Divide a Decimal by a Decimal
Dividing a Decimal by a Decimal is a Grade 5 math skill from Illustrative Mathematics Chapter 5 (Place Value Patterns and Decimal Operations) where students convert the divisor to a whole number by multiplying both the dividend and divisor by the same power of 10, then perform standard division. This technique is based on the principle that a ÷ b = (a × 10^n) ÷ (b × 10^n).
Key Concepts
Property To divide a decimal by a decimal, multiply both the dividend and the divisor by the same power of 10 to make the divisor a whole number. This creates an equivalent problem. $$a \div b = (a \times 10^n) \div (b \times 10^n)$$ For example, $1.25 \div 0.5$ is equivalent to $12.5 \div 5$.
Examples $4.8 \div 0.6 = (4.8 \times 10) \div (0.6 \times 10) = 48 \div 6 = 8$ $7.2 \div 0.09 = (7.2 \times 100) \div (0.09 \times 100) = 720 \div 9 = 80$ $1.32 \div 0.4 = (1.32 \times 10) \div (0.4 \times 10) = 13.2 \div 4 = 3.3$.
Explanation When dividing by a decimal, the goal is to convert the problem into one you already know how to solve: dividing by a whole number. You can do this by moving the decimal point in both the divisor and the dividend the same number of places to the right. This is the same as multiplying both numbers by a power of 10, like 10, 100, or 1000. Once the divisor is a whole number, you can perform the division as you normally would.
Common Questions
How do you divide a decimal by a decimal?
Multiply both the dividend and divisor by the same power of 10 to make the divisor a whole number. Then divide normally. For example, 4.8 ÷ 0.6: multiply both by 10 to get 48 ÷ 6 = 8.
What power of 10 should you use to convert a decimal divisor to a whole number?
Use a power of 10 that shifts all digits in the divisor to the left of the decimal point. For divisors in tenths (like 0.6), multiply by 10. For hundredths (like 0.09), multiply by 100.
What chapter covers dividing a decimal by a decimal in Illustrative Mathematics Grade 5?
Dividing a decimal by a decimal is covered in Chapter 5 of Illustrative Mathematics Grade 5, titled Place Value Patterns and Decimal Operations.
What is an example of dividing a decimal by a decimal?
7.2 ÷ 0.09: multiply both by 100 to get 720 ÷ 9 = 80. Another example: 1.32 ÷ 0.4 — multiply by 10 to get 13.2 ÷ 4 = 3.3.
Why is it valid to multiply both dividend and divisor by the same number?
Multiplying both by the same power of 10 creates an equivalent division problem — the quotient remains the same. This is based on the fact that (a × k) ÷ (b × k) = a ÷ b for any nonzero k.