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Learn it your way
A short class with Sarah and her students. The other ways are under More.
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Today, we're going to learn how to add rational numbers. Let's start with the addition of two fractions, like 1/2 and 1/3. Who can tell me what we need to do first?
We need to find a common denominator!
Exactly! The least common denominator for 2 and 3 is 6. So, we convert them. What do we get?
1/2 becomes 3/6 and 1/3 becomes 2/6!
Well done! Now, if we add 3/6 and 2/6, what do we get?
That's 5/6!
Great job! Remember, ACRONYM for addition is Aliens Create Really Awesome Numbers (ACR). Let’s summarize: To add, find a common denominator, convert, and then add!
Next up, let’s look at multiplication. If we take 3/4 and multiply it by 2/3, what do we do first?
Just multiply the top numbers and the bottom numbers!
That’s right! So, what does that look like?
It’s 3 times 2 over 4 times 3, which is 6/12.
Perfect! Can we simplify that?
Yeah, it simplifies to 1/2!
Excellent! Remember: Multiplication can be remembered as Multiply First, Simplify After (MFS). To recap, multiply the numerators, then the denominators, and simplify if needed.
Finally, let's tackle division. Dividing by a fraction means multiplying by its reciprocal. If we have 5/6 divided by 2/3, what do we do?
We flip the second fraction and multiply, so it’s the same as 5/6 times 3/2!
Correct! Let’s compute that.
That equals 15/12, or simplified to 5/4!
Awesome! To remember division, think of Divide Means Reciprocal (DMR)! To summarize, when dividing fractions, flip the second fraction and multiply.
To add fractions, find a common denominator, adjust the numerators accordingly, and sum them up.
Simply multiply the numerators together to get the new numerator and the same for the denominators.
Dividing by a fraction involves multiplying by the reciprocal of that fraction.
To add we first find, a common ground, convert the top, then add around.
Once there was a fraction, who met another on the path. They couldn’t combine until they found the common ground of their denominator, after which they blended perfectly!
To remember ADD (for addition): A for Align denominators, D for Do the sum!
Term
What is the result of 1/2 + 1/3?
Click to flip
Term
What do you get when you multiply 3/4 and 2/3?
Click to flip
Term
How do you divide by a fraction?
Click to flip
A number that can be expressed as the quotient of two integers, where the denominator is not zero.
A shared multiple of the denominators of two or more fractions used to add or subtract them.
The top part of a fraction, representing how many parts we have.
The bottom part of a fraction, indicating how many equal parts the whole is divided into.
This section details the operations rules for rational numbers, illustrating addition, multiplication, and division, alongside practical examples.
In this section, we explore the operations rules for rational numbers, including how to add, multiply, and divide them. Each operation is presented with examples to demonstrate proper calculation methods and reinforce understanding of rational arithmetic.
This section is crucial in understanding how we handle rational numbers in arithmetic. Rational numbers can be represented in the form p/q, where p is an integer, and q is a non-zero integer. In this context, we discuss the arithmetic operations that can be performed with these numbers. The operations covered include:
Addition: To add two rational numbers, we find a common denominator and appropriately adjust the numerators. For example, the addition of 1/2 and 1/3:
Multiplication: This operation is straightforward—multiply the numerators together and the denominators together. For instance:
Division: Dividing by a rational number involves multiplying by its reciprocal. For example:
By mastering these operations, students gain a functional understanding of rational number arithmetic that can seamlessly transition into more complex mathematical concepts.