Dividing Decimals for 5th Grade: Divisors and Quotients

Dividing decimals is used when sharing amounts equally, finding unit rates (cost per item, miles per gallon), and when computing quotients from measurements. In Grade 5, students divide decimals by whole numbers and by other decimals. The key strategy when the divisor is a decimal is to multiply both the divisor and dividend by a power of 10 to make the divisor a whole number, which preserves the quotient. This skill helps students find per-person costs, unit prices, averages, and solve real-world problems involving division.

When we divide a decimal by a whole number, we perform long division as usual and place the decimal point in the quotient directly above the decimal point in the dividend. When we divide by a decimal, we first convert the divisor to a whole number by moving its decimal point to the right; we must move the dividend’s decimal point the same number of places to keep the quotient correct. For example, 4.8 ÷ 0.6: multiply both by 10 to get 48 ÷ 6 = 8.

DETAILED EXPLANATION

Dividing by a whole number:

1. Set up long division with the dividend inside and the divisor outside.

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2. Place the decimal point in the quotient directly above the decimal point in the dividend.

3. Divide as with whole numbers, bringing down digits as needed.

Dividing by a decimal:

1. Count how many decimal places the divisor has.

2. Multiply both the divisor and dividend by 10, 100, or 1000 (as needed) so the divisor becomes a whole number.

3. Divide the new dividend by the new divisor.

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4. The quotient is the same as the original division.

Example: 6.75 ÷ 5. Divide: 5 goes into 6 once (remainder 1); bring down 7 → 17; 5 goes into 17 three times (remainder 2); bring down 5 → 25; 5 goes into 25 five times. Quotient: 1.35.

WORKED EXAMPLES WITH STEP BY STEP SOLUTIONS

Example 1

$6.75 is shared equally among 5 friends. How much does each get?

Solutions:

Step 1: We need to divide 6.75 ÷ 5. Set up long division: 5 ) 6.75

Step 2: Place the decimal point in the quotient directly above the decimal point in 6.75.

Step 3: 5 goes into 6 once. Write 1 above the 6. Subtract: 6 − 5 = 1. Bring down 7: 17.

Step 4: 5 goes into 17 three times (5 × 3 = 15). Write 3 above the 7. Subtract: 17 − 15 = 2. Bring down 5: 25.

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Step 5: 5 goes into 25 five times (5 × 5 = 25). Write 5 above the 5. Subtract: 25 − 25 = 0.

Step 6: Quotient: 1.35. Each friend gets $1.35.

Answer: $1.35 each

Example 2

Divide 4.8 ÷ 0.6

Solutions:

Step 1: The divisor 0.6 has one decimal place. Multiply both divisor and dividend by 10: 0.6 × 10 = 6; 4.8 × 10 = 48.

Step 2: The division becomes 48 ÷ 6.

Step 3: 6 goes into 48 eight times (6 × 8 = 48). Quotient: 8.

Step 4: So 4.8 ÷ 0.6 = 8.

Answer: 8

Example 3

2.4 ÷ 0.12 = ?

Solutions:

Step 1: The divisor 0.12 has two decimal places. Multiply both by 100: 0.12 × 100 = 12; 2.4 × 100 = 240.

Step 2: The division becomes 240 ÷ 12.

Step 3: 12 goes into 24 twice; 12 goes into 0 zero times. 12 × 20 = 240. Quotient: 20.

Step 4: So 2.4 ÷ 0.12 = 20.

Answer: 20

Example 4

A rope 12.6 meters long is cut into pieces of 0.9 meter each. How many pieces?

Solutions:

Step 1: Divide 12.6 ÷ 0.9. The divisor 0.9 has one decimal place. Multiply both by 10: 0.9 → 9; 12.6 → 126.

Step 2: Divide 126 ÷ 9 = 14.

Step 3: There are 14 pieces.

Answer: 14 pieces