QuestionDivide using repeated subtraction and standard algorithm: a. $508 \div 15$ b. $659 \div 24$ c. $1024 \div 99$

Studdy Solution

STEP 1

Assumptions1. We are performing division operations. . We are using both the repeated-subtraction and the standard algorithm methods.
3. The divisions to be performed are a. 508 \longdiv {15 } b. 659 \longdiv {24 } c. 1024 \longdiv {99 }
Let's start with the first division 508 \longdiv {15 }.

STEP 2

First, we will use the standard algorithm for division.In the standard algorithm, we start by dividing the first number of the dividend (5 in this case) by the divisor (15). Since5 is less than15, we take the next number from the dividend, making it50.50 \longdiv {15 }

STEP 3

We find how many times15 goes into50 without exceeding50. This is3 times because $3 \times15 =45$ which is less than50.So, the first digit of the quotient is3.

STEP 4

We then subtract the result of $3 \times15$ from50, and bring down the next digit from the dividend.
$50 -45 =$ Then we bring down the next digit (8) from the dividend, making it58.

STEP 5

We repeat the process, finding how many times15 goes into58 without exceeding58. This is3 times because $3 \times15 =45$ which is less than58.So, the next digit of the quotient is also3.

STEP 6

We then subtract the result of $3 \times15$ from58.
$58 -45 =13$ Since there are no more digits to bring down from the dividend,13 is the remainder.

STEP 7

So, the result of the division 508 \longdiv {15 } using the standard algorithm is33 remainder13.

STEP 8

Now, let's use the repeated-subtraction method for the same division.
In the repeated-subtraction method, we start by subtracting the divisor from the dividend until the result is less than the divisor.
$508 -15 =493$

STEP 9

We continue subtracting15 from the result.
$493 -15 =478$

STEP 10

We repeat this process until the result is less than15.
After33 subtractions, we get a result of13, which is less than15.

STEP 11

So, the result of the division 508 \longdiv {15 } using the repeated-subtraction method is also33 remainder13.
Now, let's move on to the second division 659 \longdiv {24 }.

STEP 12

First, we will use the standard algorithm for division.In the standard algorithm, we start by dividing the first number of the dividend (6 in this case) by the divisor (24). Since6 is less than24, we take the next number from the dividend, making it65.65 \longdiv {24 }

STEP 13

We find how many times24 goes into65 without exceeding65. This is2 times because $2 \times24 =48$ which is less than65.So, the first digit of the quotient is2.

STEP 14

We then subtract the result of $2 \times24$ from65, and bring down the next digit from the dividend.
$65 -48 =17$ Then we bring down the next digit (9) from the dividend, making it179.

STEP 15

We repeat the process, finding how many times24 goes into179 without exceeding179. This is7 times because $7 \times24 =168$ which is less than179.So, the next digit of the quotient is7.

STEP 16

We then subtract the result of $\times24$ from179.
$179 -168 =11$ Since there are no more digits to bring down from the dividend,11 is the remainder.

STEP 17

So, the result of the division 659 \longdiv {24 } using the standard algorithm is27 remainder11.

STEP 18

Now, let's use the repeated-subtraction method for the same division.
In the repeated-subtraction method, we start by subtracting the divisor from the dividend until the result is less than the divisor.
$659 -24 =635$

STEP 19

We continue subtracting24 from the result.
$635 -24 =611$

STEP 20

We repeat this process until the result is less than24.
After27 subtractions, we get a result of11, which is less than24.

STEP 21

So, the result of the division 659 \longdiv {24 } using the repeated-subtraction method is also27 remainder11.
Now, let's move on to the third division 1024 \longdiv {99 }.

STEP 22

First, we will use the standard algorithm for division.In the standard algorithm, we start by dividing the first number of the dividend (1 in this case) by the divisor (99). Since1 is less than99, we take the next two numbers from the dividend, making it102.102 \longdiv {99 }

STEP 23

We find how many times99 goes into102 without exceeding102. This is1 time because $1 \times99 =99$ which is less than102.So, the first digit of the quotient is1.

STEP 24

We then subtract the result of $1 \times99$ from102, and bring down the next digit from the dividend.
$102 -99 =3$ Then we bring down the next digit (4) from the dividend, making it34.

STEP 25

We repeat the process, finding how many times99 goes into34 without exceeding34. Since34 is less than99,99 cannot go into34.So, the next digit of the quotient is0 and34 is the remainder.

STEP 26

So, the result of the division 1024 \longdiv {99 } using the standard algorithm is10 remainder34.

