Let’s Learn!
How do we solve word problems using long division?
Goal:
Goal:
Think About It!
Goal: Solve word problems using long division.
Ava is excited to learn how to divide larger numbers! Let's get started by helping Ava review solving division problems with smaller numbers!
Divide
\( 25 \div 5 =\;? \)
That's right! \({25 \div 5 = 5}\)
That's incorrect. \({5 \times 5 = 25}\)
Divide
\( 12 \div 4 =\;? \)
That’s right! \({12 ÷ 4 = 3}\)
That’s incorrect. \({12 ÷ 4 = 3}\)
Divide
\( 36 \div 6 =\;? \)
That’s right! \({36 ÷ 6 = 6}\)
That’s incorrect. \({36 ÷ 6 = 6}\)
Divide
\( 81 \div 9 =\;? \)
That’s right! \({81 ÷ 9 = 9}\)
That’s incorrect. \({81 ÷ 9 = 9}\)
Now Ava is ready to learn how to solve long division problems. Let's start by defining some key terms!
Let's go over the parts of a division sentence. The dividend is the large number that is being separated into smaller groups. The divisor is the number of groups that the dividend is separated into. Last, the quotient is the answer to a division problem and the number of items in each group.
Now, let’s compare a standard division sentence and a division problem set up for long division. Long division is a method used for dividing large numbers into groups or parts. The symbol in long division looks like this ⟌.
Long division is just a different way to set up a division problem. Both set-ups have a dividend, a divisor, and a quotient.
Left Image: 45 divided by 5 equals 9. 45 is the
dividend, 5 is the divisor, 9 is the quotient. Right
Image: The the division problem is set up for long
division using the long division symbol. The number
5 (Divisor) is outside of the symbol, the
45(dividend) is on the inside of the symbol, and 9
(quotient) is on top of the symbol.
Let's look at the steps for using long division.
Long division follows very precise steps. Let's take a look at the steps to use long division for 90 divided by 9.
The first thing we need to do with long division is set up the problem.
90 divided by 9.
We know that 90 is the dividend because it is the amount being separated into groups.
We know that 9 is the divisor since it is doing the dividing.
Here is how we set up the problem:
Now that we are set up, let's start with our first step!
First, we divide.
We look at the first digit in the dividend and see if it can be divided by the divisor.
Since we have decided 9 can be divided by 9, we then decide how many times.
9 goes into 9 one time. So, we put a 1 above the 9 in the dividend.
Now that we have the 1, we have to multiply.
We multiply the 1 by the divisor 9.
Then, we put the product under the 9 digit in the dividend.
Next, we subtract. We subtract the product of 1 times 9 from the 9 digit in the dividend.
9 minus 9 equals 0.
Next, we need to bring down the next digit in the dividend.
Now, we start all over again.
This time, the digit from subtracting and bringing down is your new dividend.
Now, we look to see how many times 9 goes into 00.
Since 9 goes into 00 zero times, we put the 0 in the quotient next to the 1.
Now that we have the 0, we have to multiply.
We multiply the 0 by the divisor 9. Then, we put the product under the 0 digit in 00.
90 divided by 9. 9 goes into 9, 1 time. The 1
is place on the top of the long division bracket
in the 10 place. 9 minus 0 equals 0. The zero in
90 in the ones place drops down to the ones
place making 00. The zero from the ones place is
carry to the ones place on top of the long
division bracket. Next we multiply 0 times 9
equals 0. This goes under the 00 from the last
step.
Next, we subtract. We subtract the product of 0 times 9 from the 0 digit in the dividend.
90 divided by 9. 9 goes into 9, 1 time. The 1
is place on the top of the long division bracket
in the 10 place. 9 minus 0 equals 0. The zero in
90 in the ones place drops down to the ones
place making 00. The zero from the ones place is
carry to the ones place on top of the long
division bracket. Next we multiply 0 times 9
equals 0. This goes under the 00 from the last
step. Now we minus 0 minus 0 leaving us with 0.
We have no more digits in the dividend to bring down, which means we are done!
90 divided by 9 equals 10!
Let's help Ava solve a problem using long division.
Ava wants to use long division to solve 76 divided by 4.
The first thing she does is set up the problem using the long division sign. She puts the dividend, 76, inside the symbol and the divisor, 4, outside.
