Question
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Tutor-Verified Answer
Answer
Solution
Sure! Let’s add the mixed numbers
and
step by step.
Step 1: Simplify the Mixed Numbers
First, simplify the fractional parts of each mixed number if possible.
-
Simplify
: So,simplifies to . -
Simplify
:
This fraction is already in its simplest form.
Now, the problem looks like:
Step 2: Add the Whole Numbers
Add the whole number parts of the mixed numbers:
Step 3: Add the Fractional Parts
Now, add the fractional parts:
To add these fractions, they need a common denominator. The least common denominator (LCD) of 2 and 4 is 4.
-
Convert
to fourths: -
Add the fractions:
-
Simplify
to a mixed number:
Step 4: Combine the Whole Numbers and Fractions
Add the sum of the whole numbers to the sum of the fractions:
Final Answer
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Bonus Knowledge
To add the mixed numbers
and
, we first convert them to improper fractions.
Starting with
:
Convert the whole number: .
So, .
Convert the whole number:
So,
Now for
:
Convert the whole number: .
So, .
Convert the whole number:
So,
Next, we need a common denominator to add the two fractions. The least common multiple of 20 and 4 is 20.
Convert
to have a denominator of 20:
Multiply the numerator and denominator by 5: .
Multiply the numerator and denominator by 5:
Now we can add
:
Now, let’s simplify
by dividing both the numerator and the denominator by 5:
Now, convert
back to a mixed number:
remainder 1. Thus,
.
So, the simplified answer is
.