Question

When dividing 878 by 31, a student finds a quotient of 28 with a remainder of 11. Check the students work, and use the check to find the error in the solution

Answer 1

There is an error in the student's work, the remainder should be 10

Further explanation

The division operation is one of the basic arithmetic operations

Common signs used are $\large{\boxed{:}}}$ or $\large{\boxed{\slash}}$

The division is written by placing the numerator above the denominator with a horizontal line between them or use a slash with the numerator's position and the denominator is parallel

The division is actually an iterative subtraction operation (as many as the number of divisors)

Division is the opposite of multiplying

The general form of division can be stated by:

$\large{\boxed{\bold{divident:divisor=quotient+remainder}}$

example:

7: 3 = 2 + 1

• 7 = dividend
• 3 = divisor
• 2 = quotient
• 1 = remainder

Division operation statement:

"7 divided by 3 equals 2 remainder 1 "

The form of division can also be expressed in terms of fractions

In the example above, the form of mixed fractions  :

$\displaystyle \frac{7}{3} =2\frac{1}{3}$

Mixed fractions consist of whole number and proper fractions

From the task

(see also the attached image)

When dividing 878 by 31, a student finds a quotient of 28 with a remainder of 11.

Division operation statement:

"878 divided by 31 equals 28 remainder 11

Arithmetic operations :

878 : 31 = 28 + 11

• 878 = dividend
• 31 = divisor
• 28 = quotient
• 11 = remainder

Because Division is the opposite of multiplying , so we check the solution with multiplying

divident - (divisor x quotient) = remainder

878 - (31 x 28) = 11

878 - 868 = 11

10 ≠ 11

So students make mistakes in subtraction operations,remainder should be 10

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Keywords: division, mixed fraction, dividend , divisor , quotient, remainder

Answer 2

878/3 is 28 with a remainder of 10! The error is when they subtracted 258-248 wrong