Lesson 64: Division with Two-Digit Answers, Part 1

New Concept

In this lesson we will learn a pencil-and-paper method for dividing a two-digit number by a one-digit number.

What’s next

Next, you’ll apply this step-by-step process of dividing, multiplying, subtracting, and bringing down to solve problems with two-digit answers.

Property

To divide a two-digit number, we use a step-by-step process. First, divide the tens digit. Then, multiply, subtract, and bring down the ones digit. Finally, divide the new number. The process is based on the formula: Number of groups $\times$ Number in each group = Total.

• To solve $4 \overline{)96}$: First, $9 \div 4$ is 2. Multiply $2 \times 4 = 8$. Subtract $9 - 8 = 1$. Bring down the 6 to make 16. Then $16 \div 4 = 4$. The answer is 24.
• To solve $3 \overline{)84}$: First, $8 \div 3$ is 2. Multiply $2 \times 3 = 6$. Subtract $8 - 6 = 2$. Bring down the 4 to make 24. Then $24 \div 3 = 8$. The answer is 28.

Think of long division as a dance with four simple steps: Divide, Multiply, Subtract, and Bring Down! You repeat this rhythm until the problem is solved. This process breaks a huge division problem into tiny, manageable chunks. It’s a super organized way to make sure you handle every digit correctly, from the tens down to the ones place.

Property

A number is divisible by 3 if the sum of its digits is a multiple of 3. For example, for the number 87, we add the digits: $8 + 7 = 15$. Since 15 is a multiple of 3, the number 87 is divisible by 3.

• Can 75 be divided by 3? Check: $7 + 5 = 12$. Since 12 is a multiple of 3, the answer is yes. $75 \div 3 = 25$.
• Can 92 be divided by 3? Check: $9 + 2 = 11$. Since 11 is not a multiple of 3, the answer is no.
• Can 45 be divided by 3? Check: $4 + 5 = 9$. Since 9 is a multiple of 3, the answer is yes. $45 \div 3 = 15$.

Want to know if a number can be friends with 3, meaning it divides by 3 with no leftovers? Don't guess! Just add up its digits. If that sum is in the 3-times-table, like 3, 6, 9, or 12, then the original number is too! It's a super-secret handshake that only multiples of 3 know.

Property

To find a reasonable estimate for a division problem, replace the dividend with a nearby compatible number that divides evenly by the divisor. For $38 \div 4$, you can use 36 or 40 to make the division easier and find an approximate answer.

• To estimate $53 \div 5$: Compatible numbers near 53 are 50 or 55. A good estimate is $50 \div 5 = 10$ or $55 \div 5 = 11$.
• Estimate how many 8-dollar tickets you can buy with 43 dollars. Use 40 as a compatible number. $40 \div 8 = 5$. So, about 5 tickets.
• To estimate $74 \div 5$: A compatible number near 74 is 75. $75 \div 5 = 15$. So, a reasonable estimate is 15.

Division can be messy if the numbers don't play nice, so be a matchmaker! Instead of struggling with a tough problem, swap the main number for a nearby 'compatible' one that gets along great with your divisor. This trick gives you a quick, smart estimate without all the hard work. It's about working smarter, not harder!