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Division is the operation of dividing a given amount into a prescribed number of equal parts.
Division I
Division is the operation of dividing a given amount into a prescribed number of equal parts.
Division I
Division is the operation of dividing a given amount into a prescribed number of equal parts.
For example, if three people share a dozen apples, then each person gets four apples and there is no leftovers.
Division I
Division is the operation of dividing a given amount into a prescribed number of equal parts.
For example, if three people share a dozen apples, then each person gets four apples and there is no leftovers.
In this case, we say that “12 divides evenly by 3”.
Division I
Division is the operation of dividing a given amount into a prescribed number of equal parts.
For example, if three people share a dozen apples, then each person gets four apples and there is no leftovers.
In this case, we say that “12 divides evenly by 3”. We write this as “12 ÷ 3 = 4” which translates into“if 12 is divided into 3 equal parts, then each part is 4”.
Division I
Division is the operation of dividing a given amount into a prescribed number of equal parts.
For example, if three people share a dozen apples, then each person gets four apples and there is no leftovers.
In this case, we say that “12 divides evenly by 3”. We write this as “12 ÷ 3 = 4” which translates into“if 12 is divided into 3 equal parts, then each part is 4”.
In general, the expression
T ÷ D = Q
Division I
Division is the operation of dividing a given amount into a prescribed number of equal parts.
For example, if three people share a dozen apples, then each person gets four apples and there is no leftovers.
In this case, we say that “12 divides evenly by 3”. We write this as “12 ÷ 3 = 4” which translates into“if 12 is divided into 3 equal parts, then each part is 4”.
In general, the expression
T ÷ D = Q
The total T is the dividend,
Division I
Division is the operation of dividing a given amount into a prescribed number of equal parts.
For example, if three people share a dozen apples, then each person gets four apples and there is no leftovers.
In this case, we say that “12 divides evenly by 3”. We write this as “12 ÷ 3 = 4” which translates into“if 12 is divided into 3 equal parts, then each part is 4”.
In general, the expression
T ÷ D = Q
The total T is the dividend,
The number of parts D is the divisor.
Division I
Division is the operation of dividing a given amount into a prescribed number of equal parts.
For example, if three people share a dozen apples, then each person gets four apples and there is no leftovers.
In this case, we say that “12 divides evenly by 3”. We write this as “12 ÷ 3 = 4” which translates into“if 12 is divided into 3 equal parts, then each part is 4”.
In general, the expression
T ÷ D = Q
The total T is the dividend,
The number of parts D is the divisor.
Q is the quotient.
Division I
Division is the operation of dividing a given amount into a prescribed number of equal parts.
For example, if three people share a dozen apples, then each person gets four apples and there is no leftovers.
In this case, we say that “12 divides evenly by 3”. We write this as “12 ÷ 3 = 4” which translates into“if 12 is divided into 3 equal parts, then each part is 4”.
In general, the expression
T ÷ D = Q
says that “if T is divided into D equal parts, then each part is Q.”
The total T is the dividend,
The number of parts D is the divisor.
Q is the quotient.
Division I
Division is the operation of dividing a given amount into a prescribed number of equal parts.
For example, if three people share a dozen apples, then each person gets four apples and there is no leftovers.
In this case, we say that “12 divides evenly by 3”. We write this as “12 ÷ 3 = 4” which translates into“if 12 is divided into 3 equal parts, then each part is 4”.
In general, the expression
T ÷ D = Q
says that “if T is divided into D equal parts, then each part is Q.”
The total T is the dividend,
The number of parts D is the divisor.
Q is the quotient.
If T ÷ D = Q then T = D x Q or that D and Q are factors of T,
Division I
Division is the operation of dividing a given amount into a prescribed number of equal parts.
For example, if three people share a dozen apples, then each person gets four apples and there is no leftovers.
In this case, we say that “12 divides evenly by 3”. We write this as “12 ÷ 3 = 4” which translates into“if 12 is divided into 3 equal parts, then each part is 4”.
In general, the expression
T ÷ D = Q
says that “if T is divided into D equal parts, then each part is Q.”
The total T is the dividend,
The number of parts D is the divisor.
Q is the quotient.
If T ÷ D = Q then T = D x Q or that D and Q are factors of T, e.g. 12 ÷ 3 = 4 so 12 = 3(4), so both 3 and 4 are factors of 12.