Now, she goes through the steps to solve. You do each step as she does and click to see if you and Ava did the same thing!
Long division steps:
- Divide
- Multiply
- Subtract
- Bring down
- Repeat
First, Ava thinks about how many times 4 goes into 7, and she says 1. 4 goes into 7 1 time.
Next, Ava multiplies 1 times 4 and gets 4.
She puts the 4 under the 7 in the dividend.
Now, Ava needs to think how many times 4 goes into 36?
Let's go to the next slide and repeat it all!
Now, it is time to repeat it all! Work through each step again on your own. When you finish each step, click the box to see what Ava did.
Ava thinks back to her basic facts: 4 times what is 36? 9!
Ava multiplies 9 times 4 and gets 36. She puts the 36 under the 36 that is already there.
Ava subtracts 36 from 36 and gets 0.
Ava did it! How did you do?
Question
Divide using long division.
Let’s practice doing another problem. Remember to follow the steps.
Long step division steps: 1. divide. 2. Multiply. 3.
Subtract, 4. Bring Down, 5. Repeat. 6148 divided by
4.
Step 1: Divide
How many times does 4 go into 6?
Step 2: Multiply
How many times does 4 go into 6?
Step 3: Subtract
Subtract 4 from 6.
Step 4: Bring Down
Bring down the next digit in the dividend.
Step 5: Repeat
Start all over again, looking at the number that has been created from subtracting and bringing a digit down.
Now let's repeat the process for the next number.
Step 1: Divide
How many times does 4 go into 21?
Step 2: Multiply
Multiply 5 times 4.
6148 divided by 4. 4 goes into 6 one time. 1
goes on top of the 6 in the thousands place. 4
times 1 equal 4. 4 goes under the 6. 6 minus 4
equals 2. next we bring down the ones from the
hundreds place. Making 21. 4 goes into 21 5
times. place a 5 above the 1 on the long
division bracket. 5 times 4 equals 20. Place the
20 under the twenty 21.
Step 3: Subtract
Subtract 20 from 21.
6148 divided by 4. 4 goes into 6 one time. 1
goes on top of the 6 in the thousands place. 4
times 1 equal 4. 4 goes under the 6. 6 minus 4
equals 2. next we bring down the ones from the
hundreds place. Making 21. 4 goes into 21 5
times. place a 5 above the 1 on the long
division bracket. 5 times 4 equals 20. Place the
20 under the twenty 21. 21 minus 20 equals 1.
Step 4: Bring Down
Bring down the next digit in the dividend.
6148 divided by 4. 4 goes into 6 one time. 1
goes on top of the 6 in the thousands place. 4
times 1 equal 4. 4 goes under the 6. 6 minus 4
equals 2. next we bring down the ones from the
hundreds place. Making 21. 4 goes into 21 5
times. place a 5 above the 1 on the long
division bracket. 5 times 4 equals 20. Place the
20 under the twenty 21. 21 minus 20 equals 1.
next bring down the 4 making 4.
Step 5: Repeat
Start all over again, looking at the number that has been created from subtracting and bringing a digit down.
Finish the rest of the problem on your own. Click the Show Me button to see how the problem should look when solved!
6148 divided by 4. 4 goes into 6 one time. 1
goes on top of the 6 in the thousands place. 4
times 1 equal 4. 4 goes under the 6. 6 minus 4
equals 2. next we bring down the ones from the
hundreds place. Making 21. 4 goes into 21 5
times. place a 5 above the 1 on the long
division bracket. 5 times 4 equals 20. Place the
20 under the twenty 21. 21 minus 20 equals 1.
next bring down the 4 making 4. 4 goes into 14,
3 times. 3 times 4 equals 12. 14 minus 12 equals
2. Next bring down the 8. 4 goes into 28, 7
times. 4 times 7 equals 28. 28 goes under 28. 28
minus 28 equals 0. 6148, divided by 4 equals
1537.
How did you do? Ava thinks she is ready to try playing the game with her family. Let’s see how she does!
Ava will use her long division skills to solve trivia questions that are word problems. Her mom gives her a card to practice what she will need to do. Ava’s card says:
The human body has this number of bones: 412 divided by 2. How many bones are in the human body?
Ava sees that she needs to divide 412 by 2.
Can you use long division to solve the problem with Ava? Click the box to check your work when you are done!
How did you do?
Ava is ready to start playing her game!