To solve these problems, we need to divide decimals by decimals. The easiest way to do this without a calculator is to move the decimal point in both numbers to the right until the number you are dividing *by* (the divisor) becomes a whole number. Then, you perform long division as usual.
Here is the step-by-step solution for each problem:
1. $79.65 \div 2.7$
* Move the decimal one place to the right for both numbers: $796.5 \div 27$.
* $27$ goes into $79$ two times ($27 \times 2 = 54$). Remainder is $25$.
* Bring down the $6$ to make $256$. $27$ goes into $256$ nine times ($27 \times 9 = 243$). Remainder is $13$.
* Bring down the $5$ to make $135$. $27$ goes into $135$ five times exactly ($27 \times 5 = 135$).
*
Answer: 29.5
2. $51.52 \div 1.6$
* Move the decimal one place to the right: $515.2 \div 16$.
* $16$ goes into $51$ three times ($16 \times 3 = 48$). Remainder is $3$.
* Bring down the $5$ to make $35$. $16$ goes into $35$ two times ($16 \times 2 = 32$). Remainder is $3$.
* Bring down the $2$ to make $32$. $16$ goes into $32$ two times exactly.
*
Answer: 32.2
3. $13.96 \div 0.4$
* Move the decimal one place to the right: $139.6 \div 4$.
* $4$ goes into $13$ three times ($4 \times 3 = 12$). Remainder is $1$.
* Bring down the $9$ to make $19$. $4$ goes into $19$ four times ($4 \times 4 = 16$). Remainder is $3$.
* Bring down the $6$ to make $36$. $4$ goes into $36$ nine times exactly.
*
Answer: 34.9
4. $45.6 \div 2.4$
* Move the decimal one place to the right: $456 \div 24$.
* $24$ goes into $45$ one time ($24 \times 1 = 24$). Remainder is $21$.
* Bring down the $6$ to make $216$. $24$ goes into $216$ nine times exactly ($24 \times 9 = 216$).
*
Answer: 19
5. $84 \div 3.5$
* Move the decimal one place to the right: $840 \div 35$.
* $35$ goes into $84$ two times ($35 \times 2 = 70$). Remainder is $14$.
* Bring down the $0$ to make $140$. $35$ goes into $140$ four times exactly ($35 \times 4 = 140$).
*
Answer: 24
6. $96.2 \div 2.6$
* Move the decimal one place to the right: $962 \div 26$.
* $26$ goes into $96$ three times ($26 \times 3 = 78$). Remainder is $18$.
* Bring down the $2$ to make $182$. $26$ goes into $182$ seven times exactly ($26 \times 7 = 182$).
*
Answer: 37
7. $79.23 \div 0.1$
* Moving the decimal one place to the right for $0.1$ makes it $1$. Do the same for $79.23$ to get $792.3$.
* Dividing any number by $1$ gives you the number itself.
*
Answer: 792.3
8. $5.6 \div 2.8$
* Move the decimal one place to the right: $56 \div 28$.
* $28$ goes into $56$ exactly two times.
*
Answer: 2
9. $10.6 \div 0.2$
* Move the decimal one place to the right: $106 \div 2$.
* Half of $100$ is $50$, and half of $6$ is $3$. So, $50 + 3 = 53$.
*
Answer: 53
Final Answer:
1. 29.5
2. 32.2
3. 34.9
4. 19
5. 24
6. 37
7. 792.3
8. 2
9. 53
Parent Tip: Review the logic above to help your child master the concept of decimal division worksheet 7th grade.