Division I
If four people are to share 11 apples, assuming that no cutting is allowed, then each person gets two and there are three apples left over:
Division I
If four people are to share 11 apples, assuming that no cutting is allowed, then each person gets two and there are three apples left over:
the remainder R
Division I
If four people are to share 11 apples, assuming that no cutting is allowed, then each person gets two and there are three apples left over:
We call the three leftover apples the remainder R.
the remainder R
Division I
If four people are to share 11 apples, assuming that no cutting is allowed, then each person gets two and there are three apples left over:
We call the three leftover apples the remainder R. We write this as “11 ÷ 4 = 2 with R = 3, or with remainder 3.”
the remainder R
Division I
If four people are to share 11 apples, assuming that no cutting is allowed, then each person gets two and there are three apples left over:
We call the three leftover apples the remainder R. We write this as “11 ÷ 4 = 2 with R = 3, or with remainder 3.”
the remainder R
In general, the expression“T ÷ D = Q with remainder R”
says that “if the total T is divided into D equal parts or groups, then each part is Q, with R leftover.”
Division I
If four people are to share 11 apples, assuming that no cutting is allowed, then each person gets two and there are three apples left over:
We call the three leftover apples the remainder R. We write this as “11 ÷ 4 = 2 with R = 3, or with remainder 3.”
the remainder R
In general, the expression“T ÷ D = Q with remainder R”
says that “if the total T is divided into D equal parts or groups,
For example, 7 ÷ 2 = 3 with R = 1 means:
then each part is Q, with R leftover.”
Division I
If four people are to share 11 apples, assuming that no cutting is allowed, then each person gets two and there are three apples left over:
We call the three leftover apples the remainder R. We write this as “11 ÷ 4 = 2 with R = 3, or with remainder 3.”
the remainder R
In general, the expression“T ÷ D = Q with remainder R”
says that “if the total T is divided into D equal parts or groups,
For example, 7 ÷ 2 = 3 with R = 1 means:
2 groups
then each part is Q, with R leftover.”
Division I
If four people are to share 11 apples, assuming that no cutting is allowed, then each person gets two and there are three apples left over:
We call the three leftover apples the remainder R. We write this as “11 ÷ 4 = 2 with R = 3, or with remainder 3.”
the remainder R
In general, the expression“T ÷ D = Q with remainder R”
says that “if the total T is divided into D equal parts or groups,
For example, 7 ÷ 2 = 3 with R = 1 means:
2 groups 3 in a group
then each part is Q, with R leftover.”
Division I
If four people are to share 11 apples, assuming that no cutting is allowed, then each person gets two and there are three apples left over:
We call the three leftover apples the remainder R. We write this as “11 ÷ 4 = 2 with R = 3, or with remainder 3.”
the remainder R
In general, the expression“T ÷ D = Q with remainder R”
says that “if the total T is divided into D equal parts or groups,
For example, 7 ÷ 2 = 3 with R = 1 means:
2 groups 3 in a group 1 remains
then each part is Q, with R leftover.”
Division I
If four people are to share 11 apples, assuming that no cutting is allowed, then each person gets two and there are three apples left over:
We call the three leftover apples the remainder R. We write this as “11 ÷ 4 = 2 with R = 3, or with remainder 3.”
the remainder R
In general, the expression“T ÷ D = Q with remainder R”
says that “if the total T is divided into D equal parts or groups,
Note we may recover the total by back tracking:
For example, 7 ÷ 2 = 3 with R = 1 means:
2 groups 3 in a group 1 remains
then each part is Q, with R leftover.”
Division I
If four people are to share 11 apples, assuming that no cutting is allowed, then each person gets two and there are three apples left over:
We call the three leftover apples the remainder R. We write this as “11 ÷ 4 = 2 with R = 3, or with remainder 3.”
the remainder R
In general, the expression“T ÷ D = Q with remainder R”
says that “if the total T is divided into D equal parts or groups,
Note we may recover the total by back tracking:
For example, 7 ÷ 2 = 3 with R = 1 means:
2 groups 3 in a group 1 remains
then each part is Q, with R leftover.”
2 x 3
Division I
If four people are to share 11 apples, assuming that no cutting is allowed, then each person gets two and there are three apples left over:
We call the three leftover apples the remainder R. We write this as “11 ÷ 4 = 2 with R = 3, or with remainder 3.”
the remainder R
In general, the expression“T ÷ D = Q with remainder R”
says that “if the total T is divided into D equal parts or groups,
Note we may recover the total by back tracking:
For example, 7 ÷ 2 = 3 with R = 1 means:
2 groups 3 in a group 1 remains
then each part is Q, with R leftover.”
