Addition and subtraction are fundamental math operations used in daily life. Follow these steps to master them.
Addition combines two or more numbers to find the total (sum).
47
+ 35
------
82
Align the decimal points and add as you would with whole numbers.
3.45
+ 1.26
--------
4.71
Subtraction finds the difference between two numbers.
82
- 47
------
35
Align the decimal points and borrow if necessary.
5.80
- 2.45
--------
3.35
By mastering these steps, you can confidently tackle math problems in everyday life!
Algebra is a branch of mathematics that helps us represent problems using variables and symbols.
In algebra, we use alphabet letters like a, b, c, etc. to represent unknown values. These are called variables.
Example: If a = 5 and b = 3, then:
a + b = 5 + 3 = 8a - b = 5 - 3 = 2An equation is like a balance. To keep it equal, whatever we do to one side, we must do to the other.
Example: Solve for x in x + 4 = 10
Subtract 4 from both sides: x + 4 - 4 = 10 - 4 x = 6
Sometimes equations involve multiplication or division.
Example: Solve 3x = 12
Divide both sides by 3: (3x)/3 = 12/3 x = 4
A ratio is a comparison of two numbers, while a proportion shows that two ratios are equal.
Example: If the ratio of boys to girls is 3:2 and there are 15 boys, how many girls are there?
Using cross multiplication: (15 / x) = (3 / 2) x = (15 × 2) / 3 x = 10 There are 10 girls.
Exponents show how many times a number is multiplied by itself.
Example: 2³ means 2 × 2 × 2 = 8
Common Rules:
a⁰ = 1 (Any number to the power of 0 is 1)a¹ = a (Any number to the power of 1 is itself)a² is called "a squared"a³ is called "a cubed"When solving algebraic expressions, follow the order of operations:
Many use this phrase as a mnemonic device: "Please Excuse My Dear Aunt Sally"
Example: Solve 3² + 5 × (4 - 1)
Step 1: Parentheses → (4 - 1) = 3 ==> 3² + 5 x 3 Step 2: Exponents → 3 x 3 = 9 ==> 9 + 5 x 3 Step 3: Multiplication → 5 × 3 = 15 ==> 9 + 15 Step 4: Addition → 9 + 15 = 24 ==> 24 Answer: 24
Numbers are randomly generated based on the user's grade level:
Depending on the grade level, numbers may be:
If fractions are used, they are converted into decimal format for easier comparison.
The comparison is done using:
> if the first number is greater than the second.< if the first number is smaller than the second.= if both numbers are equal.The user is presented with a comparison question in one of the following formats:
5 ? 8
Choose the correct symbol: >, <, or =
We have different shapes on the screen. Your goal is to count how many of the target shape appear.
Some shapes are target shapes, while others are distractor shapes. The distractor shapes are there to challenge you!
Each time, the target shape is chosen randomly. Look at the question carefully to find out which shape you need to count.
For example, if the question asks: "How many stars do you see?", you only need to count the stars.
Go through all the shapes on the screen and count only the ones that match the target shape.
Ignore all other shapes – they are just there to make the challenge more fun!
After counting, select the correct answer from the multiple-choice options.
Think carefully before selecting, and double-check your counting!
A decimal is a way to represent fractions using place value. It helps express numbers between whole numbers.
If we divide 1 whole into 10 equal parts, each part is called a tenth.
A fraction is made of two parts: a numerator (top number) and a denominator (bottom number). To convert a fraction to a decimal, divide the numerator by the denominator.
For example:
| Fraction | Decimal |
|---|---|
| 1/10 | 0.1 |
| 3/10 | 0.3 |
| 7/10 | 0.7 |
When working with decimals, sometimes we need to round them to a certain place value.
Example: 0.276 rounded to the nearest hundredth is 0.28.
Convert 4/10 into a decimal.
Division is the process of splitting a number into equal parts. Follow these steps to master division.
Division finds how many times one number fits into another.
_______
4 | 145
- 12 (4 × 3)
------
25
- 24 (4 × 6)
------
1 (Remainder)
Answer: 36 R 1 (36 remainder 1)
When dividing decimals, move the decimal point in the divisor and dividend to make it a whole number.
Move decimal → 45 ÷ 15
_______
15 | 45
- 45 (15 × 3)
-----
0
Answer: 3
To divide fractions, multiply the first fraction by the reciprocal of the second fraction.
2 3 2 4 8
--- ÷ --- → --- x --- = ----
5 4 5 3 15
Answer: 8/15
Master these division steps and solve problems with confidence!
Fractions represent parts of a whole and are used in various mathematical operations.
A fraction consists of two parts:
For example, in 1⁄2, 1 is the numerator, and 2 is the denominator.
