Division using partial quotients worksheet with two-digit dividends and no remainders.

Here are the solutions for the division problems using partial quotients.

1) $63 \div 4$
* Easy Multiples:
* $4 \times 1 = 4$
* $4 \times 2 = 8$
* $4 \times 5 = 20$
* $4 \times 10 = 40$
* $4 \times 20 = 80$
* Division Steps:
* Subtract $40$ ($4 \times 10$) from $63$. Result: $23$.
* Subtract $20$ ($4 \times 5$) from $23$. Result: $3$.
* Add the partial quotients: $10 + 5 = 15$.
* The remainder is $3$.
* Answer: $15$ R $3$

2) $72 \div 3$
* Easy Multiples:
* $3 \times 1 = 3$
* $3 \times 2 = 6$
* $3 \times 5 = 15$
* $3 \times 10 = 30$
* $3 \times 20 = 60$
* Division Steps:
* Subtract $60$ ($3 \times 20$) from $72$. Result: $12$.
* Subtract $12$ ($3 \times 4$, or two groups of $6$) from $12$. Result: $0$. Let's use the provided multiples: subtract $6$ ($3 \times 2$) twice, or just recognize $12$ is $3 \times 4$. Since $4$ isn't listed, let's do $3 \times 2 = 6$ and another $3 \times 2 = 6$. Or simpler: $3 \times 10 = 30$, $3 \times 20 = 60$. $72-60=12$. $12 \div 3 = 4$. So add $4$ to $20$. Total $24$.
* Using strictly the box multiples: Subtract $60$ ($3 \times 20$). Remainder $12$. We can split $12$ into $6 + 6$. So subtract $6$ ($3 \times 2$) and another $6$ ($3 \times 2$).
* Add partial quotients: $20 + 2 + 2 = 24$.
* The remainder is $0$.
* Answer: $24$

3) $88 \div 2$
* Easy Multiples:
* $2 \times 1 = 2$
* $2 \times 2 = 4$
* $2 \times 5 = 10$
* $2 \times 10 = 20$
* $2 \times 20 = 40$
* Division Steps:
* Subtract $40$ ($2 \times 20$) from $88$. Result: $48$.
* Subtract $40$ ($2 \times 20$) from $48$. Result: $8$.
* Subtract $8$ ($2 \times 4$, or four $2$s). Let's use $2 \times 2 = 4$ twice. Or simply know $8 \div 2 = 4$.
* Add partial quotients: $20 + 20 + 4 = 44$.
* The remainder is $0$.
* Answer: $44$

4) $75 \div 5$
* Easy Multiples:
* $5 \times 1 = 5$
* $5 \times 2 = 10$
* $5 \times 5 = 25$
* $5 \times 10 = 50$
* Division Steps:
* Subtract $50$ ($5 \times 10$) from $75$. Result: $25$.
* Subtract $25$ ($5 \times 5$) from $25$. Result: $0$.
* Add partial quotients: $10 + 5 = 15$.
* The remainder is $0$.
* Answer: $15$

5) $79 \div 2$
* Easy Multiples:
* $2 \times 1 = 2$
* $2 \times 2 = 4$
* $2 \times 5 = 10$
* $2 \times 10 = 20$
* $2 \times 20 = 40$
* Division Steps:
* Subtract $40$ ($2 \times 20$) from $79$. Result: $39$.
* Subtract $20$ ($2 \times 10$) from $39$. Result: $19$. (Or subtract another $40$? No, $39 < 40$). Let's stick to easy chunks.
* Actually, easier path: Subtract $40$ ($2 \times 20$). Remainder $39$. Subtract $20$ ($2 \times 10$)? No, let's subtract $2 \times 10 = 20$. Remainder $19$. Subtract $2 \times 5 = 10$. Remainder $9$. Subtract $2 \times 4 = 8$. Remainder $1$.
* Let's try bigger chunks: $2 \times 20 = 40$. $79 - 40 = 39$. $2 \times 10 = 20$. $39 - 20 = 19$. $2 \times 5 = 10$. $19 - 10 = 9$. $2 \times 4 = 8$. $9 - 8 = 1$. Sum: $20+10+5+4 = 39$.
* Simpler path with given multiples: $2 \times 20 = 40$. $79-40=39$. Another $2 \times 20 = 40$ is too big. Use $2 \times 10 = 20$. $39-20=19$. Use $2 \times 5 = 10$. $19-10=9$. Use $2 \times 2 = 4$ twice? $9-4=5$, $5-4=1$. That's messy.
* Best standard path: $2 \times 30 = 60$ (not in list). List has $20$.
* $79 - 40 (2\times20) = 39$.
* $39 - 20 (2\times10) = 19$.
* $19 - 10 (2\times5) = 9$.
* $9 - 8 (2\times4) = 1$. Note: $4$ is not explicitly in the "easy multiples" box as a multiplier, but $2\times2=4$ is. So we can take two groups of $2\times2$. Or just see that $9 \div 2$ is $4$ r $1$.
* Sum: $20 + 10 + 5 + 4 = 39$.
* The remainder is $1$.
* Answer: $39$ R $1$

6) $89 \div 6$
* Easy Multiples:
* $6 \times 1 = 6$
* $6 \times 2 = 12$
* $6 \times 5 = 30$
* $6 \times 10 = 60$
* Division Steps:
* Subtract $60$ ($6 \times 10$) from $89$. Result: $29$.
* Subtract $24$ ($6 \times 4$) from $29$. We don't have $4$ in the list, but we have $2$ and $1$. Or we can subtract $30$? No, $29 < 30$.
* Subtract $12$ ($6 \times 2$) from $29$. Result: $17$.
* Subtract $12$ ($6 \times 2$) from $17$. Result: $5$.
* Add partial quotients: $10 + 2 + 2 = 14$.
* The remainder is $5$.
* Answer: $14$ R $5$

Final Answer:
1) 15 R 3
2) 24
3) 44
4) 15
5) 39 R 1
6) 14 R 5