Method 1: Rounding

Step 1: Round the dividend (number being divided) to the nearest whole number

Step 2: Round the divisor (number dividing by) to the nearest whole number

Step 3: Divide the rounded numbers

Method 2: Compatible Numbers

Compatible numbers are numbers that are easy to divide mentally. They divide evenly with no remainder.

Step 1: Find compatible numbers close to the actual numbers

Step 2: Use basic division facts

Step 3: Calculate the quotient

Example 1 (Rounding): Estimate 62.9 ÷ 7.48

• 62.9 rounds to 63

• 7.48 rounds to 7

• 63 ÷ 7 = 9

Estimated Quotient ≈ 9

Example 2 (Compatible Numbers): Estimate 23.8 ÷ 4.75

• 23.8 is close to 24

• 4.75 is close to 4

• 24 and 4 are compatible (24 ÷ 4 = 6)

Estimated Quotient ≈ 6

✓ To check if your answer is reasonable

✓ When an approximate answer is acceptable

✗ Do NOT use when exact answers are required

Flat = 1 whole = 1.0

Rod (Long) = 1 tenth = 0.1

Cube (Unit) = 1 hundredth = 0.01

Step 1: Represent the dividend (number being divided) using base ten blocks

Step 2: Divide the blocks into equal groups based on the divisor

Step 3: If needed, trade larger blocks for smaller ones (1 flat = 10 rods, 1 rod = 10 cubes)

Step 4: Distribute all blocks equally into groups

Step 5: Count the value in ONE group to find the quotient

Example 1: 1.4 ÷ 7 = ?

• Represent 1.4 → 1 flat + 4 rods

• Trade 1 flat for 10 rods → Total: 14 rods (14 tenths)

• Divide 14 rods into 7 equal groups

• Each group has 2 rods = 0.2

Answer: 1.4 ÷ 7 = 0.2

Example 2: 0.63 ÷ 3 = ?

• Represent 0.63 → 6 rods + 3 cubes

• Divide 6 rods into 3 groups → 2 rods per group

• Divide 3 cubes into 3 groups → 1 cube per group

• Each group has 2 rods + 1 cube = 0.2 + 0.01 = 0.21

Answer: 0.63 ÷ 3 = 0.21

Area = Length × Width

Dividend = Divisor × Quotient

Step 1: Treat decimals as whole numbers temporarily

Step 2: Break the dividend into parts that are easier to divide

Step 3: Divide each part by the divisor

Step 4: Add the partial quotients together

Step 5: Place the decimal point in the correct position

Divide: 225.5 ÷ 5

Step 1: Remove decimal: 2255 ÷ 5

Step 2: Break 2255 into parts: 2000 + 200 + 50 + 5

Step 3: Divide each part:

Step 4: Add: 400 + 40 + 10 + 1 = 451

Step 5: Place decimal: 225.5 ÷ 5 = 45.1

Answer: 45.1

• Think about the dividend in terms of its place value units (ones, tenths, hundredths)

• Convert to the same unit (all tenths, all hundredths, etc.)

• Divide as whole numbers, then adjust the place value

Step 1: Identify the place value of the decimal

Step 2: Think of the decimal as a whole number (in tenths, hundredths, etc.)

Step 3: Divide the whole numbers

Step 4: Adjust the answer to match the place value

Example 1: 8.4 ÷ 2

• 8.4 = 84 tenths

• 84 tenths ÷ 2 = 42 tenths

• 42 tenths = 4.2

Answer: 4.2

Example 2: 0.48 ÷ 4

• 0.48 = 48 hundredths

• 48 hundredths ÷ 4 = 12 hundredths

• 12 hundredths = 0.12

Answer: 0.12

Step 1: Set up the division problem (dividend inside, divisor outside)

Step 2: Place the decimal point in the quotient directly above the decimal in the dividend

