In this lesson, we'll learn how to solve division problems with remainders without using models.
For example, let's consider the following division problem:
We solve this division problem by finding the quotient and remainder separately:
To find the quotient, we need to determine how many times goes into To do that, we list the multiples of until we get to one that's larger than Notice that is larger than but is smaller than So, goes into a total of times.
Therefore, the quotient of our division problem is
To find the remainder, we write the last equation as a multiplication plus the remainder: This equation simplifies as follows: Therefore, the remainder must be
Finally, we have
Find the quotient in the division problem below.
To find the quotient, we need to determine how many times goes into
We list the multiples of until we get to one that's larger than
So, goes into a total of times. Therefore, the quotient is
Finally, we can write
What are the quotient and the remainder of
Hint: Use the fact that and
Let's compute the quotient and remainder:
To find the quotient, we list the multiples of until we get to one that's larger than Therefore, the quotient is and we can write the following:
To find the remainder, we write the last equation as a multiplication plus the remainder: This equation simplifies as follows:
Therefore, the remainder must be Finally, we have
What are the quotient and the remainder of $37 \div 5?$
Hint: Use the fact that $7 \times 5 = 35$ and $8 \times 5 = 40.$
a
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$6 \, \textrm{R} \, 5$ |
b
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$7 \, \textrm{R} \, 4$ |
c
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$7 \, \textrm{R} \, 2$ |
d
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$6 \, \textrm{R} \, 1$ |
e
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$7 \, \textrm{R} \, 3$ |
Using the fact that $6 \times 4 = 24$ and $7 \times 4 = 28,$ find the quotient and remainder in the divison problem below.
a
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b
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c
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d
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e
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What are the quotient and the remainder of $34 \div 7?$
Hint: Use the fact that $4 \times 7 = 28$ and $5 \times 7 = 35.$
a
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$4 \, \textrm{R} \, 1$ |
b
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$5 \, \textrm{R} \, 2$ |
c
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$4 \, \textrm{R} \, 5$ |
d
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$4 \, \textrm{R} \, 6$ |
e
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$5 \, \textrm{R} \, 4$ |
Find the quotient and the remainder of
Let's compute the quotient and remainder:
To find the quotient, we list the multiples of until we get to one that's larger than Therefore, the quotient is and we can write the following:
To find the remainder, we write the last equation as a multiplication plus the remainder: This equation simplifies as follows:
Therefore, the remainder must be Finally, we have
$49 \div 5 =$
a
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$9 \, \textrm{R} \, 4$ |
b
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$8 \, \textrm{R} \, 3$ |
c
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$9 \, \textrm{R} \, 2$ |
d
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$8 \, \textrm{R} \, 4$ |
e
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$9 \, \textrm{R} \, 1$ |