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To perform the division [tex]\(630 \div 5\)[/tex] using long division, follow these steps:
1. Set up the division: Write 630 (the dividend) under the long division symbol and 5 (the divisor) outside.
2. Divide the first digit:
- Look at the first digit of the dividend, which is 6.
- Ask yourself, how many times does 5 go into 6? It goes into 6 exactly 1 time.
- Write 1 above the line, aligned with the 6.
[tex]\[ \begin{array}{r|l} 1 & 5\( \shortmid \) 630 \\ \end{array} \][/tex]
3. Multiply and subtract:
- Multiply 1 (the quotient digit) by 5, which equals 5.
- Write 5 below the 6.
- Subtract 5 from 6, which gives a remainder of 1.
[tex]\[ \begin{array}{r|l} 1 & 5\( \shortmid \) 630 \\ & -5 \\ & 1 \\ \end{array} \][/tex]
4. Bring down the next digit:
- Bring down the next digit of the dividend, which is 3, making the new number 13.
[tex]\[ \begin{array}{r|l} 1 & 5\( \shortmid \) 630 \\ & -5 \\ & 13 \\ \end{array} \][/tex]
5. Divide the new number:
- Ask yourself, how many times does 5 go into 13? It goes into 13 exactly 2 times.
- Write 2 above the line, aligned with the 3.
[tex]\[ \begin{array}{rr|l} 12 & & 5\( \shortmid \) 630 \\ & -5 \\ & 13 \\ \end{array} \][/tex]
6. Multiply and subtract again:
- Multiply 2 (the new quotient digit) by 5, which equals 10.
- Write 10 below the 13.
- Subtract 10 from 13, which gives a remainder of 3.
[tex]\[ \begin{array}{rr|l} 12 & & 5\( \shortmid \) 630 \\ & -5 \\ & 13 \\ & -10 \\ & 3 \\ \end{array} \][/tex]
7. Bring down the next digit:
- Bring down the next and final digit of the dividend, which is 0, making the new number 30.
[tex]\[ \begin{array}{rr|l} 12 & & 5\( \shortmid \) 630 \\ & -5 \\ & 13 \\ & -10 \\ & 30 \\ \end{array} \][/tex]
8. Divide the new number:
- Ask yourself, how many times does 5 go into 30? It goes into 30 exactly 6 times.
- Write 6 above the line, aligned with the 0.
[tex]\[ \begin{array}{rrr|l} 126 & & 5\( \shortmid \) 630 \\ & -5 \\ & 13 \\ & -10 \\ & 30 \\ \end{array} \][/tex]
9. Multiply and subtract one last time:
- Multiply 6 (the quotient digit) by 5, which equals 30.
- Write 30 below the 30.
- Subtract 30 from 30, which gives a remainder of 0.
[tex]\[ \begin{array}{rrr|l} 126 & & 5\( \shortmid \) 630 \\ & -5 \\ & 13 \\ & -10 \\ & 30 \\ & -30 \\ & 0 \\ \end{array} \][/tex]
Hence, the quotient is 126 and the remainder is 0. The final result of the division [tex]\(630 \div 5\)[/tex] is:
[tex]\[ 630 \div 5 = 126 \,R0 \][/tex]
So, [tex]\( 5 \longdiv { 6 3 0 } = 126\)[/tex] with a remainder of 0.
1. Set up the division: Write 630 (the dividend) under the long division symbol and 5 (the divisor) outside.
2. Divide the first digit:
- Look at the first digit of the dividend, which is 6.
- Ask yourself, how many times does 5 go into 6? It goes into 6 exactly 1 time.
- Write 1 above the line, aligned with the 6.
[tex]\[ \begin{array}{r|l} 1 & 5\( \shortmid \) 630 \\ \end{array} \][/tex]
3. Multiply and subtract:
- Multiply 1 (the quotient digit) by 5, which equals 5.
- Write 5 below the 6.
- Subtract 5 from 6, which gives a remainder of 1.
[tex]\[ \begin{array}{r|l} 1 & 5\( \shortmid \) 630 \\ & -5 \\ & 1 \\ \end{array} \][/tex]
4. Bring down the next digit:
- Bring down the next digit of the dividend, which is 3, making the new number 13.
[tex]\[ \begin{array}{r|l} 1 & 5\( \shortmid \) 630 \\ & -5 \\ & 13 \\ \end{array} \][/tex]
5. Divide the new number:
- Ask yourself, how many times does 5 go into 13? It goes into 13 exactly 2 times.
- Write 2 above the line, aligned with the 3.
[tex]\[ \begin{array}{rr|l} 12 & & 5\( \shortmid \) 630 \\ & -5 \\ & 13 \\ \end{array} \][/tex]
6. Multiply and subtract again:
- Multiply 2 (the new quotient digit) by 5, which equals 10.
- Write 10 below the 13.
- Subtract 10 from 13, which gives a remainder of 3.
[tex]\[ \begin{array}{rr|l} 12 & & 5\( \shortmid \) 630 \\ & -5 \\ & 13 \\ & -10 \\ & 3 \\ \end{array} \][/tex]
7. Bring down the next digit:
- Bring down the next and final digit of the dividend, which is 0, making the new number 30.
[tex]\[ \begin{array}{rr|l} 12 & & 5\( \shortmid \) 630 \\ & -5 \\ & 13 \\ & -10 \\ & 30 \\ \end{array} \][/tex]
8. Divide the new number:
- Ask yourself, how many times does 5 go into 30? It goes into 30 exactly 6 times.
- Write 6 above the line, aligned with the 0.
[tex]\[ \begin{array}{rrr|l} 126 & & 5\( \shortmid \) 630 \\ & -5 \\ & 13 \\ & -10 \\ & 30 \\ \end{array} \][/tex]
9. Multiply and subtract one last time:
- Multiply 6 (the quotient digit) by 5, which equals 30.
- Write 30 below the 30.
- Subtract 30 from 30, which gives a remainder of 0.
[tex]\[ \begin{array}{rrr|l} 126 & & 5\( \shortmid \) 630 \\ & -5 \\ & 13 \\ & -10 \\ & 30 \\ & -30 \\ & 0 \\ \end{array} \][/tex]
Hence, the quotient is 126 and the remainder is 0. The final result of the division [tex]\(630 \div 5\)[/tex] is:
[tex]\[ 630 \div 5 = 126 \,R0 \][/tex]
So, [tex]\( 5 \longdiv { 6 3 0 } = 126\)[/tex] with a remainder of 0.
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