2 x 3 + 1 = 7
Division I
Following are important observations about the notation
“T ÷ D = Q with remainder R.”
Division I
* The expression T ÷ 0 does not make sense.
Following are important observations about the notation
“T ÷ D = Q with remainder R.”
Division I
* The expression T ÷ 0 does not make sense.
Following are important observations about the notation
“T ÷ D = Q with remainder R.”
We may leave the total items as one group “T ÷ 1,” or separate them into two groups “T ÷ 2,” or three groups, etc…
Division I
But we can’t ask people to get in the bus(es) when there is no bus, we can’t divide something into no group.
* The expression T ÷ 0 does not make sense.
Following are important observations about the notation
“T ÷ D = Q with remainder R.”
We may leave the total items as one group “T ÷ 1,” or separate them into two groups “T ÷ 2,” or three groups, etc…
Division I
But we can’t ask people to get in the bus(es) when there is no bus, we can’t divide something into no group.
* The expression T ÷ 0 does not make sense.
Following are important observations about the notation
“T ÷ D = Q with remainder R.”
We may leave the total items as one group “T ÷ 1,” or separate them into two groups “T ÷ 2,” or three groups, etc…
* 0 ÷ T = 0, e.g. 0 ÷ 5 = 0.
Division I
But we can’t ask people to get in the bus(es) when there is no bus, we can’t divide something into no group.
* The expression T ÷ 0 does not make sense.
Following are important observations about the notation
“T ÷ D = Q with remainder R.”
We may leave the total items as one group “T ÷ 1,” or separate them into two groups “T ÷ 2,” or three groups, etc…
* 0 ÷ T = 0, e.g. 0 ÷ 5 = 0. If you divide nothing into groups, each group has nothing.
Division I
But we can’t ask people to get in the bus(es) when there is no bus, we can’t divide something into no group.
* T ÷ 1 = T, e.g. 5 ÷ 1 = 5.
* The expression T ÷ 0 does not make sense.
Following are important observations about the notation
“T ÷ D = Q with remainder R.”
We may leave the total items as one group “T ÷ 1,” or separate them into two groups “T ÷ 2,” or three groups, etc…
* 0 ÷ T = 0, e.g. 0 ÷ 5 = 0. If you divide nothing into groups, each group has nothing.
Division I
But we can’t ask people to get in the bus(es) when there is no bus, we can’t divide something into no group.
* T ÷ 1 = T, e.g. 5 ÷ 1 = 5.
* The expression T ÷ 0 does not make sense.
Following are important observations about the notation
“T ÷ D = Q with remainder R.”
We may leave the total items as one group “T ÷ 1,” or separate them into two groups “T ÷ 2,” or three groups, etc…
“T ÷ 1” means to leave the total as one group, and that one group consists of everyone.
* 0 ÷ T = 0, e.g. 0 ÷ 5 = 0. If you divide nothing into groups, each group has nothing.
Division I
But we can’t ask people to get in the bus(es) when there is no bus, we can’t divide something into no group.
* T ÷ 1 = T, e.g. 5 ÷ 1 = 5.
* The expression T ÷ 0 does not make sense.
Following are important observations about the notation
“T ÷ D = Q with remainder R.”
We may leave the total items as one group “T ÷ 1,” or separate them into two groups “T ÷ 2,” or three groups, etc…
“T ÷ 1” means to leave the total as one group, and that one group consists of everyone.
* 0 ÷ T = 0, e.g. 0 ÷ 5 = 0. If you divide nothing into groups, each group has nothing.
* Given that T ÷ D = Q with remainder R ,then the remainder R must be smaller than D.
Division I
But we can’t ask people to get in the bus(es) when there is no bus, we can’t divide something into no group.
* T ÷ 1 = T, e.g. 5 ÷ 1 = 5.
* The expression T ÷ 0 does not make sense.
Following are important observations about the notation
“T ÷ D = Q with remainder R.”
We may leave the total items as one group “T ÷ 1,” or separate them into two groups “T ÷ 2,” or three groups, etc…
“T ÷ 1” means to leave the total as one group, and that one group consists of everyone.