STEP 27

Now, let's use the repeated-subtraction method for the same division.
In the repeated-subtraction method, we start by subtracting the divisor from the dividend until the result is less than the divisor.
$1024 -99 =925$

STEP 28

We continue subtracting99 from the result.
$925 -99 =826$

STEP 29

We repeat this process until the result is less than99.
After10 subtractions, we get a result of34, which is less than99.

STEP 30

So, the result of the division 1024 \longdiv {99 } using the repeated-subtraction method is also10 remainder34.

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QuestionDivide using repeated subtraction and standard algorithm: a. 508÷15508 \div 15508÷15 b. 659÷24659 \div 24659÷24 c. 1024÷991024 \div 991024÷99

Studdy Solution

STEP 1

Assumptions1. We are performing division operations. . We are using both the repeated-subtraction and the standard algorithm methods.3. The divisions to be performed are a. 508 \longdiv {15 } b. 659 \longdiv {24 } c. 1024 \longdiv {99 }Let's start with the first division 508 \longdiv {15 }.

STEP 2

First, we will use the standard algorithm for division.In the standard algorithm, we start by dividing the first number of the dividend (5 in this case) by the divisor (15). Since5 is less than15, we take the next number from the dividend, making it50.50 \longdiv {15 }

STEP 3

We find how many times15 goes into50 without exceeding50. This is3 times because 3×15=453 \times15 =453×15=45 which is less than50.So, the first digit of the quotient is3.

STEP 4

We then subtract the result of 3×153 \times153×15 from50, and bring down the next digit from the dividend.50−45=50 -45 =50−45=Then we bring down the next digit (8) from the dividend, making it58.

STEP 5

We repeat the process, finding how many times15 goes into58 without exceeding58. This is3 times because 3×15=453 \times15 =453×15=45 which is less than58.So, the next digit of the quotient is also3.

STEP 6

We then subtract the result of 3×153 \times153×15 from58.58−45=1358 -45 =1358−45=13Since there are no more digits to bring down from the dividend,13 is the remainder.

STEP 7

So, the result of the division 508 \longdiv {15 } using the standard algorithm is33 remainder13.

STEP 8

Now, let's use the repeated-subtraction method for the same division.In the repeated-subtraction method, we start by subtracting the divisor from the dividend until the result is less than the divisor.508−15=493508 -15 =493508−15=493

STEP 9

We continue subtracting15 from the result.493−15=478493 -15 =478493−15=478

STEP 10

We repeat this process until the result is less than15.After33 subtractions, we get a result of13, which is less than15.

STEP 11

So, the result of the division 508 \longdiv {15 } using the repeated-subtraction method is also33 remainder13.Now, let's move on to the second division 659 \longdiv {24 }.

STEP 12

First, we will use the standard algorithm for division.In the standard algorithm, we start by dividing the first number of the dividend (6 in this case) by the divisor (24). Since6 is less than24, we take the next number from the dividend, making it65.65 \longdiv {24 }

STEP 13

We find how many times24 goes into65 without exceeding65. This is2 times because 2×24=482 \times24 =482×24=48 which is less than65.So, the first digit of the quotient is2.

STEP 14

We then subtract the result of 2×242 \times242×24 from65, and bring down the next digit from the dividend.65−48=1765 -48 =1765−48=17Then we bring down the next digit (9) from the dividend, making it179.

STEP 15

We repeat the process, finding how many times24 goes into179 without exceeding179. This is7 times because 7×24=1687 \times24 =1687×24=168 which is less than179.So, the next digit of the quotient is7.

STEP 16

We then subtract the result of ×24 \times24×24 from179.179−168=11179 -168 =11179−168=11Since there are no more digits to bring down from the dividend,11 is the remainder.

STEP 17

So, the result of the division 659 \longdiv {24 } using the standard algorithm is27 remainder11.

STEP 18

Now, let's use the repeated-subtraction method for the same division.In the repeated-subtraction method, we start by subtracting the divisor from the dividend until the result is less than the divisor.659−24=635659 -24 =635659−24=635

STEP 19

We continue subtracting24 from the result.635−24=611635 -24 =611635−24=611

STEP 20

We repeat this process until the result is less than24.After27 subtractions, we get a result of11, which is less than24.

STEP 21

So, the result of the division 659 \longdiv {24 } using the repeated-subtraction method is also27 remainder11.Now, let's move on to the third division 1024 \longdiv {99 }.

STEP 22

First, we will use the standard algorithm for division.In the standard algorithm, we start by dividing the first number of the dividend (1 in this case) by the divisor (99). Since1 is less than99, we take the next two numbers from the dividend, making it102.102 \longdiv {99 }

STEP 23

We find how many times99 goes into102 without exceeding102. This is1 time because 1×99=991 \times99 =991×99=99 which is less than102.So, the first digit of the quotient is1.

