Master Dividing Decimals with Compatible Numbers, Mental Math, and Long Division

Quotients	Exact Value	Use Compatible Numbers	Estimate
$615 \div 8$	$76.875$	$640 \div 8$	$80$
$36 \div 11.25$	$3.2$	$36 \div 12$	$3$
$52.82 \div 4.75$	$11.12$	$50 \div 5$	$10$

Quotients

Exact Value

Use Compatible Numbers

Estimate

615 \div 8

76.875

640 \div 8

80

36 \div 11.25

3.2

36 \div 12

3

52.82 \div 4.75

11.12

50 \div 5

10

So you want to approximate the number of bees in that hive huh? Well, count the number of bees that leave the hive in one minute. Then multiply it by $3$ and divide by $0.014 .$

Dividend	Divisor	Quotient
$3000$	$100$	$30$
$300$	$10$	$30$
$30$	$1$	$30$
$3$	$0.1$	$30$
$0.3$	$0.01$	$30$

Dividend

Divisor

Quotient

3000

100

30

300

10

30

30

1

30

3

0.1

30

0.3

0.01

30

Estimate each quotient.

37 \div 7.3

11.76 \overline{) 52.9}

Let's take a look at the given quotient. 37 ÷ 7.3 We want to estimate the quotient of a whole number and a decimal number. We will do two things to estimate it.

Round the divisor to the nearest whole number.
Round the dividend so that the divisor and the dividend are compatible numbers.

We use compatible numbers because they are numbers that are more manageable when dividing using mental math. Let's round the divisor. We look at the digit in the tenths place to round it to the nearest whole number.

Now we will look for a number that is around 37 and compatible with 7. The best way to do so is to round 37 to a number that is a multiple of 7. Let's list some multiples of 7. Some Multiples of7 21,28, 35,42,49 The closest multiple of 7 to 37 is 35. Let's round 37 to 35 and then divide 35 by 7.

The given quotient is about 5 by our estimation.

We want to estimate the quotient of two decimal numbers. 11.76 ) 52.9 In this case, the divisor is 11.76 and the dividend is 52.9. We will first round 11.76 to the nearest whole number. Then, we will round 52.9 so that the numbers are compatible. Let's round the divisor. We can round the digit in the tenths place to the nearest whole number.

Now we will look for a number that is around 52.9 and compatible with 12. A good way to do this is by rounding 52.9 to a number that is a multiple of 12. Let's list some multiples of 12. Some Multiples of12 24,36, 48,60,72 The closest multiple of 12 to 52.9 is 48. Let's round 52.9 to 48 and then divide 48 by 12.

The given quotient is about 4 by our estimation.

Find each quotient.

8.94 \div 15

64.064 \div 26

We want to calculate the given quotient. 8.94 ÷ 15 Here, we need to divide a decimal number by a whole number. We will use long division to calculate it.

Since 8 ones divided by 15 is 0, we write a 0 in the ones place of the quotient. Then we place the decimal point in the quotient directly above its place in the dividend.

We can now continue the division process as usual. We will not stop until the remainder becomes 0.

Therefore, the quotient is 0.596.

We will use long division to calculate the given quotient.

The first digit of the quotient will be in the ones place because 64 contains two groups of 26. After that we can place the decimal point in the quotient directly above its place in the dividend.

We can now continue the division process as usual.

Therefore, the quotient is 2.464.

Find each quotient.

7 \div 0.14

34 \div 4.25

We are asked to find the value of the following quotient. 7 ÷ 0.14 We will use long division to find it. Notice that the divisor is a decimal number. We will first make it a whole number by multiplying it by a power of 10. Since 0.14 has two decimal places, we multiply it by 10 to the power of 2. We also have to multiply the dividend by the number. Given 7 ÷ 0.14 ⇓ Use Long Division 0.14 ) 7 ⇓ Multiply by 10^2 14 ) 700 Now both numbers are whole numbers. We can perform the division as usual.

The quotient is 50.

We will use long division to calculate the given quotient. 34 ÷ 4.25 Again, we need to multiply the dividend and the divisor by 10^2. This is because the divisor has two decimal places and multiplying by 10^2 moves the decimal point two places to the right. Given 34 ÷ 4.25 ⇓ Use Long Division 4.25 ) 34 ⇓ Multiply by 10^2 425 ) 3400 There are eight groups of 425 in 3400. Therefore, the quotient is 8.