To add or subtract fractions, make sure they have the same denominator. If not, find the least common denominator (LCD).
Multiply the numerators together and the denominators together:
a⁄b × c⁄d = a×c⁄b×d
Flip the second fraction and multiply:
a⁄b ÷ c⁄d = a⁄b × d⁄c
Divide the numerator by the denominator.
Convert to a decimal, then multiply by 100.
A polygon is a 2D shape with straight sides. Common polygons include:
Triangles can be classified based on their sides and angles:
Angles are measured in degrees. Common types include:
3D shapes have depth, width, and height. Examples include:
Transformations include:
Money comes in different forms, and coins are one of them! Here are the main types of coins used in the U.S.:
Each coin has a different value, and you can combine them to make different amounts of money.
Let's practice counting coins! Here are some questions to try:
We can add different coins together to make a total amount. Here are some examples:
Try creating your own combinations to see how money adds up!
Multiplication is a fundamental math operation used to find the total when combining equal groups. Follow these steps to master it.
Multiplication is repeated addition. It helps in scaling numbers efficiently.
47
× 35
------
235 (5 × 47)
141 (3 × 47, shifted left)
------
1645
Ignore the decimal point at first, then adjust the decimal position at the end.
3.4
× 1.2
------
68 (2 × 34)
34 (1 × 34, shifted left)
------
4.08 (Move decimal 2 places)
Multiply the numerators (top numbers) and denominators (bottom numbers) separately.
2 3 6
--- x --- = ---- → Simplified to 3/10
5 4 20
By mastering these multiplication steps, you can solve math problems with confidence!
Learn how patterns are generated and identified in a sequence of shapes.
The system defines a set of shapes, each represented by a FontAwesome icon:
The system randomly selects 2 or 3 shapes to create a pattern.
Example: If the system selects and , the pattern will only use these two shapes.
A sequence of 5 to 10 shapes is generated by repeating the selected shapes.
Example: ...
The next shape in the pattern is determined by looking at the repeating order.
If the pattern follows , the next shape must be .
To test understanding, multiple choice options are generated. One is correct, while the others are randomly selected.
Example Choices:
Look at the sequence and select the correct shape that comes next.
Learn how to determine the place value of a digit in a number!
Every digit in a number has a specific place value depending on its position. The place values, from right to left, are:
Let's take an example: 36,482. What is the place value of the digit 4?
Follow these steps:
Try answering this question:
A ratio is a comparison between two numbers showing how many times one value contains another.
It can be expressed in three ways:
Given two numbers, you can write them as a ratio:
Example: Express 8 to 12 as a ratio.
Solution: 8:12 or 8/12
Just like fractions, ratios can be simplified by dividing both numbers by their greatest common divisor (GCD).
Example: Simplify the ratio 8:12.
GCD of 8 and 12 is 4, so:
8 ÷ 4 : 12 ÷ 4 = 2:3
Two ratios are equivalent if they represent the same relationship.
Example: The ratio 2:3 is equivalent to 4:6 because:
(2 × 2) : (3 × 2) = 4:6
Ratios are used in many real-world scenarios, such as:
Try these exercises:
A sequence is a list of numbers that follow a pattern. Let's explore different types of sequences!
An arithmetic sequence is a list of numbers where each term increases or decreases by the same amount.
Example: 2, 5, 8, 11, 14, ...
Each term increases by 3. The missing term in 2, 5, ?, 11, 14 is 8.
A geometric sequence is a list of numbers where each term is multiplied by the same factor.
Example: 3, 6, 12, 24, ...
Each term is multiplied by 2. The missing term in 3, 6, ?, 24 is 12.
Some sequences alternate between different operations, such as adding and subtracting.
Example: 50, 55, 53, 58, ...
This pattern follows +5, -2, +5, -2. The missing term in 50, 55, ?, 58 is 53.
Sequences can also include fractions!
Example: 1/4, 2/4, 3/4, 4/4, ...
The numerator increases by 1 each time. The missing term in 1/4, ?, 3/4, 4/4 is 2/4.
Can you find the missing number in this sequence?
4, 9, ?, 19, 24
Hint: What is the pattern?
Welcome! Today, we will learn how to determine the correct shape based on what we see.
Look at the shape(s) shown on the screen. This shape will be represented using an HTML icon, like the ones below:
The system will randomly choose one of these shapes and display it multiple times. Your task is to identify which shape is being shown.
You will be given four multiple-choice options. Select the one that matches the displayed shape.
Once you select your answer, the system will check if it's correct. If correct, you will move to the next challenge!
Great job! Now you know how to identify and select the right shape. Keep practicing!
Time is divided into different units. Here are some important ones:
Try answering these questions to test your knowledge:
How many minutes are in a quarter hour?
When we tell time, we use words like:
What time is half past 4?