Final answer:
To find the quotient of 874 and 23 using an area model, we would break down 874 into parts that are multiples of 23. However, using long division, 874 divided by 23 is equal to 38, with 69 and 184 both being divisible by 23 and adding up to 3 and 8 respectively.
Step-by-step explanation:
The question relates to finding the quotient of 874 and 23 using an area model. To approach this problem, we would normally decompose the number 874 into parts that are easier to divide by 23. An initial step could be to determine how many times 23 goes into 874, which can be done through trial and estimation or by breaking down 874 into amounts that are multiples of 23. However, as there's a lack of specific area model steps in the given information, the traditional long division method can be applied to find the quotient.
To solve 874 ÷ 23, we start by finding the largest multiple of 23 that is less than or equal to 874. The whole process would entail:
- Finding how many times 23 fits into 87 (the first two digits of 874), which is 3 times, since 3 × 23 = 69.
- Subtracting 69 from 87 leaves 18, then we bring down the last digit 4 to get 184.
- Now, determining how many times 23 fits into 184, which is 8 times, since 8 × 23 = 184.
- With no remainder, we conclude that 874 ÷ 23 equals 38.
Therefore, the blank spots in the equation 874 ÷ 23 = ( ÷ 23) + ( ÷ 23) would be filled as follows: 874 ÷ 23 = (69 ÷ 23) + (184 ÷ 23), where both 69 and 184 are divisible by 23, giving us 3 and 8 respectively. Thus, the full equation is 874 ÷ 23 = 3 + 8 = 38.