Evaluate each quotient.

1.476 \div 0.9

0.0364 \div 0.013

We see that the divisor is a decimal number with one decimal place. 1.476 ÷ 0.9 We will make the divisor a whole number by multiplying it by 10. We also have to multiply the dividend by the number. Given 1.476 ÷ 0.9 ⇓ Use Long Division 0.9 ) 1.476 ⇓ Multiply by 10 9 ) 14.76 We can divide 14.76 by 9 as we would with whole numbers. We will place the first digit of the quotient in the ones places because 14 contains one group of 9. After that we place the decimal point in the quotient directly above its place in the dividend.

The given quotient is 1.64.

This time we are given a quotient whose divisor is a decimal with three decimal places. 0.0364 ÷ 0.013 We multiply the dividend and the divisor by 10^3. This is because the divisor has three decimal places and multiplying by 10^3 moves the decimal point three places to the right. Given 0.0364 ÷ 0.013 ⇓ Use Long Division 0.013 ) 0.0364 ⇓ Multiply by 10^3 13 ) 36.4 Since 2 * 13 is 26 and 3* 13 is greater than 36, the number in the ones place will be 2. Let's start with writing it!

Evaluate the expressions.

6.2 \times 10.32 \div 6.45

(2^{2} - 2.34) \div 1.6

Let's recall the order of operations. We use the acronym PEMDAS to remember the correct order!

Expressions inside parentheses are evaluated first, followed by exponents, then multiplication and division, and finally addition and subtraction are evaluated last. For the given expression, this means multiplying 6.2 and 10.32 first and then dividing it by 6.45. 6.2 * 10.32 ÷ 6.45 When we multiply two decimals, we ignore any decimal points and multiply as we would with whole numbers. Then we count the number of decimal places in each factor. cr & 1 0 3 2 * & 6 2 & 2 0 6 4 + & 6 1 9 2 0 & 6 3 9 8 4 Since 6.2 has one decimal place and 10.32 has two decimal places, their product will have three decimal places. Then the product of the numbers is 63.984. 6.2 * 10.32 ÷ 6.45 ⇓ 63.984 ÷ 6.45 Our goal is to find this quotient now. But first, we need to convert the divisor into a whole number. We can do it by multiplying the divisor by 10^2. We must multiply the dividend by the same power of 10 so that the value of the quotient remains the same. Given 63.984 ÷ 6.45 ⇓ Use Long Division 6.45 ) 63.984 ⇓ Multiply by 10 645 ) 6398.4 Let's find it!

The expression is equal to 9.92.

We need to follow the order of operations. For the given expression, this means evaluating the expression inside the parentheses completely before dividing. (2^2-2.34) ÷ 1.6 Even within the expression inside the parentheses, we must follow the order of operations. We will first evaluate the exponent. It is equal to 4. (4-2.34) ÷ 1.6 To subtract 2.34 from 4, we rewrite 4 as 4.00 and subtract by regrouping. cr & 3 9 10 & 4 . 0 0 - & 2 . 3 4 & 1 . 6 6 Now that we found the value of the expression inside the parentheses, we can divide it by 1.6. (2^2-2.34) ÷ 1.6 ⇓ 1.66 ÷ 1.6 The divisor is a decimal number. We need to make it a whole number. We multiply the dividend and the divisor by 10 because the divisor has one decimal place. Given 1.66 ÷ 1.6 ⇓ Use Long Division 1.6 ) 1.66 ⇓ Multiply by 10 16 ) 16.6 The first digit of the quotient will be 1 since 16 times 1 is 16.

The value of the expression is 1.0375.

Divide Decimals

Catch-Up and Review

LaShay's Piggy Bank

Compatible Numbers

Estimating the Number of Dimes in Piggy Bank

Hint

Solution

Dividing Decimals

How Many Hours Should LaShay Work?

Hint

Solution

How Far Does the Drone Go?

Hint

Solution

Finding the Quotient of Two Decimal Numbers

Money in the Piggy Bank

Hint

Solution

Divide Decimals

Recommended exercises

	9 Theory slides
	10 Exercises - Grade E - A
	Each lesson is meant to take 1-2 classroom sessions