Frazier Floyd
04/03/2024 · Elementary School
a. \( 241_{\text {eight }}-45 \) eight b. \( 321_{\text {eight }}-32 \) eight
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To solve these problems, we need to convert the numbers from base 8 to base 10 and then perform the subtraction.
a. \( 241_{\text {eight }}-45 \)
First, let's convert \( 241_{\text {eight }} \) to base 10:
\( 241_{\text {eight }} = 2 \times 8^2 + 4 \times 8^1 + 1 \times 8^0 = 2 \times 64 + 4 \times 8 + 1 \times 1 = 128 + 32 + 1 = 161 \)
Now, we can perform the subtraction:
\( 161 - 45 = 116 \)
Therefore, \( 241_{\text {eight }}-45 = 116 \) in base 10.
b. \( 321_{\text {eight }}-32 \)
First, let's convert \( 321_{\text {eight }} \) to base 10:
\( 321_{\text {eight }} = 3 \times 8^2 + 2 \times 8^1 + 1 \times 8^0 = 3 \times 64 + 2 \times 8 + 1 \times 1 = 192 + 16 + 1 = 209 \)
Now, we can perform the subtraction:
\( 209 - 32 = 177 \)
Therefore, \( 321_{\text {eight }}-32 = 177 \) in base 10.
Quick Answer
a. \( 241_{\text {eight }}-45 = 116 \)
b. \( 321_{\text {eight }}-32 = 177 \)
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