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Solution - Long division

42 R 2

42{\;R}2

Decimal form:

42.4

42.4

Mixed number form

42 \frac{2}{5}

42\frac{2}{5}

See steps

Step-by-step explanation

1. Write the divisor, which is 5, and then write the dividend, which is 212, in order to populate the table.

TABLE_COL_WHOLE_DIGIT2_PLACE1	TERM_TABLE_COL_DIVISION_ACTION	hundreds	tens	ones
/
5		2	1	2

2. Divide the dividend digits by the divisor one at a time, starting from the left.

To divide 2 by divisor 5, we ask: 'How many times can we fit 5 into 2?
2/5=0
Write the quotient 0, above the digit we divided.

TABLE_COL_WHOLE_DIGIT2_PLACE1	TERM_TABLE_COL_DIVISION_ACTION	hundreds	tens	ones
/		0
5		2	1	2

We multiply the quotient by the divisor to get the product.
5*0=0
Write 0 below the digits we just divided (2), so we can subtract to get the remainder.

TABLE_COL_WHOLE_DIGIT2_PLACE1	TERM_TABLE_COL_DIVISION_ACTION	hundreds	tens	ones
×		0
5		2	1	2
		0

Subtract to get the remainder
2-0=2
Write the remainder 2

TABLE_COL_WHOLE_DIGIT2_PLACE1	TERM_TABLE_COL_DIVISION_ACTION	hundreds	tens	ones
		0
5		2	1	2
-		0
		2

Since we have a remainder from the previous division, we bring down the next digit, which is (1), and add it to the remainder (2).

TABLE_COL_WHOLE_DIGIT2_PLACE1	TERM_TABLE_COL_DIVISION_ACTION	hundreds	tens	ones
		0
5		2	1	2
-		0
		2	1

To divide 21 by divisor 5, we ask: 'How many times can we fit 5 into 21?
21/5=4
Write the quotient 4, above the digit we divided.

TABLE_COL_WHOLE_DIGIT2_PLACE1	TERM_TABLE_COL_DIVISION_ACTION	hundreds	tens	ones
		0	4
5		2	1	2
-		0
		2	1

We multiply the quotient by the divisor to get the product.
5*4=20
Write 20 below the digits we just divided (21), so we can subtract to get the remainder.

TABLE_COL_WHOLE_DIGIT2_PLACE1	TERM_TABLE_COL_DIVISION_ACTION	hundreds	tens	ones
×		0	4
5		2	1	2
-		0
		2	1
		2	0

Subtract to get the remainder
21-20=1
Write the remainder 1

TABLE_COL_WHOLE_DIGIT2_PLACE1	TERM_TABLE_COL_DIVISION_ACTION	hundreds	tens	ones
		0	4
5		2	1	2
-		0
		2	1
	-	2	0
			1

Since we have a remainder from the previous division, we bring down the next digit, which is (2), and add it to the remainder (1).

TABLE_COL_WHOLE_DIGIT2_PLACE1	TERM_TABLE_COL_DIVISION_ACTION	hundreds	tens	ones
		0	4
5		2	1	2
-		0
		2	1
	-	2	0
			1	2

To divide 12 by divisor 5, we ask: 'How many times can we fit 5 into 12?
12/5=2
Write the quotient 2, above the digit we divided.

TABLE_COL_WHOLE_DIGIT2_PLACE1	TERM_TABLE_COL_DIVISION_ACTION	hundreds	tens	ones
		0	4	2
5		2	1	2
-		0
		2	1
	-	2	0
			1	2

We multiply the quotient by the divisor to get the product.
5*2=10
Write 10 below the digits we just divided (12), so we can subtract to get the remainder.

TABLE_COL_WHOLE_DIGIT2_PLACE1	TERM_TABLE_COL_DIVISION_ACTION	hundreds	tens	ones
×		0	4	2
5		2	1	2
-		0
		2	1
	-	2	0
			1	2
			1	0

Subtract to get the remainder
12-10=2
Write the remainder 2

TABLE_COL_WHOLE_DIGIT2_PLACE1	TERM_TABLE_COL_DIVISION_ACTION	hundreds	tens	ones
		0	4	2
5		2	1	2
-		0
		2	1
	-	2	0
			1	2
		-	1	0
				2

If there is a remainder, we add it to the final result and write it as 'R' followed by the remainder value 2.

TABLE_COL_WHOLE_DIGIT2_PLACE1	TERM_TABLE_COL_DIVISION_ACTION	hundreds	tens	ones	5	6	7
		0	4	2		R	2
5		2	1	2
-		0
		2	1
	-	2	0
			1	2
		-	1	0
				2

The final result is: 42 R2

Decimal and mixed form:
To get the decimal part of the result, divide the remainder (2) by the divisor (5) to get 42.4
or to write it in mixed form as $42 \frac{2}{5}$

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Why learn this

Hey students! Have you ever wondered why you need to learn long division? Well, let me tell you - long division is like a superhero power that can help you solve a lot of cool problems!

Here are 4 examples of how long division can be used in fun ways:

Pizza party time! Let's say you and your friends ordered 20 slices of pizza. How many slices of pizza will each person get? To figure it out, you can use long division to divide the total number of slices by the number of people at the party.

It's candy time! You have 60 pieces of candy and you want to share it equally with your three best friends. How many pieces of candy will each of you get? Long division to the rescue!

Are we there yet? If you're going on a long car trip and you want to know how long it will take to get there, you can use long division to figure out your average speed and the total distance.

Budgeting for groceries: Let's say you have a budget of $200 for groceries this month, and you want to know how much you can spend per week. You can use long division to divide your total budget by the number of weeks in the month.

These are just a few examples of how long division can be used in real life. By learning this important mathematical tool, you'll be equipped to tackle a wide range of problems in school, work, and everyday life.

Terms and topics

Long division