Writing and Checking Division with Remainders

Core Concepts

Learn the correct format for writing answers with remainders and, most importantly, the method to check your work to ensure it's accurate.

Writing and Checking Division with Remainders

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How do you write the answer for "17 divided by 5 is 3 with a remainder of 2"?

You can write it as \(17 \div 5 = 3 \text{ R } 2\), where \(\text{ R }\) stands for Remainder.

What is the formula to check the answer to a division problem with a remainder?

(Divisor \(\times\) Quotient) \(+\) Remainder \(=\) Dividend

The answer to \(23 \div 4\) is \(5 \text{ R } 3\). Use the formula to check if this is correct.

Check: (\(4 \times 5\)) \(+\) \(3\) \(=\) \(20 + 3\) \(=\) \(23\). The answer is correct because it equals the dividend.

A student says \(19 \div 3 = 5 \text{ R } 4\). Is this correct? Why or why not?

No. The remainder (\(4\)) cannot be greater than or equal to the divisor (\(3\)). The correct answer is \(6 \text{ R } 1\).

Check this answer: \(38 \div 7 = 5 \text{ R } 3\).

Check: (\(7 \times 5\)) \(+\) \(3\) \(=\) \(35 + 3\) \(=\) \(38\). This is correct.

What is missing from this equation to make it correct for problems with remainders? \((\text{Divisor} \times \text{Quotient}) = \text{Dividend}\)

You must also add the remainder. The correct check is (Divisor \(\times\) Quotient) \(+\) Remainder \(=\) Dividend.

Solve and write the answer in \(\text{R}\) notation: \(41 \div 6\).

\(6 \text{ R } 5\). (Check: \(6 \times 6 + 5 = 36 + 5 = 41\))

Check this answer: \(52 \div 8 = 6 \text{ R } 4\).

Check: (\(8 \times 6\)) \(+\) \(4\) \(=\) \(48 + 4\) \(=\) \(52\). This is correct.

A student's work shows \(29 \div 5 = 5 \text{ R } 4\). How would you tell them to check their answer?

Multiply the divisor (\(5\)) by the quotient (\(5\)), then add the remainder (\(4\)). See if the result is the original dividend (\(29\)).

If \(Divisor = 9\), \(Quotient = 8\), and \(Remainder = 2\), what is the Dividend?

Dividend \(= (9 \times 8) + 2 = 72 + 2 = 74\). The original problem was \(74 \div 9\).

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