Choosing Maths Tools

Question 1

Mia needs to calculate 9,537 ÷ 17 for her science‑fair budget. Which statement best explains why the long‑division algorithm is the smarter tool to use instead of trying to do the division only in her head?

Accepted Answer

Long division splits the problem into small, ordered steps and records each remainder, so the exact quotient is found reliably; doing it mentally would require many repeated subtractions or rough estimates, which is easy to mess up with a four‑digit dividend and a two‑digit divisor.

Answer

Because 17 is a prime number, it cannot be divided without a calculator, so the only way is to use long division.

Answer

Numbers that end in 7, like 9,537, must be divided with long division; mental methods give wrong answers for such numbers.

Answer

Since the answer will be a whole number, long division is required; mental methods only give approximate results.

Question 2

Jenna is preparing 5,184 beads to make equal bracelets for her class. If she wants to put the same number of beads on each of the 16 bracelets, which reason best shows why using the long‑division algorithm is the better tool instead of trying to do the division only in her head?

Accepted Answer

Because the dividend is large and the divisor is a two‑digit number that doesn’t fit neatly into place‑value tricks, long division lets her work one digit at a time and keeps mistakes low.

Answer

Because she can repeatedly subtract 16 from 5,184 until she reaches zero, which is the most reliable way for big numbers.

Answer

Because she can split 5,184 into 5,000 + 180 + 4, divide each part mentally, and add the results, which is faster than long division.

Answer

Because any division larger than 100 should be done with a calculator, and long division is just a way to copy what a calculator would do.

Question 3

Jamal is sharing 5,643 stickers equally among 17 friends. Which explanation best shows why using the long‑division algorithm is the smarter tool instead of trying to do the division only in his head?

Accepted Answer

Long division lets him work one digit at a time, keeping track of remainders, so he gets the exact whole‑number quotient and any leftover stickers.

Answer

He can quickly multiply 17 by 300 in his head and then subtract, which is faster than any written method.

Answer

He can round 17 up to 20, divide 5,643 by 20 mentally, and then adjust the answer to get the exact result.

Answer

He could keep subtracting 17 from 5,643 until he reaches zero, which is just another way to do long division.

Try three questions

Mia needs to calculate 9,537 ÷ 17 for her science‑fair budget. Which statement best explains why the long‑division algorithm is the smarter tool to use instead of trying to do the division only in her head?

Jenna is preparing 5,184 beads to make equal bracelets for her class. If she wants to put the same number of beads on each of the 16 bracelets, which reason best shows why using the long‑division algorithm is the better tool instead of trying to do the division only in her head?

Jamal is sharing 5,643 stickers equally among 17 friends. Which explanation best shows why using the long‑division algorithm is the smarter tool instead of trying to do the division only in his head?

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