# Tutor profile: Yuxi C.

## Questions

### Subject: Pre-Algebra

200 is what percent of 24? (Round to the nearest tenth of the percentage.)

Students always struggle with percent questions. To solve this questions, there are two efficient methods. Method 1: Use ratio to set up proportion. basic idea to step of the proportion is : part / total = percent / 100. Be careful that the "total" does NOT mean the bigger number. the "total" means the standard that will be compared. The trick is to look for the key word "of", the number (or variable) after "of" is the "total(standard)". In this question, the "total" is 24. Another key word is "what" to repesent the unknown variable. In this question, pay attention that the varoable is "what percent". Therefore the percentage shoule be written as x / 100. Since "total"(standaed to be compare with) is 24. so the "part" is 200. The proportion is 200 / 24 = x / 100. We could solve the proportion using cross multiplication method, x = 833.3. Therefore the final answer is 833.3%. If we can't clearly identidy the standard number, we will make the common mistake as making the bigger numnber 200 as the denominator in the proportion. Method 2: Translate the question into an one-step equation. "Is" will be translated as the "=" equal sign. "What" will be translated as the variable "x". "Of" will be translated as multiply. The question will be translated as: 200 = x * 24 x = 8.333...... The last key point to be careful is the tenth of percent. 8.333... will not be the perfect final answer. to change decimal as a percent we should move the deciaml point to the right two spaces. Noted that the tenth of percent means the thousandths of decimal. So the final answer is 833.3%.

### Subject: Basic Math

Find the area of a triangle with the base as 5cm and height as 6cm.

From the formula of the area of triangle, we know the area = base * height / 2 = 5 * 6 / 2 = 15 cm^2. It looks like a very basic question, however, at least half students forget to divided by 2 every time. To teach the reasoning of "dividing by 2" for the area of triangle, I will show students the picture of two congruent triangles together as a parallelogram with the same base and height as the triangles. (One of the triangle will be up side down in the parallelogram.) To find out the area of the parallegram, we could just operate Base * Height, which is also two times of the triangle's area. Therefore to findout the triangle's area, we should do base * height / 2.

### Subject: Algebra

Solve the following multi-step equation: (3n^2 + 27) / 18 - 10 = -7

To solve a multi-step equation, we have to be careful with the order. Since we have to always follow the order of operation, the order to solve the value of the variable is acatully the "reverse order of operation". When I teach my students, I always say "Start to solve from the farest one from the variable untril you meet the 'big boss'." The "big boss" means the closest operation from the variable. Remember to solve the question, we should make the varibale alone by itself by cancelling the operation around the variable. To cancel the operation around the variable, we should use the inverse operation with the same number. Noted that if you operate the same number using the same operation on both sides of the equation, the equation will still be balanced. In this equation, the "farest" one is "-10". As the reverse of the order of operation, the subtraction in this questions should be the first part to be solved. We will "+10" on both sides of the operation to cancel the "-10" on the left. (Since subtraction and addition are inverse operations.) so (3n^2 + 27) / 18 = -7 + 10 = 3. Next we will cancel the "/18, divided by 18" by multiplying 18 on both sides of the equation. So the equation will be simplified as 3n^2 + 27 = 3 * 18 = 54. The next "farest" one is "+27". Therefore we will minus 27 on both sides of the equation to cancel the "+27" on the left side. So the equation will be 3n^2 = 54 - 27 = 27. Next step we "divided by 3" on both sides of the equation to cancel the "times 3" on the left side of the equation with the variable. Therefore the equation becomes n^2 = 27 / 3 = 9. Since n^2 = 9, then n = 3 or -3. (Don't forget the negative answer.)

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