Add and subtract rational numbers unit test
Bot
To add and subtract rational numbers, follow these steps:
1. Make sure that the rational numbers have the same denominator. If they don't, find a common denominator by finding the least common multiple (LCM) of the denominators.
2. Once you have the same denominator, you can add or subtract the numerators of the rational numbers.
3. Keep the denominator the same.
4. Simplify the resulting fraction, if necessary, by reducing it to its lowest terms.
Here is an example to illustrate the steps:
Example: Add 3/4 and 2/3.
Step 1: Find the common denominator. The LCM of 4 and 3 is 12.
Step 2: Convert the fractions to have the common denominator:
3/4 becomes 9/12 (multiply the numerator and denominator by 3)
2/3 becomes 8/12 (multiply the numerator and denominator by 4)
Step 3: Add the numerators while keeping the denominator the same:
9/12 + 8/12 = 17/12
Step 4: Simplify the fraction, if necessary:
The fraction 17/12 can be reduced to the mixed number 1 5/12.
For subtraction, follow the same steps but subtract the numerators in Step 3 instead of adding them.
I hope this helps! Let me know if you have any further questions.
To add and subtract rational numbers, you'll need to follow the rules of operations and remember a few key concepts. Let's break down the steps on how to solve problems involving adding and subtracting rational numbers:
1. Understand the concept of rational numbers: Rational numbers include integers, fractions, and decimals that can be expressed as a ratio of two integers. Examples of rational numbers are -2, 1/2, and 0.75.
2. Identify the operations involved: Determine whether you need to add or subtract the given rational numbers. The addition symbol (+) indicates that you need to add, while the subtraction symbol (-) tells you to subtract.
3. Make sure the rational numbers have the same denominator (for addition and subtraction of fractions): If you are adding or subtracting fractions, check if they have the same denominator. If not, you need to find the lowest common denominator (LCD) to make the fractions compatible for addition or subtraction.
4. Perform the addition or subtraction operation: Once you have determined the correct operation and made the fractions (if applicable) compatible, apply the rules of addition and subtraction.
- Addition: Add the numerators while keeping the denominator constant. For example, if you have 1/2 + 1/3, you add the numerators to get 1 + 1 = 2, and the denominator stays the same. So the sum is 2/6.
- Subtraction: Subtract the numerators while keeping the denominator constant. For example, if you have 3/4 - 1/4, you subtract the numerators to get 3 - 1 = 2, and the denominator stays the same. So the difference is 2/4.
5. Simplify the result (if necessary): If the fraction can be simplified further, divide the numerator and denominator by their greatest common divisor (GCD). For example, 2/6 can be simplified to 1/3 by dividing both the numerator and denominator by 2.
Now that we have gone through the steps, you can apply these concepts to solve the problems in your unit test related to adding and subtracting rational numbers. Make sure to carefully read each question, identify the operation, find the common denominator (if required), and then perform the addition or subtraction. Don't forget to simplify your answer if needed!
1) Perform the following addition:
\(2 + \frac{5}{8}\)
a) \(\frac{21}{8}\)
b) \(\frac{13}{8}\)
c) \(\frac{11}{10}\)
d) \(\frac{3}{8}\)
2) Perform the following subtraction:
\(\frac{3}{4} - \frac{1}{3}\)
a) \(\frac{5}{12}\)
b) \(\frac{7}{12}\)
c) \(\frac{1}{12}\)
d) \(\frac{2}{3}\)