### 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 (Part 2)

In the previous post (Standards of limits and fits for mating parts), we talked about the definitions of each term related to limits and fits as well as the formulas to determine the values of tolerances. In this post, we're going to convert those information into the real calculation using Microsoft Excel (as usual). As stated earlier, the calculation results may be different from the real values used in general mechanical design handbook. So please use this just for educational purpose only, but use the real table from general limits and fits table if you want to get higher accuracy values.

This is the screen shot of excel file to calculate upper deviation and lower deviation according to the selected shaft diameter and tolerance grade.

Let's see how to manually calculate the deviation values before using the program.

Example: To calculate the upper deviation and lower deviation of a shaft with diameter of 40 mm and tolerance g6.

Please refer to previous post (Standards of limits and fits for mating parts) for more details.

Shaft diameter = 40 mm has Dmin = 30 mm and Dmax = 50 mm as shown in the following table.

The geometric mean of the size range (D) = SQRT(30 x 50) = 38.73 mm
Then "i" can be calculated using the following formula.

i = 0.001 x [ 0.45 x (38.73)^(1/3) + 0.001 x 38.73 ] = 0.00156
Tolerance "g6" has grade = 6
From the table (in previous post), the formula of IT grade 6 is 10i = 10 x 0.00156 = 0.0156
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.

Tolerance "g6" has a = 0; b = -2.5 and g = 0.34
From Fundamental deviation = a + (bDg)/1000
We have Fundamental deviation = 0 + (-2.5 x 38.730.34)/1000 = -0.009

Upper deviation = fundamental deviation = -0.009
Lower deviation = fundamental deviation - IT grade = -0.009 - 0.0156 = -0.025

To use the program calculate the upper deviation and lower deviation of a shaft with diameter of 40g6, do the followings.

1) Enter 40 in cell D5 and the program automatically highlights the row that has Dmin <= d < Dmax as shown below.

2) Select "g" from the drop-down list in cell D6 and "6" from the drop-down list in cell E6. Then the result is displayed as shown below.