In some division problems, we do not obtain an exact result because there is a remainder. For example,
This means that is more than but less than It is somewhere in between.
So what is exactly?
We can write the exact result of this division problem as a mixed number, where the quotient () is the whole number part, and the remainder () is expressed as a fraction.
To write the remainder as a fraction, we just need to divide it by the original divisor (). Therefore, expressed as a mixed number, our result is
What is
The whole number part of must be because
can go into a total of times (), but
cannot go into a total of times ().
The remainder is so
To write the remainder as a fraction, we divide it by the original divisor (). Therefore,
What is $53 \div 8?$
|
a
|
$6\,\dfrac{5}{8}$ |
|
b
|
$5\,\dfrac{3}{4}$ |
|
c
|
$5\,\dfrac{2}{3}$ |
|
d
|
$6\,\dfrac{3}{8}$ |
|
e
|
$6\,\dfrac{1}{4}$ |
What is $28 \div 3?$
|
a
|
$10 \, \dfrac{2}{3}$ |
|
b
|
$9 \, \dfrac{1}{3}$ |
|
c
|
$9 \, \dfrac{1}{2}$ |
|
d
|
$9 \, \dfrac{2}{3}$ |
|
e
|
$10 \, \dfrac{1}{3}$ |
We can apply the idea of representing a remainder as a fraction to any problem involving the division of whole numbers. To illustrate, let's write as a mixed number.
We start by going through the long division procedure as usual:
From the long division, we conclude that
To write the remainder as a fraction, we divide it by the original divisor (). Therefore, expressed as a mixed number, our result is
A fisherman evenly distributed pounds of fish into boxes. How many pounds of fish did he put in each box?
We need to work out We start by going through the long division procedure as usual:
From the long division, we conclude that
To write the remainder as a fraction, we divide it by the original divisor (). So, the mixed number is
Therefore, the fisherman put pounds of fish in each box.
Alice cut a $77$-inch long piece of ribbon into $6$ smaller pieces of equal size. How long is each piece?
|
a
|
$12\,\dfrac 5 6$ inches |
|
b
|
$10\,\dfrac 6 5$ inches |
|
c
|
$5\,\dfrac 5 7$ inches |
|
d
|
$6\,\dfrac 4 5$ inches |
|
e
|
$8\,\dfrac 5 6$ inches |
A $99$-pound sack of rice is to be split equally among $8$ people. How much rice will each person get?
|
a
|
$12\,\dfrac 3 8$ pounds |
|
b
|
$5$ pounds |
|
c
|
$8\,\dfrac 1 3$ pounds |
|
d
|
$11\,\dfrac 2 3$ pounds |
|
e
|
$10\,\dfrac 3 4$ pounds |
What is
We start by going through the long division procedure as usual:
From the long division, we conclude that
To write the remainder as a fraction, we divide it by the original divisor (). So, the mixed number is
We can simplify the fractional part by dividing the numerator and denominator by
Therefore, the simplified mixed number is
What is $62 \div 4 ?$
|
a
|
$15 \, \dfrac{1}{4}$ |
|
b
|
$15 \, \dfrac{1}{2}$ |
|
c
|
$16 \, \dfrac{1}{3}$ |
|
d
|
$15 \, \dfrac{1}{3}$ |
|
e
|
$16 \, \dfrac{1}{2}$ |
What is $54 \div 4?$
|
a
|
$13 \, \dfrac{1}{3}$ |
|
b
|
$14 \, \dfrac{1}{4}$ |
|
c
|
$13 \, \dfrac{3}{4}$ |
|
d
|
$13 \, \dfrac{1}{2}$ |
|
e
|
$14 \, \dfrac{1}{2}$ |
What is
We start by going through the long division procedure as usual:
From the long division, we conclude that
To write the remainder as a fraction, we divide it by the original divisor (). So, the mixed number is
We can simplify the fractional part by dividing the numerator and denominator by
Therefore, the simplified mixed number is
A farmer wants to evenly split a $323$-acre field into $7$ plots of the same size. How big will each plot be?
|
a
|
$46 \, \dfrac{1}{7}$ acres |
|
b
|
$32 \, \dfrac{3}{7}$ acres |
|
c
|
$44 \, \dfrac{6}{7}$ acres |
|
d
|
$47 \, \dfrac{3}{7}$ acres |
|
e
|
$45 \, \dfrac{2}{7}$ acres |
What is $495 \div 6 ?$
|
a
|
$82 \, \dfrac{1}{2}$ |
|
b
|
$83 \, \dfrac{1}{6}$ |
|
c
|
$82 \, \dfrac{2}{3}$ |
|
d
|
$82 \, \dfrac{1}{6}$ |
|
e
|
$81 \, \dfrac{5}{6}$ |