Lesson 4: Dividing Decimals

Property

Division as fair sharing can be modeled by representing the dividend with base-ten blocks (flats, rods, and units) and distributing them into a number of equal groups equal to the divisor.
The value of the blocks in one group is the quotient.

Examples

Property

Partial quotients is a method for solving division problems by repeatedly subtracting "friendly" multiples of the divisor from the dividend.
The final quotient is the sum of all the partial quotients.

Examples

Property

When the divisor or the dividend has more than one digit, it is usually easier to use the $b)\overline{a}$ notation. This process is called long division.

How to divide whole numbers:

1. Divide the first digit(s) of the dividend by the divisor.
2. Write the quotient above the dividend.
3. Multiply the quotient by the divisor and write the product under the dividend.
4. Subtract that product from the dividend.
5. Bring down the next digit of the dividend.
6. Repeat from Step 1 until there are no more digits to bring down.
7. Check by multiplying the quotient by the divisor.

Examples

• To divide 96 by 4: 4 goes into 9 two times. $2 \cdot 4 = 8$. $9-8=1$. Bring down the 6 to make 16. 4 goes into 16 four times. So, $96 \div 4 = 24$.
• To divide 345 by 5: 5 goes into 34 six times. $6 \cdot 5 = 30$. $34-30=4$. Bring down the 5 to make 45. 5 goes into 45 nine times. So, $345 \div 5 = 69$.
• To divide 852 by 6: 6 goes into 8 one time. $1 \cdot 6 = 6$. $8-6=2$. Bring down the 5 to make 25. 6 goes into 25 four times. $4 \cdot 6 = 24$. $25-24=1$. Bring down the 2 to make 12. 6 goes into 12 two times. So, $852 \div 6 = 142$.

Property

To divide a whole number by a whole number and find a decimal quotient, perform long division.
If there is a remainder, place a decimal point in the dividend and the quotient.
Then, annex zeros to the dividend and continue the division process until the remainder is zero or you reach the desired number of decimal places.

Examples

• $13 \div 4 = 3.25$

Dividing 13 by 4 gives 3 with a remainder of 1. Adding a decimal point and a zero makes 10, which divided by 4 gives 2, and bringing down another zero gives 10 ÷ 4 = 2.5, resulting in 3.25.

• $99 \div 12 = 8.25$

Dividing 99 by 12 gives 8 with a remainder of 3. Adding a decimal point and a zero turns it into 30, which divided by 12 gives 2 with a remainder of 6. Bringing down another zero makes 60 ÷ 12 = 5, so the result is 8.25.

• $7 \div 8 = 0.875$

Dividing 7 by 8 gives 0 with a remainder of 7. Adding a decimal point and a zero gives 70 ÷ 8 = 8 remainder 6. Bringing down another zero gives 60 ÷ 8 = 7 remainder 4, and another zero gives 40 ÷ 8 = 5, so the final answer is 0.875.

Explanation

When a whole number division results in a remainder, you can continue dividing to find an exact decimal answer. This is done by adding a decimal point and zeros to the end of the dividend. Remember to place the decimal point in your answer (the quotient) directly above the new decimal point in the dividend. This process converts the remainder into a decimal part of the quotient.