STEP 24

We then subtract the result of 1×991 \times991×99 from102, and bring down the next digit from the dividend.102−99=3102 -99 =3102−99=3Then we bring down the next digit (4) from the dividend, making it34.

STEP 25

We repeat the process, finding how many times99 goes into34 without exceeding34. Since34 is less than99,99 cannot go into34.So, the next digit of the quotient is0 and34 is the remainder.

STEP 26

So, the result of the division 1024 \longdiv {99 } using the standard algorithm is10 remainder34.

STEP 27

Now, let's use the repeated-subtraction method for the same division.In the repeated-subtraction method, we start by subtracting the divisor from the dividend until the result is less than the divisor.1024−99=9251024 -99 =9251024−99=925

STEP 28

We continue subtracting99 from the result.925−99=826925 -99 =826925−99=826

STEP 29

We repeat this process until the result is less than99.After10 subtractions, we get a result of34, which is less than99.

STEP 30

So, the result of the division 1024 \longdiv {99 } using the repeated-subtraction method is also10 remainder34.

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QuestionDivide using repeated subtraction and standard algorithm: a. $508 \div 15$ b. $659 \div 24$ c. $1024 \div 99$

Assumptions1. We are performing division operations. . We are using both the repeated-subtraction and the standard algorithm methods.
3. The divisions to be performed are a. 508 \longdiv {15 } b. 659 \longdiv {24 } c. 1024 \longdiv {99 }
Let's start with the first division 508 \longdiv {15 }.

We find how many times15 goes into50 without exceeding50. This is3 times because $3 \times15 =45$ which is less than50.So, the first digit of the quotient is3.

We then subtract the result of $3 \times15$ from50, and bring down the next digit from the dividend.
$50 -45 =$ Then we bring down the next digit (8) from the dividend, making it58.

We repeat the process, finding how many times15 goes into58 without exceeding58. This is3 times because $3 \times15 =45$ which is less than58.So, the next digit of the quotient is also3.

We then subtract the result of $3 \times15$ from58.
$58 -45 =13$ Since there are no more digits to bring down from the dividend,13 is the remainder.

Now, let's use the repeated-subtraction method for the same division.
In the repeated-subtraction method, we start by subtracting the divisor from the dividend until the result is less than the divisor.
$508 -15 =493$

We continue subtracting15 from the result.
$493 -15 =478$

We repeat this process until the result is less than15.
After33 subtractions, we get a result of13, which is less than15.

So, the result of the division 508 \longdiv {15 } using the repeated-subtraction method is also33 remainder13.
Now, let's move on to the second division 659 \longdiv {24 }.

We find how many times24 goes into65 without exceeding65. This is2 times because $2 \times24 =48$ which is less than65.So, the first digit of the quotient is2.

We then subtract the result of $2 \times24$ from65, and bring down the next digit from the dividend.
$65 -48 =17$ Then we bring down the next digit (9) from the dividend, making it179.

We repeat the process, finding how many times24 goes into179 without exceeding179. This is7 times because $7 \times24 =168$ which is less than179.So, the next digit of the quotient is7.

We then subtract the result of $\times24$ from179.
$179 -168 =11$ Since there are no more digits to bring down from the dividend,11 is the remainder.

Now, let's use the repeated-subtraction method for the same division.
In the repeated-subtraction method, we start by subtracting the divisor from the dividend until the result is less than the divisor.
$659 -24 =635$

We continue subtracting24 from the result.
$635 -24 =611$

We repeat this process until the result is less than24.
After27 subtractions, we get a result of11, which is less than24.

So, the result of the division 659 \longdiv {24 } using the repeated-subtraction method is also27 remainder11.
Now, let's move on to the third division 1024 \longdiv {99 }.

We find how many times99 goes into102 without exceeding102. This is1 time because $1 \times99 =99$ which is less than102.So, the first digit of the quotient is1.

We then subtract the result of $1 \times99$ from102, and bring down the next digit from the dividend.
$102 -99 =3$ Then we bring down the next digit (4) from the dividend, making it34.

Now, let's use the repeated-subtraction method for the same division.
In the repeated-subtraction method, we start by subtracting the divisor from the dividend until the result is less than the divisor.
$1024 -99 =925$

We continue subtracting99 from the result.
$925 -99 =826$

We repeat this process until the result is less than99.
After10 subtractions, we get a result of34, which is less than99.