Compound interest for kids

Compound interest is a way for your money to grow faster because it earns interest on the interest that has already been earned. Here’s how it works:

Let’s say you have $100 in a savings account that earns 10% compound interest per year. At the end of the first year, you would have earned $10 in interest because 100 x .10 = 10. So now you have a total of $110 in your account.

The next year, you would earn interest on the $110 that you have in your account. 10% of 110 is $11, so you would earn $11 in interest that year. Now you have a total of $121 in your account.

Each year, the amount of money in your account grows because you are earning interest on the money that you already have, as well as the interest that has been earned in previous years. This is what makes compound interest different from simple interest, where you only earn interest on the original amount of money that you have.

Compound interest can be paid monthly, quarterly, or yearly, and the more often it is compounded, the faster your money will grow. For example, if you have the same $100 in a savings account that earns 10% compound interest per year, but the interest is compounded monthly, you would earn a little bit more money each year because the interest is being added to your account more frequently.

It’s important to start saving and investing as early as possible so that you can take advantage of compound interest. The longer you have your money in an account earning compound interest, the more it will grow. So, if you start saving when you are young, you will have more time for your money to grow, and you will end up with more money in the long run.

It’s also a good idea to save and invest a portion of the money that you earn, rather than spending it all. This will help you build up a strong financial foundation for the future.

In conclusion, compound interest is a powerful tool that can help your money grow faster over time. By saving and investing wisely, you can take advantage of compound interest to build a strong financial future for yourself.

What are simultaneous equations and how to solve them?

A simultaneous equation is a set of two or more equations that contain multiple variables. These equations are called simultaneous because they are meant to be solved at the same time.

Here’s an example of a set of simultaneous equations:

Equation 1: 2x + 3y = 8 Equation 2: x – y = 1

To solve these equations, we need to find the values of x and y that make both equations true at the same time. One way to do this is by using the substitution method.

First, we can solve one of the equations for one of the variables. Let’s solve the second equation for y:

x – y = 1 y = x – 1

Now, we can substitute this expression for y in the first equation:

2x + 3(x – 1) = 8

We can then simplify this equation by combining like terms:

2x + 3x – 3 = 8 5x – 3 = 8 5x = 11 x = 11/5

Now that we know the value of x, we can substitute it back into one of the original equations to find the value of y. Let’s use the second equation:

x – y = 1 (11/5) – y = 1 y = 1 – (11/5) y = 6/5

So, the solution to this set of simultaneous equations is x = 11/5 and y = 6/5.

That’s one way to solve simultaneous equations. There are also other methods you can use, like graphing or using matrices. But the substitution method is often a good place to start because it’s fairly easy to understand and usually works well for a small number of equations.

Concept of proportions

Proportions are a mathematical concept that express the relationship between two or more quantities. In other words, they describe how one quantity is related to another in terms of size or amount. Proportions can be expressed as a ratio, such as 3:2, or as a fraction, such as 3/2. The concept of proportions is used in many different fields, including mathematics, science, and engineering, to describe and compare the sizes or amounts of different quantities.

One common use of proportions is to express the relationship between two quantities that are in direct proportion to each other. This means that as one quantity increases, the other also increases, and vice versa. For example, the number of hours that a person works may be directly proportional to the amount of money that they earn. If a person works 10 hours, they may earn $100, but if they work 20 hours, they may earn $200. In this case, the proportionality can be expressed as a ratio, such as 10:100 or 20:200, or as a fraction, such as 10/100 or 20/200.

Proportions can also be used to express the relationship between two quantities that are in inverse proportion to each other. This means that as one quantity increases, the other decreases, and vice versa. For example, the speed of a car may be inversely proportional to the time it takes to travel a certain distance. If a car travels at a speed of 50 miles per hour, it may take 2 hours to travel 100 miles. If the car increases its speed to 75 miles per hour, it will take less time to travel the same distance, such as 1.5 hours. In this case, the proportionality can be expressed as a ratio, such as 50:2 or 75:1.5, or as a fraction, such as 50/2 or 75/1.5.