* 0 ÷ T = 0, e.g. 0 ÷ 5 = 0. If you divide nothing into groups, each group has nothing.
* Given that T ÷ D = Q with remainder R ,then the remainder R must be smaller than D. e.g. 11 ÷ 4 = 2 has remainder 3, which is smaller than 4.
Division I
But we can’t ask people to get in the bus(es) when there is no bus, we can’t divide something into no group.
* T ÷ 1 = T, e.g. 5 ÷ 1 = 5.
* The expression T ÷ 0 does not make sense.
Following are important observations about the notation
“T ÷ D = Q with remainder R.”
We may leave the total items as one group “T ÷ 1,” or separate them into two groups “T ÷ 2,” or three groups, etc…
“T ÷ 1” means to leave the total as one group, and that one group consists of everyone.
* 0 ÷ T = 0, e.g. 0 ÷ 5 = 0. If you divide nothing into groups, each group has nothing.
* Given that T ÷ D = Q with remainder R ,then the remainder R must be smaller than D. e.g. 11 ÷ 4 = 2 has remainder 3, We could have made the quotient more if there’s more to share.
which is smaller than 4.
Division I
* If T ÷ D = Q, i.e. T may be divided evenly by D, then T = D x Q,
Division I
* If T ÷ D = Q, i.e. T may be divided evenly by D, then T = D x Q, e.g. 12 ÷ 3 = 4 so 12 = 3(4).
Division I
* If T ÷ D = Q, i.e. T may be divided evenly by D, then T = D x Q, e.g. 12 ÷ 3 = 4 so 12 = 3(4).
* If T ÷ D = Q has remainder R, then T = D x Q + R
Division I
* If T ÷ D = Q, i.e. T may be divided evenly by D, then T = D x Q, e.g. 12 ÷ 3 = 4 so 12 = 3(4).
* If T ÷ D = Q has remainder R, then T = D x Q + R e.g. 7 ÷ 2 = 3 with R = 1
Division I
* If T ÷ D = Q, i.e. T may be divided evenly by D, then T = D x Q, e.g. 12 ÷ 3 = 4 so 12 = 3(4).
* If T ÷ D = Q has remainder R, then T = D x Q + R e.g. 7 ÷ 2 = 3 with R = 1
2 groups 3 in a group 1 remains
Division I
* If T ÷ D = Q, i.e. T may be divided evenly by D, then T = D x Q, e.g. 12 ÷ 3 = 4 so 12 = 3(4).
* If T ÷ D = Q has remainder R, then T = D x Q + R e.g. 7 ÷ 2 = 3 with R = 1 so 7 = 2 x 3 + 1
2 groups 3 in a group 1 remains
Division I
* If T ÷ D = Q, i.e. T may be divided evenly by D, then T = D x Q, e.g. 12 ÷ 3 = 4 so 12 = 3(4).
* If T ÷ D = Q has remainder R, then T = D x Q + R e.g. 7 ÷ 2 = 3 with R = 1 so 7 = 2 x 3 + 1
2 groups 3 in a group 1 remains
Example A.a. What is 1 ÷ 0?
b. What is 0 ÷1?
c. What is 7 ÷ 1?
d. Write the division 12 ÷ 6 = 2 in the multiplicative form.
e. Write the division “13 ÷ 6 = 2 with remainder 1” in the multiplication and addition form.
Division I
* If T ÷ D = Q, i.e. T may be divided evenly by D, then T = D x Q, e.g. 12 ÷ 3 = 4 so 12 = 3(4).
* If T ÷ D = Q has remainder R, then T = D x Q + R e.g. 7 ÷ 2 = 3 with R = 1 so 7 = 2 x 3 + 1
2 groups 3 in a group 1 remains
Example A.a. What is 1 ÷ 0?
b. What is 0 ÷1?
c. What is 7 ÷ 1?
d. Write the division 12 ÷ 6 = 2 in the multiplicative form.
e. Write the division “13 ÷ 6 = 2 with remainder 1” in the multiplication and addition form.
1 ÷ 0 is undefined.
Division I
* If T ÷ D = Q, i.e. T may be divided evenly by D, then T = D x Q, e.g. 12 ÷ 3 = 4 so 12 = 3(4).
