JIT 1.1-1.3
Trinity White・19 minutes read
When working with fractions and parentheses in math, remember to simplify by following the order of operations and cancel common terms when multiplying or dividing. To avoid confusion with variables, use dots or parentheses for multiplication and always find the least common denominator when adding or subtracting fractions.
Insights
- Using dots or parentheses for multiplication in math class helps avoid confusion with variables.
- Different types of numbers include real numbers, rational numbers, integers, and irrational numbers, each with distinct characteristics and representations.
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Recent questions
How do you simplify fractions?
Combine fractions into one, reduce if possible.
What are the different types of numbers?
Real, rational, integers, and irrational numbers.
How do you multiply fractions?
Multiply numerators, then denominators, simplify if possible.
What is the order of operations in math?
Parentheses, exponents, multiplication, division, addition, subtraction.
How do you divide fractions?
Invert and multiply or use "keep change flip" method.
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Summary
00:00
Math Basics: Fractions, Operations, and Parentheses
- In math class, use a dot or parentheses for multiplication to avoid confusion with variables.
- Any number can be written as a fraction, even whole numbers like 3 (written as 3/1).
- Different types of numbers include real numbers (infinite digits), rational numbers (fractions), integers (whole numbers with negatives), and irrational numbers (infinite non-repeating digits).
- When multiplying fractions, multiply numerators and denominators, canceling common terms if possible.
- Cancel numbers that are factors of both the numerator and denominator.
- To divide fractions, invert and multiply or use the "keep change flip" method.
- Adding and subtracting fractions require a common denominator, found by least common multiple or multiplying by the opposite denominator.
- Simplifying fractions involves combining them into one fraction, reducing if possible.
- Parentheses group numbers together in equations, simplify inside them first following the order of operations (PEMDAS).
- Simplify inside parentheses by adding or subtracting, or distribute a number outside the parentheses to each term inside.
20:52
Mastering Operations with Fractions and Negatives
- When multiplying -2 by 1 and -2 by 3, the result is -8, which is the same as multiplying -2 by 1 and adding 3, emphasizing the distribution of a negative sign to both terms in parentheses.
- To add and subtract fractions with different denominators, finding the least common multiple, such as 18 in this case, is crucial to simplify the fractions effectively.
- Dividing fractions involves changing the division sign to multiplication and inverting the denominator, simplifying common factors like x and y to streamline the calculation.
- Distributing a negative sign to terms within parentheses, even when a number is not explicitly shown, is essential to simplify expressions correctly, combining like terms when applicable.