Proportions can also be used to solve problems, such as finding missing values in a given set of quantities. This is done by setting up a proportion and solving for the unknown value. For example, if it is known that the ratio of apples to oranges is 3:4, and there are 12 apples, the number of oranges can be found by setting up the proportion 3/4 = 12/x and solving for x. In this case, x = 16, so there are 16 oranges.

Proportions are also used in geometry to describe the relationship between the sides and angles of similar figures. Two figures are considered similar if they have the same shape, but not necessarily the same size. If two figures are similar, the ratios of their corresponding sides are equal, and the angles between these sides are also equal. This can be used to find missing values in similar figures, such as the length of a missing side in a triangle.

In summary, proportions are a mathematical concept that describe the relationship between two or more quantities. They can be expressed as a ratio or a fraction, and are used to compare the sizes or amounts of different quantities, solve problems, and describe the relationship between the sides and angles of similar figures.

Learning to solve equation using BODMAS / PEMDAS

The order of operations is a set of rules that tells us the correct order to solve math problems. It helps us to make sure that we get the right answer every time.

The order of operations can be remembered with the acronym PEMDAS:

P: Parentheses first. Anything inside parentheses should be solved first.

E: Exponents (ie Powers and Square Roots, etc.)

MD: Multiplication and Division (left-to-right)

AS: Addition and Subtraction (left-to-right)

Here’s an example:

Say you have the math problem: 3 + 4 x 5

Using the order of operations, we first solve the part inside the parentheses. There are no parentheses in this problem, so we move on. Next, we look for exponents. There are none, so we move on. Now we look for multiplication and division, and we find that 4 x 5 is 20. We solve this part first and get:

3 + 20 = 23

Finally, we add 3 + 20 to get our answer: 23.

If we had not followed the order of operations, we might have gotten a different answer. For example, if we had added 3 + 4 first and then multiplied the result by 5, we would have gotten 35, which is not the correct answer.

It’s important to follow the order of operations carefully to make sure that we get the right answer every time.

Examples:

1. 6 + 3 x 4 = 18
2. (6 + 3) x 4 = 24
3. 8 – 4 + 6 x 3 = 14
4. 8 – (4 + 6) x 3 = -10
5. 2 + 3 x 4 ÷ 6 = 2
6. 2 + (3 x 4) ÷ 6 = 3
7. 8 – 4 x 3 + 2 = 2
8. 8 – (4 x 3) + 2 = -2

Remember, the order of operations is important because it helps us to solve math problems correctly. Always start with the part inside the parentheses, then exponents, then multiplication and division (from left to right), and finally addition and subtraction (from left to right). By following these rules, you’ll be able to solve math problems confidently and correctly.

Learn to interpret tables

Interpreting tables is a important skill that can help kids better understand and analyze information. Tables are a common way to organize and present data, and they can be found in many different places, such as in newspapers, magazines, and online. Here are some tips to help kids interpret tables:

1. Look at the title of the table. The title should give you an idea of what the table is about.
2. Look at the column and row labels. These labels tell you what each column and row represents.
3. Look at the data in the cells. Each cell in the table contains a piece of information.
4. Look for patterns and trends. Do you notice any patterns or trends in the data? For example, is there a relationship between two different pieces of information?
5. Make comparisons. Compare the data in different cells or rows to see how they are similar or different.
6. Draw conclusions. Based on the data in the table, what conclusions can you draw?
7. Be cautious. Make sure to carefully read and interpret the data in the table. Sometimes, the data may be presented in a way that can be misleading.

Here’s an example of a table:

In this table, the column labels are “Fruit,” “Color,” and “Price,” and the row labels are the different types of fruit. The data in the cells tells us the color and price of each type of fruit. We can see that apples are red and cost $0.50, bananas are yellow and cost $0.30, and oranges are orange and cost $0.40.

I hope these tips help kids understand and interpret tables!