Problem 75 - Prealgebra

Question

Perform the indicated operations. $$35 \div 5$$

Step-by-Step Solution

Answer

The result of 35 divided by 5 is 7.

Step 1: Identify the Operation

The problem presented is a division operation. The expression \(35 \div 5\) means that 35 is divided by 5.

Step 2: Set Up the Division

Imagine or write down the division setup: 35 is the dividend (the number to be divided) and 5 is the divisor (the number by which we divide).

Step 3: Perform the Division

Determine how many times 5 can go into 35 evenly. Since 5 times 7 equals 35, you can divide 35 by 5 completely, giving a result of 7.

Step 4: Write the Result

Since 5 times 7 is 35 exactly, no remainder is left, and the solution to the division \(35 \div 5 = 7\).

Key Concepts

Division Operation

The division operation is a fundamental arithmetic process used to distribute a number into equal parts. Whenever you see the division symbol "\(\div\)" or a fraction bar, it signals that you are supposed to perform a division. It's akin to asking how many times one number can fit into another.

For example, in our exercise, the operation expressed as \(35 \div 5\) tells us we need to determine how many groups of 5 can fit into 35. It's the same concept as sharing 35 apples fairly among 5 people—everyone would get the same amount without any apple left over.

Dividend and Divisor

In any division operation, two main components dictate how the process works: the dividend and the divisor.

• Dividend: This is the number you want to divide up. In the expression \(35 \div 5\), 35 is our dividend.
• Divisor: This is the number you are dividing by. In the expression, 5 is the divisor.

These roles determine how the operation proceeds, just like in our example where we divide 35 (the total) into pieces of size 5 (the divisor). Understanding these terms is crucial for setting up and solving division problems correctly.

Division Without Remainder

Division without remainder means that the dividend can be completely divided by the divisor with no leftover pieces. This situation occurs when the divisor fits exactly into the dividend a whole number of times. In mathematical terms, if a division operation results in an integer without a fraction or decimal place, it means there's no remainder.

In our example, \(35 \div 5\) gives us 7 as the result. This indicates that 35 is perfectly divisible by 5, with no numbers left unaccounted for. When such neat division happens, it not only simplifies calculations but also fosters a clearer understanding of how numbers interact through division.