app for students who seriously want to improve arithmetic calculation skills.

Standards of limits and fits for mating parts


1. Basic size is the size to which limits or deviations are assigned and is the same for both members of a fit. It is measured in millimeters.
2. Deviation is the algebraic difference between a size and the corresponding basic size.
3. Upper deviation is the algebraic difference between the maximum limit and the corresponding basic size.
4. Lower deviation is the algebraic difference between the minimum limit and the corresponding basic size.
5. Fundamental deviation is either the upper or the lower deviation, depending on which is closest to the basic size.
6. Tolerance is the difference between the maximum and minimum size limits of a part.
7. International tolerance grade (IT) is a group of tolerances which have the same relative level of accuracy but which vary depending on the basic size.
8. Hole basis represents a system of fits corresponding to a basic hole size.
9. Shaft basis represents a system of fits corresponding to a basic shaft size.

International Tolerance Grades
The variation in part size, also called the magnitude of the tolerance zone, is expressed in grade or IT numbers. Seven grade numbers are used for high-precision parts; these are

IT01, IT0, IT1, IT2, IT3, IT4, IT5

The most commonly used grade numbers are IT6 through IT16. For these, the basic equation is

where D is the geometric mean of the size range under consideration and is obtained from the formula
Basic size ranges (sizes are for over the lower limit and including the upper limits in millimeters.
0-3; for this range use Dmin = 1 mm

Formulas for finding tolerance grades.
Grade - Formula
IT5 - 7i
IT6 - 10i
IT7 - 16i
IT8 - 25i
IT9 - 40i
IT10 - 64i
IT11 - 100i
IT12 - 160i
IT13 - 250i
IT14 - 400i
IT15 - 640i
IT16 - 1000i

Fundamental deviations are expressed by tolerance position letters using capital letters for internal dimensions (holes) e.g. 20G7, 40F8, etc. and lowercase letters for external dimensions (shafts) e.g. 20h6, 16g7, etc.

The formula for the fundamental deviation for shafts is
Fundamental deviation = a + (bDg)/1000
where those 3 coefficients can be obtained from the separate table (not shown here).

Shaft Deviations.
For shafts designated a through h, the upper deviation is equal to the fundamental deviation. Subtract the IT grade from the fundamental deviation to get the lower deviation. Remember, the deviations are defined as algebraic, so be careful with signs.

Shafts designated j through zc have the lower deviation equal to the fundamental deviation. For these, the upper deviation is the sum of the IT grade and the fundamental deviation.

Hole Deviations.
Holes designated A through H have a lower deviation equal to the negative of the upper deviation for shafts. Holes designated as J through ZC have an upper deviation equal to the negative of the lower deviation for shafts.

An exception to the rule occurs for a hole designated as N having an IT grade from 9 to 16 inclusive and a size over 3 mm. For these, the fundamental deviation is zero.

A second exception occurs for holes J, K, M, and N up to grade IT8 inclusive and holes P through ZC up to grade 7 inclusive for sizes over 3 mm. For these, the upper deviation of the hole is equal to the negative of the lower deviation of the shaft plus the change in tolerance of that grade and the next finer grade.

source: google books

We will see more examples with excel file later in the next post [Standards of limits and fits for mating parts (Part 2)]


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