QuestionLesson Summary
- Use the properties of operations to add and subtract rational numbers more efficiently. For instance, .
- The opposite of a sum is the sum of its opposites as shown in the examples that follow:
Problem Set
Show all steps taken to rewrite each of the following as a single rational number.
1.
2.
3.
4.
Studdy Solution
STEP 1
1. We are working with rational numbers, which include integers, fractions, and decimals.
2. We will use the properties of operations, such as the associative and commutative properties, to simplify expressions.
3. We will convert mixed numbers to improper fractions where necessary for easier calculation.
4. We will simplify each expression to a single rational number.
STEP 2
1. Simplify each expression by applying the properties of operations.
2. Convert mixed numbers to improper fractions if needed.
3. Perform arithmetic operations to combine terms into a single rational number.
STEP 3
Expression:
Convert the mixed number to an improper fraction:
Combine the terms:
Simplify the fraction:
STEP 4
Expression:
Convert the mixed number to an improper fraction:
Combine the terms:
Simplify the fraction:
STEP 5
Expression:
Convert the mixed number to an improper fraction:
Apply the opposite operation:
Convert to a fraction:
Find a common denominator and combine:
Simplify the fraction:
STEP 6
Expression:
Apply the opposite operation:
Convert to a common denominator with :
Combine the terms:
The simplified expressions are:
1.
2.
3.
4.
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