* If T ÷ D = Q has remainder R, then T = D x Q + R e.g. 7 ÷ 2 = 3 with R = 1 so 7 = 2 x 3 + 1
2 groups 3 in a group 1 remains
Example A.a. What is 1 ÷ 0?
b. What is 0 ÷1?
c. What is 7 ÷ 1?
d. Write the division 12 ÷ 6 = 2 in the multiplicative form.
e. Write the division “13 ÷ 6 = 2 with remainder 1” in the multiplication and addition form.
1 ÷ 0 is undefined.0 ÷ 1 = 0.
Division I
* If T ÷ D = Q, i.e. T may be divided evenly by D, then T = D x Q, e.g. 12 ÷ 3 = 4 so 12 = 3(4).
* If T ÷ D = Q has remainder R, then T = D x Q + R e.g. 7 ÷ 2 = 3 with R = 1 so 7 = 2 x 3 + 1
2 groups 3 in a group 1 remains
Example A.a. What is 1 ÷ 0?
b. What is 0 ÷1?
c. What is 7 ÷ 1?
d. Write the division 12 ÷ 6 = 2 in the multiplicative form.
e. Write the division “13 ÷ 6 = 2 with remainder 1” in the multiplication and addition form.
1 ÷ 0 is undefined.0 ÷ 1 = 0.
Division I
7 ÷ 1 = 7
* If T ÷ D = Q, i.e. T may be divided evenly by D, then T = D x Q, e.g. 12 ÷ 3 = 4 so 12 = 3(4).
* If T ÷ D = Q has remainder R, then T = D x Q + R e.g. 7 ÷ 2 = 3 with R = 1 so 7 = 2 x 3 + 1
2 groups 3 in a group 1 remains
Example A.a. What is 1 ÷ 0?
b. What is 0 ÷1?
c. What is 7 ÷ 1?
d. Write the division 12 ÷ 6 = 2 in the multiplicative form.
e. Write the division “13 ÷ 6 = 2 with remainder 1” in the multiplication and addition form.
1 ÷ 0 is undefined.0 ÷ 1 = 0.
7 ÷ 1 = 7
12 ÷ 6 = 2 in the multiplicative form is 12 = 6 x 2.
Division I
* If T ÷ D = Q, i.e. T may be divided evenly by D, then T = D x Q, e.g. 12 ÷ 3 = 4 so 12 = 3(4).
* If T ÷ D = Q has remainder R, then T = D x Q + R e.g. 7 ÷ 2 = 3 with R = 1 so 7 = 2 x 3 + 1
2 groups 3 in a group 1 remains
Example A.a. What is 1 ÷ 0?
b. What is 0 ÷1?
c. What is 7 ÷ 1?
d. Write the division 12 ÷ 6 = 2 in the multiplicative form.
e. Write the division “13 ÷ 6 = 2 with remainder 1” in the multiplication and addition form.
1 ÷ 0 is undefined.0 ÷ 1 = 0.
7 ÷ 1 = 7
12 ÷ 6 = 2 in the multiplicative form is 12 = 6 x 2.
The multiplicative form is “13 = 6 x 2 + 1”.
Division I
The Vertical Format Division I
We demonstrate the vertical long-division format below.The Vertical Format
Division I
We demonstrate the vertical long-division format below.The Vertical Format
Steps. i. (Front-in Back-out)Put the problem in the long division format with the back-number (the divisor) outside, and the front-number (the dividend) inside the scaffold.
Division I
We demonstrate the vertical long-division format below.The Vertical Format
Example B. a. Write 6 ÷ 2 as Steps. i. (Front-in Back-out)Put the problem in the long division format with the back-number (the divisor) outside, and the front-number (the dividend) inside the scaffold.“back-one”
outside )2 6
“front-one” inside
Division I
We demonstrate the vertical long-division format below.The Vertical Format
Example B. a. Write 6 ÷ 2 as
ii. Enter the quotient on top,
Steps. i. (Front-in Back-out)Put the problem in the long division format with the back-number (the divisor) outside, and the front-number (the dividend) inside the scaffold.“back-one”
outside )2 6
“front-one” inside
Division I
We demonstrate the vertical long-division format below.The Vertical Format
Example B. a. Write 6 ÷ 2 as
ii. Enter the quotient on top,
Steps. i. (Front-in Back-out)Put the problem in the long division format with the back-number (the divisor) outside, and the front-number (the dividend) inside the scaffold.“back-one”
outside )2 6
“front-one” inside
Enter the quotient on top
3
Division I
We demonstrate the vertical long-division format below.The Vertical Format
Example B. a. Write 6 ÷ 2 as
ii. Enter the quotient on top,Multiply the quotient back into the problem and subtract the results from the dividend (and bring down the rest of the digits, if any. This is the new dividend.)