Step 3: Divide as if working with whole numbers

Step 4: Bring down digits one at a time

Step 5: Continue until remainder is 0

Example 1: 8.4 ÷ 4

Example 2: 6.75 ÷ 5

• When the dividend doesn't divide evenly by the divisor

• When we continue dividing past the whole number part

• When we add zeros to the dividend to continue dividing

Step 1: Divide as usual with whole numbers

Step 2: If there's a remainder, add a decimal point to the quotient

Step 3: Add a zero to the dividend after the decimal point

Step 4: Bring down the zero and continue dividing

Step 5: Repeat until remainder is 0 or you have enough decimal places

Example 1: 7 ÷ 4

Example 2: 9 ÷ 8

If the digit to the right is 5 or greater → Round UP (add 1 to the rounding place)

If the digit to the right is less than 5 → Round DOWN (keep the digit the same)

• Nearest tenth: 1 decimal place (0.1)

• Nearest hundredth: 2 decimal places (0.01)

• Nearest thousandth: 3 decimal places (0.001)

Step 1: Divide until you have one more decimal place than needed

Step 2: Look at the digit in the place right after your rounding place

Step 3: Apply the rounding rule

Step 4: Drop all digits after the rounding place

Example 1: 10 ÷ 3 (round to nearest hundredth)

Example 2: 22 ÷ 7 (round to nearest tenth)

• Shared equally

• Divided into groups

• Each person gets

• Per, each, every

• How many in each?

• Average, mean

Step 1: Read the problem carefully

Step 2: Identify what you're trying to find

Step 3: Find the dividend (total amount) and divisor (number of groups)

Step 4: Write the division equation

Step 5: Solve and check if the answer makes sense

Example 1: Sarah bought 5 pounds of apples for $8.75. What is the cost per pound?

Example 2: A ribbon is 12.6 meters long. It is cut into 9 equal pieces. How long is each piece?

To divide by a decimal, convert the divisor to a whole number by multiplying BOTH the dividend and divisor by the same power of 10.

6 ÷ 2 = 3

(6 × 10) ÷ (2 × 10) = 60 ÷ 20 = 3

Same answer!

Step 1: Count how many decimal places are in the divisor

Step 2: Move the decimal point in the divisor to the RIGHT to make it a whole number

Step 3: Move the decimal point in the dividend to the RIGHT the same number of places

Step 4: Divide as usual with the new numbers

Example 1: 4.5 ÷ 0.5

Example 2: 0.63 ÷ 0.09

Step 1: Move the decimal in the divisor to make it a whole number

Step 2: Move the decimal in the dividend the same number of places

Step 3: Place the decimal point in the quotient above the new position in the dividend

Step 4: Divide as usual

Step 5: The division completes with no remainder

Example 1: 3.6 ÷ 1.2

Example 2: 8.4 ÷ 0.7

Make the divisor a whole number, then divide!

Step 1: Write the division problem

Step 2: Count decimal places in the divisor

Step 3: Move both decimal points RIGHT by that amount

Step 4: Add zeros to the dividend if needed

Step 5: Place the decimal point in the quotient

Step 6: Divide using long division

Step 7: Add zeros after the dividend's decimal point if there's a remainder

Step 8: Continue until remainder is 0 or round as instructed

Example 1: 5.75 ÷ 2.5

Example 2: 7.65 ÷ 0.15

✓ Always make the divisor a whole number when dividing by decimals

✓ Move decimal points the same number of places in both dividend and divisor

✓ Line up the decimal point in your quotient with the decimal in the dividend

✓ Add zeros to the dividend if needed to continue dividing

✓ Use estimation to check if your answer is reasonable

✓ When rounding, divide to one more place than required

✓ In word problems, identify key words that signal division

✓ Check your work by multiplying: quotient × divisor should equal dividend

Trick 1: "Move Move Divide"
When dividing by a decimal: Move the decimal in the divisor, move it the same way in the dividend, then divide!

Trick 2: "Straight Up"
The decimal point in your answer goes straight up from the decimal point in the dividend.

Trick 3: "Make It Whole"
Always turn the divisor into a whole number first—it makes division much easier!

Trick 4: "Check with Multiplication"
Answer × Divisor = Dividend (If it doesn't, check your work!)