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

878 ÷ 31 = 28 remainder of 10

28 × 31 = 868

878
-868
10

Answer 2

The solution of the student work is wrong

The remainder number should be 10

Further explanation

The division operation is one of the basic arithmetic operations

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

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:

$\large{\boxed{\bold{dividend~\div~divisor=quotient+remainder}}}$

example:

7: 3 = 2 + 1

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

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

In the number above, the form of fraction obtained is the form of mixed fractions

Mixed fractions consist of integers and ordinary fractions

Division operation statement:

"7 divided by 3 equals 2 remainder 1

mixed fractional form

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

Mixed fractions can be expressed as ordinary fractions

$a\frac{b}{c}$ = $\frac{(c\times~a)+b}{c}$

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

This division operation is declared true if the result of:

(divisor x quotient) + remainder = dividend

So from the students work above we can check:

(31x28) +11 = 878

868 + 11 = 878

879 ≠ 878

So the results of the division of tasks from students are wrong

The remainder should be 10

878- (31x28) = 10

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Keywords: division, fraction,