Steps. i. (Front-in Back-out)Put the problem in the long division format with the back-number (the divisor) outside, and the front-number (the dividend) inside the scaffold.“back-one”
outside )2 6
“front-one” inside
Enter the quotient on top
3
Division I
We demonstrate the vertical long-division format below.The Vertical Format
Example B. a. Write 6 ÷ 2 as
ii. Enter the quotient on top,Multiply the quotient back into the problem and subtract the results from the dividend (and bring down the rest of the digits, if any. This is the new dividend.)
Steps. i. (Front-in Back-out)Put the problem in the long division format with the back-number (the divisor) outside, and the front-number (the dividend) inside the scaffold.“back-one”
outside )2 6
“front-one” inside
Enter the quotient on top
3
multiply the quotientback into the scaffold.
63 x 2
Division I
We demonstrate the vertical long-division format below.The Vertical Format
Example B. a. Write 6 ÷ 2 as
ii. Enter the quotient on top,Multiply the quotient back into the problem and subtract the results from the dividend (and bring down the rest of the digits, if any. This is the new dividend.)
Steps. i. (Front-in Back-out)Put the problem in the long division format with the back-number (the divisor) outside, and the front-number (the dividend) inside the scaffold.“back-one”
outside )2 6
“front-one” inside
Enter the quotient on top
3
multiply the quotientback into the scaffold.
63 x 2 0
The new dividend is 0,
Division I
We demonstrate the vertical long-division format below.The Vertical Format
Example B. a. Write 6 ÷ 2 as
ii. Enter the quotient on top,Multiply the quotient back into the problem and subtract the results from the dividend (and bring down the rest of the digits, if any. This is the new dividend.)
Steps. i. (Front-in Back-out)Put the problem in the long division format with the back-number (the divisor) outside, and the front-number (the dividend) inside the scaffold.“back-one”
outside )2 6
“front-one” inside
Enter the quotient on top
3
iii. If the new dividend is not enough to be divided by the divisor, stop. This is the remainder R. Otherwise, repeat steps i and ii.
multiply the quotientback into the scaffold.
63 x 2 0
The new dividend is 0,
Division I
We demonstrate the vertical long-division format below.The Vertical Format
Example B. a. Write 6 ÷ 2 as
ii. Enter the quotient on top,Multiply the quotient back into the problem and subtract the results from the dividend (and bring down the rest of the digits, if any. This is the new dividend.)
Steps. i. (Front-in Back-out)Put the problem in the long division format with the back-number (the divisor) outside, and the front-number (the dividend) inside the scaffold.“back-one”
outside )2 6
“front-one” inside
Enter the quotient on top
3
iii. If the new dividend is not enough to be divided by the divisor, stop. This is the remainder R. Otherwise, repeat steps i and ii.
multiply the quotientback into the scaffold.
63 x 2 0
The new dividend is 0, not enough to be divided again, stop. This is the remainder R.
Division I
We demonstrate the vertical long-division format below.The Vertical Format
Example B. a. Write 6 ÷ 2 as
ii. Enter the quotient on top,Multiply the quotient back into the problem and subtract the results from the dividend (and bring down the rest of the digits, if any. This is the new dividend.)
Steps. i. (Front-in Back-out)Put the problem in the long division format with the back-number (the divisor) outside, and the front-number (the dividend) inside the scaffold.“back-one”
outside )2 6
“front-one” inside
Enter the quotient on top
3
iii. If the new dividend is not enough to be divided by the divisor, stop. This is the remainder R. Otherwise, repeat steps i and ii.
multiply the quotientback into the scaffold.
63 x 2 0
The new dividend is 0, not enough to be divided again, stop. This is the remainder R.
So the remainder R is 0 and we have that 6 ÷ 2 = 3 evenly.
Division I
b. Carry out the long division 7 ÷ 3.Division I
b. Carry out the long division 7 ÷ 3.
Steps. i. (Front-in Back-out)Put the problem in the long division format with the back-number (the divisor) outside, and the front-number (the dividend) inside the scaffold.
Division I
b. Carry out the long division 7 ÷ 3.
Steps. i. (Front-in Back-out)Put the problem in the long division format with the back-number (the divisor) outside, and the front-number (the dividend) inside the scaffold.
