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Chapter 1: Problem 32

Divide and then check by multiplying. $$121 \div 11$$

Short Answer

Expert verified
121 梅 11 = 11, verified by multiplication (11 脳 11 = 121).

Step by step solution

01

Perform Division

Divide 121 by 11. To do this, see how many times 11 goes into 121 without exceeding it. 11 times 11 equals 121. So, 121 divided by 11 equals 11.
02

Verify by Multiplication

To check the division result, multiply the quotient by the divisor. Calculate \(11 \times 11\). This should give you the original dividend, 121.
03

Confirm the Result

Since \(11 \times 11 = 121\), the division is verified and the result is correct.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Multiplication
Multiplication is a fundamental arithmetic operation, often seen as repeated addition. It involves increasing a number by a factor of another number. For example, when we multiply 11 by 11, we are essentially adding 11 to itself 11 times. The calculation looks like this: - First, multiply 11 by 1 to get 11.- Then, multiply 11 by 10 (which is the same as multiplying by 1 and appending a zero), resulting in 110.- Add these two results together: 11 + 110 = 121.Therefore, \(11 \times 11 = 121\).
Multiplication helps verify the accuracy of our division result by reconstructing the original number.
Quotient
The quotient is the result obtained when one number is divided by another. In this exercise, when 121 is divided by 11, the quotient is 11. The quotient tells us how many times the divisor fits into the dividend without exceeding it. To find the quotient: - Decide how many times 11 fits into 121. - Since 11 multiplied by 11 gives exactly 121, the quotient is 11. This value helps us understand the distribution of the total when spread equally in groups of 11.
Divisor
The divisor is the number by which another number is divided. In the example of dividing 121 by 11, 11 is the divisor. The divisor determines how many groups of itself can fit within the dividend. Processing the division involves: - Seeing how many times the divisor (11) can subtract from the dividend (121). - We use the divisor to discover that it fits 11 times in 121 perfectly. This clarity about the divisor ensures the completion of a correct division, guiding us to the right quotient.
Arithmetic Verification
Arithmetic verification is a crucial step in ensuring the accuracy of numerical solutions. In this example, verifying the division result steps up by using multiplication. To verify: - Take the quotient (11) and multiply it by the divisor (11). - This multiplication should yield the original number (121). If the result matches the dividend, the division is correct. Verification acts as a check to confirm calculations didn鈥檛 go astray, giving a reliable foundation for the answer obtained.

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Most popular questions from this chapter

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