Math Test Flashcards
Practice for Math Test (20 cards)
What are divisibility rules?
Divisibility rules are a set of shortcuts that help you determine if a whole number is evenly divisible by another whole number without performing the actual division. They are based on patterns within the digits of the number.
For example:
A number is divisible by 2 if its last digit is 0, 2, 4, 6, or 8 (an even number).
What are factors?
Factors are whole numbers that can be multiplied together to get another whole number (the product). In other words, if a number can be divided evenly by another number with no remainder, then that second number is a factor of the first.
Examples:
The factors of 12 are 1, 2, 3, 4, 6, and 12 because:
1×12=12
2×6=12
3×4=12
What is the Mean?
The mean is like finding the “fair share” or the “average” of a group of numbers. To find it, you need to do two things:
- Add up all the numbers.
- Divide that total by how many numbers you added.
Example: Maria got 3 stickers, David got 5 stickers, and Lisa got 4 stickers. What’s the mean number of stickers they got?
- Add them up: 3+5+4=12
- Count how many kids: 3
- Divide: 12÷3=4
The mean (average) number of stickers is 4.
What is the Median
The median is the middle number in a set of numbers when they are ordered from least to greatest.
To find the median:
- Put the numbers in order from the smallest to the biggest.
- Find the number in the middle.
For example:
Find the median of the numbers: 10, 20, 15, 5, 25
Put them in order: 5, 10, 15, 20, 25
The middle number is 15. So, the median is 15.
What is the Mode
The mode is the number that appears most often in a set of numbers. It’s the number you see the most.
For example:
Look at these numbers: 2, 5, 2, 8, 2, 9, 5
Which number shows up the most? The number 2 appears 3 times, which is more than any other number. So, the mode is 2.
What is a Trapezoid?
A trapezoid is a four-sided shape that has exactly one pair of parallel sides. These parallel sides are called the bases of the trapezoid. The other two sides are not parallel.
What is a Quadrilateral?
A quadrilateral is a shape in math that has four straight sides and four corners.
What is a Product?
The product is the answer you get when you multiply two or more numbers together.
Examples:
3×4=12. The product is 12.
5×2=10. The product is 10.
7×1=7. The product is 7.
Evaluating expressions: Parenthesis
When you see parentheses () in a math problem, they are like a special instruction that says: “Do this part FIRST!”
It’s like the parentheses are giving that part of the problem extra importance. You have to solve what’s inside the parentheses before you do anything else.
Example:
Evaluate: 8+(3×2)
- Do what’s inside the parentheses first: 3×2=6
- Now do the rest of the problem: 8+6=14
- So, 8+(3×2)=14
Evaluating expressions: Brackets
Sometimes, you might see brackets [] in a math problem too. When you have both parentheses and brackets, you usually do what’s inside the parentheses first, and then do what’s inside the brackets.
Example:
Evaluate: [15−(2+3)]×4
- Do what’s inside the parentheses first: 2+3=5
- Now the problem looks like this: [15−5]×4
- Do what’s inside the brackets next: 15−5=10
- Finally, do the last step: 10×4=40
- So, [15−(2+3)]×4=40
Converting Improper Fractions to mixed numbers:
An improper fraction has a top number (numerator) that is bigger than or equal to the bottom number (denominator). To change it to a mixed number (a whole number and a fraction), you need to divide!
Steps:
- Divide the numerator by the denominator.
- The quotient (the whole number answer) becomes the whole number part of your mixed number.
- The remainder (what’s left over after dividing) becomes the new numerator.
- The denominator stays the same.
Example:
Convert 3/7 to a mixed number.
- Divide 7 by 3: 7÷3=2 with a remainder of 1.
- The whole number is 2.
- The new numerator is 1.
- The denominator stays 3.
- So 7/3 = 2 1/3
Converting a mixed number to an improper fraction:
A mixed number has a whole number part and a fraction part. To change it to an improper fraction, you need to multiply and add!
Steps:
- Multiply the whole number by the denominator.
- Add the numerator to that answer.
- This new number becomes the numerator of your improper fraction.
- The denominator stays the same.
Example:
Convert 3 1/2 to an improper fractions
- Multiply the whole number (3) by the denominator (2): 3×2=6
- Add the numerator (1) to that answer: 6+1=7
- The new numerator is 7.
- The denominator stays 2.
- So, 3 1/2= 7/2
How do you multiply a fraction by a whole number?
Make the whole number look like a fraction! Put the whole number over the number 1. (Remember, any whole number divided by 1 is still that whole number!)