“back-one” outside )3 7
“front-one” inside
Division I
b. Carry out the long division 7 ÷ 3.
Steps. i. (Front-in Back-out)Put the problem in the long division format with the back-number (the divisor) outside, and the front-number (the dividend) inside the scaffold.
“back-one” outside )3 7
“front-one” inside
Enter the quotient on top
2
Division I
b. Carry out the long division 7 ÷ 3.
ii. Enter the quotient on top,Multiply the quotient back into the problem and subtract the results from the dividend (and bring down the rest of the digits, if any. This is the new dividend).
Steps. i. (Front-in Back-out)Put the problem in the long division format with the back-number (the divisor) outside, and the front-number (the dividend) inside the scaffold.
“back-one” outside )3 7
“front-one” inside
Division I
Enter the quotient on top
2
b. Carry out the long division 7 ÷ 3.
ii. Enter the quotient on top,Multiply the quotient back into the problem and subtract the results from the dividend (and bring down the rest of the digits, if any. This is the new dividend).
Steps. i. (Front-in Back-out)Put the problem in the long division format with the back-number (the divisor) outside, and the front-number (the dividend) inside the scaffold.
“back-one” outside )3 7
“front-one” inside
Enter the quotient on top
2
multiply the quotientback into the scaffold.
62 x 3 1
Division I
b. Carry out the long division 7 ÷ 3.
ii. Enter the quotient on top,Multiply the quotient back into the problem and subtract the results from the dividend (and bring down the rest of the digits, if any. This is the new dividend).
Steps. i. (Front-in Back-out)Put the problem in the long division format with the back-number (the divisor) outside, and the front-number (the dividend) inside the scaffold.
“back-one” outside )3 7
“front-one” inside
Enter the quotient on top
2
iii. If the new dividend is not enough to be divided by the divisor, stop. This is the remainder. Otherwise, repeat steps i and ii.
multiply the quotientback into the scaffold.
62 x 3 1
Division I
b. Carry out the long division 7 ÷ 3.
ii. Enter the quotient on top,Multiply the quotient back into the problem and subtract the results from the dividend (and bring down the rest of the digits, if any. This is the new dividend).
Steps. i. (Front-in Back-out)Put the problem in the long division format with the back-number (the divisor) outside, and the front-number (the dividend) inside the scaffold.
“back-one” outside )3 7
“front-one” inside
Enter the quotient on top
2
iii. If the new dividend is not enough to be divided by the divisor, stop. This is the remainder. Otherwise, repeat steps i and ii.
multiply the quotientback into the scaffold.
62 x 3 1
The new dividend is 1, not enough to be divided again, so stop. This is the remainder.
Division I
b. Carry out the long division 7 ÷ 3.
ii. Enter the quotient on top,Multiply the quotient back into the problem and subtract the results from the dividend (and bring down the rest of the digits, if any. This is the new dividend).
Steps. i. (Front-in Back-out)Put the problem in the long division format with the back-number (the divisor) outside, and the front-number (the dividend) inside the scaffold.
“back-one” outside )3 7
“front-one” inside
Enter the quotient on top
2
iii. If the new dividend is not enough to be divided by the divisor, stop. This is the remainder. Otherwise, repeat steps i and ii.
multiply the quotientback into the scaffold.
62 x 3 1
The new dividend is 1, not enough to be divided again, so stop. This is the remainder.
So the remainder is 1 and we have that 7 ÷ 3 = 2 with R = 1.
Division I
b. Carry out the long division 7 ÷ 3.
ii. Enter the quotient on top,Multiply the quotient back into the problem and subtract the results from the dividend (and bring down the rest of the digits, if any. This is the new dividend).
Steps. i. (Front-in Back-out)Put the problem in the long division format with the back-number (the divisor) outside, and the front-number (the dividend) inside the scaffold.
“back-one” outside )3 7
“front-one” inside
Enter the quotient on top
2
iii. If the new dividend is not enough to be divided by the divisor, stop. This is the remainder. Otherwise, repeat steps i and ii.
multiply the quotientback into the scaffold.
62 x 3 1
The new dividend is 1, not enough to be divided again, so stop. This is the remainder.
So the remainder is 1 and we have that 7 ÷ 3 = 2 with R = 1.
Put the result in the multiplicative form, we have that 7 = 2 x 3 + 1.
Division I
