Dividing a Whole Number by a Decimal
Dividing a Whole Number by a Decimal is a Grade 5 math skill from Illustrative Mathematics Chapter 5 (Place Value Patterns and Decimal Operations) where students convert the decimal divisor to a whole number by multiplying both the dividend and divisor by the same power of 10, then perform standard long division. This creates an equivalent problem with a whole number divisor that is easier to solve.
Key Concepts
Property To divide a whole number by a decimal, convert the divisor into a whole number by multiplying both the divisor and the dividend by the same power of 10. This is equivalent to moving the decimal point in both numbers to the right by the same number of places. Then, perform the division as you would with whole numbers. $$a \div b = (a \times 10^n) \div (b \times 10^n)$$.
Examples To solve $42 \div 0.7$, multiply both numbers by 10: $$42 \div 0.7 \rightarrow (42 \times 10) \div (0.7 \times 10) \rightarrow 420 \div 7 = 60$$ To solve $15 \div 0.03$, multiply both numbers by 100: $$15 \div 0.03 \rightarrow (15 \times 100) \div (0.03 \times 100) \rightarrow 1500 \div 3 = 500$$.
Explanation When dividing a whole number by a decimal, the key is to transform the problem into one you already know how to solve: division by a whole number. You can do this by multiplying both the dividend (the number being divided) and the divisor (the number you are dividing by) by the same power of 10 (like 10, 100, or 1000). This process effectively moves the decimal point in both numbers to the right, creating an equivalent division problem with a whole number divisor. After setting up the equivalent problem, you can use long division to find the final answer.
Common Questions
How do you divide a whole number by a decimal?
Multiply both the whole number dividend and the decimal divisor by the same power of 10 to make the divisor a whole number. Then divide normally. For example, 42 ÷ 0.7: multiply both by 10 → 420 ÷ 7 = 60.
What power of 10 should you use when dividing by a decimal?
Use a power of 10 that eliminates the decimal in the divisor. For tenths (0.7), multiply by 10. For hundredths (0.03), multiply by 100. The goal is to make the divisor a whole number.
What chapter covers dividing whole numbers by decimals in Illustrative Mathematics Grade 5?
Dividing a whole number 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 whole number by a decimal?
15 ÷ 0.03: multiply both by 100 → 1500 ÷ 3 = 500. So 15 ÷ 0.03 = 500. Another: 42 ÷ 0.7 → 420 ÷ 7 = 60.
Why does multiplying both numbers by the same power of 10 give an equivalent problem?
Multiplying both dividend and divisor by the same number creates an equivalent ratio. Since a ÷ b = (a × k) ÷ (b × k) for any nonzero k, the quotient is unchanged while the divisor becomes a whole number.