What is the quotient of 56÷34?
The Correct Answer and Explanation is:
To find the quotient of 56 divided by 34, we perform the division calculation:
[
56 \div 34 \approx 1.6471
]
When rounded to two decimal places, the quotient is approximately 1.65.
Detailed Explanation:
1. Understanding Division:
Division is one of the four basic arithmetic operations. In this operation, we take a number (the dividend) and divide it by another number (the divisor) to find out how many times the divisor fits into the dividend. The result is known as the quotient.
In this case, we are dividing 56 (the dividend) by 34 (the divisor). The division can be expressed in fraction form as:
[
\frac{56}{34}
]
2. Simplifying the Division:
Before performing the division, it can be helpful to simplify the fraction if possible. Both numbers can be divided by 2:
[
\frac{56 \div 2}{34 \div 2} = \frac{28}{17}
]
3. Performing the Division:
Next, we can perform the division of 28 by 17. Since 17 does not fit into 28 perfectly, we proceed to find how many times it fits. We can see that:
- ( 17 \times 1 = 17 ) (fits once)
- ( 17 \times 2 = 34 ) (too much)
Thus, 17 fits into 28 once. To find the remainder, we subtract:
[
28 – 17 = 11
]
Now we can express the result as:
[
1 \quad \text{(the whole number)} \quad \frac{11}{17} \quad \text{(the remainder)}
]
So, ( 28 \div 17 = 1 \frac{11}{17} ).
To convert ( \frac{11}{17} ) into a decimal, we perform the division, which approximates to ( 0.6471 ). Adding this to the whole number gives us:
[
1 + 0.6471 = 1.6471
]
Thus, the quotient of 56 ÷ 34 is approximately 1.65 when rounded to two decimal places. This process highlights the steps involved in performing division and understanding the relationships between the numbers involved.