For Example:
- If you have the whole number of 3, you can write it as 1/3
- Multiply the numerators (the top numbers) together. This will be the new numerator of your answer.
- Multiply the denominators (the bottom numbers) together. This will be the new denominator of your answer.
- Simplify your answer if you can! This means finding the smallest equivalent fraction.
How to multiply a mixed number by a whole number:
- Change the mixed number: Turn the mixed number into an improper fraction.
- Multiply the numerators: Multiply the top number of the improper fraction by the whole number.
- Keep the denominator: The bottom number of the fraction stays the same.
- Simplify (if needed): If the resulting fraction is improper, change it back to a mixed number or a whole number.
Dividing unit fractions by whole numbers
When you divide a unit fraction (like 2/1 or 5/1) by a whole number, you’re essentially splitting that fraction into even smaller pieces. Here’s how to do it:
- Keep the first fraction: Write down the unit fraction you’re starting with.
- Change the operation: Turn the division sign (÷) into a multiplication sign (×).
- Flip the whole number: Think of the whole number as a fraction with a denominator of 1 (for example, 3 is 1/3). Flip this fraction so the denominator becomes the numerator and the numerator becomes the denominator (so 1/3 becomes 3/1). This is called the reciprocal.
- Multiply the numerators: Multiply the top numbers of the two fractions.
- Multiply the denominators: Multiply the bottom numbers of the two fractions.
Dividing with decimal quotients
Sometimes when you divide, the numbers don’t divide evenly and you end up with a remainder. But you can keep going to get a decimal answer! Here’s how:
- Set up the problem: Write the division problem with the number being divided (dividend) inside the division bracket and the number you’re dividing by (divisor) outside.
- Divide as usual: Divide as you normally would with whole numbers.
- Add a decimal point and zeros: If you have a remainder, add a decimal point to the end of the dividend (the number inside the bracket). Then, add a zero after the decimal point. You can add more zeros if you need to keep dividing.
- Bring the decimal point up: Place a decimal point in your answer directly above the decimal point in the dividend.
Continue dividing: Bring down the zero and continue dividing as usual. - Keep adding zeros and dividing: If you still have a remainder, add another zero to the dividend and bring it down. Keep doing this until you get an answer with no remainder or the decimal repeats.
Coordinate planes
Imagine a giant grid made of two special number lines that cross each other. This grid is called a coordinate plane. It helps us find exact locations (like spots on a map!) using pairs of numbers.
- The horizontal number line (going left and right) is called the x-axis.
- The vertical number line (going up and down) is called the y-axis.
- The point where the x-axis and y-axis cross is called the origin.
- It’s location is always (0, 0).
Stem and Leaf Chart
A stem-and-leaf chart is a special way to organize numbers so you can see all the individual values and also see how the numbers are grouped together.
Here’s how it works:
- The stem is usually the first digit or digits of the numbers. It’s written on the left side of a line.
- The leaves are the last digit of each number. They are written on the right side of the line, next to their stem.
Example:
Stem | Leaf
—–|——
2 | 3, 5
3 | 1, 6, 6
4 | 0, 2
- The stem “2” with leaves “3, 5” means the numbers 23 and 25.
- The stem “3” with leaves “1, 6, 6” means the numbers 31, 36, and 36.
- The stem “4” with leaves “0, 2” means the numbers 40 and 42.
Parallelograms
A parallelogram is a shape with four sides where some special things are always true:
- Opposite sides are parallel: This means they run alongside each other and will never cross, like train tracks!
- Opposite sides are equal in length: The sides across from each other are the same length.
Opposite angles are equal: The angles across from each other have the same measurement.
Examples of Parallelograms:
- Rectangles: They have all the parallelogram rules AND four right angles (square corners).
- Squares: They have all the parallelogram rules AND four equal sides AND four right angles!
- Rhombuses (Diamonds): They have all the parallelogram rules AND four equal sides.
Area of compound figures: Shapes made of other shapes
A compound figure is just a shape made up of two or more simpler shapes put together (like rectangles, squares, or triangles). To find the total area of a compound figure, you need to break it down!
Here’s the main idea:
- Divide the figure: Split the compound figure into smaller, simpler shapes that you know how to find the area of (like rectangles or squares).
- Find the area of each simple shape: Calculate the area of each of the smaller shapes you created.
Remember:
- Area of a rectangle = length × width
- Area of a square = side × side
- Add the areas together: Add up the areas of all the smaller shapes to find the total area of the compound figure.
- Sometimes you might need to subtract the area of a smaller shape if it’s been cut out of a larger one to find the area of the remaining compound figure. But for now, focus on adding the areas of the smaller shapes!
