24five
x 3five
------
132five
27eight
65eight
+43eight
-------
157eight
75eight
-37eight
-------
36eight
1213five/3five???
-If someone could please confirm my answers for the others as well as help me with the last division problem thank you! these are all equating in different bases.
The first ones are correct. Does it matter what base your solution is for the last one?
checking
24*3
3*4=22
3*2=11
110+22=132
7+5+3= 17
6+2+4= 14
adding 140+17=157
36+37=15+60=75
all check.
In order to solve these problems involving numbers in different bases, we need to understand how to perform addition, subtraction, and division in those bases. Let's go through each problem one by one and explain how to solve them:
1. 24five + 3five = 132five:
To add two numbers in base 5, we start by adding the rightmost digits. If the sum is 5 or more, we carry over the excess to the next column. In this case, 4 + 3 equals 7, which is greater than 5. So we write down 7 and carry over the 1 to the next column. Then, we add the carried-over 1 to 2, resulting in 3. Finally, we write down the 3 in the leftmost column. Hence, the answer is 132five.
2. 27eight + 65eight + 43eight = 157eight:
Similar to the previous example, we add the rightmost digits, carrying over any excess. In this case, 7 + 5 equals 12, which is greater than 8 (the highest digit in base 8), so we carry over the 1 to the next column. Then, we add the carried-over 1 to 2 + 6 + 4, resulting in 13. We write down 13 (since 13 is less than 16, which is the next power of 8), carry over 1 to the next column, and write down the final carried-over 1. Therefore, the answer is 157eight.
3. 75eight - 37eight = 36eight:
To subtract two numbers in base 8, we start by subtracting the rightmost digits. If the digit being subtracted is larger than the other digit, we borrow from the left column. In this case, 5 minus 7 results in a negative number in base 8. So we borrow 8 from the left column, which becomes 7 in base 8. Then we subtract 7 from 15, resulting in 10. We write down 10, carry over 1, and subtract 3 from the carried-over 7, which results in 4. Hence, the answer is 36eight.
4. 1213five divided by 3five:
To divide a number in base 5 by another number in base 5, we want to find how many times the divisor can be subtracted from the dividend without going into negative values. We start by dividing the leftmost digit of the dividend (1) by the divisor (3). In base 5, 1 divided by 3 results in 0 remainder 1.
Since the quotient is 0, we move to the next digit of the dividend (2). We now have 12 as the new partial dividend. We divide 12 by 3, resulting in a quotient of 4 and no remainder.
Next, we bring down the next digit (1) to the right of the partial dividend, resulting in 41 as the new partial dividend. We divide 41 by 3, resulting in a quotient of 13 and no remainder.
Finally, we bring down the last digit (3) to the right of the partial dividend, resulting in 133 as the new partial dividend. We divide 133 by 3, resulting in a quotient of 44 and a remainder of 1.
Therefore, the answer to 1213five divided by 3five is 4044 with a remainder of 1.