what is a quickway to learn how to mutlplying fractions
flash cards: make and use them.
how do you do Adding and Subtracting Rational Expressions?
I want ot know what the numbers or factors of the number 81 are becasues that uis mapt of the homework in my homework
9,1
To learn how to multiply fractions quickly, you can follow these steps:
1. Understand the concept: Remember that when you multiply fractions, you multiply the numerators (top numbers) together and the denominators (bottom numbers) together.
2. Simplify if necessary: Check if there are any common factors between the numerators and denominators that can be canceled out to simplify the fraction beforehand.
3. Multiply the numerators: Multiply the numerators of the fractions together to get the new numerator.
4. Multiply the denominators: Multiply the denominators of the fractions together to get the new denominator.
5. Simplify the result: If possible, simplify the fraction further by canceling out any common factors.
For example, if you have the fractions 2/3 and 4/5:
Step 1: Understand the concept
Multiplying the numerators (2 and 4) gives 8, and multiplying the denominators (3 and 5) gives 15.
Step 2: Simplify if necessary
There are no common factors to cancel out.
Step 3: Multiply the numerators
2 x 4 = 8
Step 4: Multiply the denominators
3 x 5 = 15
Step 5: Simplify the result (already simplified)
Therefore, the product of 2/3 and 4/5 is 8/15.
For adding and subtracting rational expressions, you can follow these steps:
1. Find a common denominator: Determine the least common multiple (LCM) of the denominators of the rational expressions. This will be the common denominator for adding or subtracting.
2. Rewrite the expressions: Rewrite each rational expression with the common denominator.
3. Perform the addition or subtraction: Add or subtract the numerators of the rational expressions, keeping the common denominator.
4. Simplify if necessary: Simplify the resulting rational expression by canceling out any common factors between the numerator and denominator.
For example, if you have the rational expressions (3/x) + (2/3x):
Step 1: Find a common denominator
The least common multiple (LCM) of x and 3x is 3x.
Step 2: Rewrite the expressions
(3/x) can be rewritten as (9/3x).
(2/3x) stays the same.
Step 3: Perform the addition
(9/3x) + (2/3x) = (11/3x)
Step 4: Simplify if necessary (already simplified)
Therefore, the sum of (3/x) and (2/3x) is (11/3x).
For finding the factors of a number like 81, you can use the following approach:
1. Start with the number 1 and divide it by increasing numbers to see if it evenly divides into 81.
- Divide 81 by 1: 81 ÷ 1 = 81 (remainder 0)
- Divide 81 by 2: 81 ÷ 2 = 40.5 (not divisible since the result is not a whole number)
- Divide 81 by 3: 81 ÷ 3 = 27 (remainder 0)
- Divide 81 by 4: 81 ÷ 4 = 20.25 (not divisible)
- Continue this process until you reach the square root of the number (in this case, the square root of 81 is 9).
2. List the pairs of factors you find until you reach the square root of the number:
- Factors of 81: 1, 3, 9, 27, 81
So, the factors of 81 are 1, 3, 9, 27, and 81.