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Grade 6 (age 11-12)

grade 6 Decimal Division

To divide by a decimal, move the decimal point in both numbers by the same number of places until the divisor is a whole number. In 2.4 ÷ 0.6, multiplying both numbers by 10 gives 24 ÷ 6; both were made 10 times bigger, so the quotient stays 4. It is the same as counting how many 0.6 m pieces you can cut from a 2.4 m ribbon, or how many jumps of 0.6 take you from 0 to 2.4 on a number line. Change the two numbers below to see the number of jumps and the shifted division side by side.

Why you shift the decimal point

📏 Shift the decimal point to get whole numbers
①When the divisor is a decimal, as in 2.4 ÷ 0.6, it is hard to work out directly
②Multiply both the dividend and the divisor by 10 and you get 24 ÷ 6 = 4
③Making both numbers the same number of times bigger does not change the quotient, so 2.4 ÷ 0.6 is also 4
④Move the decimal point far enough to make the divisor a whole number, and move it the same number of places in both numbers

Checking on a number line

2.4
0.6
💡 Jumps of 0.6 up to 2.4
①Starting at 0, 4 jumps of 0.6 reach 2.4
②Left over: 0.0
③Quotient = 4

Summary

Dividing by a decimal
Shift both decimal points equally until the divisor is a whole number
2.4 ÷ 0.6 → 24 ÷ 6, 4.8 ÷ 0.12 → 480 ÷ 12
Checking
quotient × divisor = dividend
Multiply back to check your answer
🎯 At a glance
①Move both decimal points by the same number of places until the divisor is a whole number
②Then divide as with whole numbers
③If it does not divide exactly, round the quotient and write ≈
④Dividing by a number less than 1 gives a quotient bigger than the dividend
⑤Check with quotient × divisor

Examples & Unit Review

Example 1
Work out 7.5 ÷ 0.5.
1
Multiply both numbers by 10 so that the divisor is a whole number: 75 ÷ 5.
2
75 ÷ 5 = 15. Check: 15 × 0.5 = 7.5.
▸ 15
Multiplying the dividend and the divisor by the same number does not change the quotient.
Example 2
Work out 4.8 ÷ 0.12.
1
To make 0.12 a whole number you must move the decimal point two places, so multiply both numbers by 100: 480 ÷ 12.
2
480 ÷ 12 = 40. Check: 40 × 0.12 = 4.8.
▸ 40
Move the decimal point as far as the divisor needs, and move the dividend's by the same amount.
Unit Review
What is 9.6 ÷ 0.8?
①12
②1.2
③120
④8.8
▸ ① 12
1
Multiply both numbers by 10: 96 ÷ 8.
2
96 ÷ 8 = 12.
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Fraction Division
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Variables and Expressions

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