Divide a Whole Number by a Mixed Number
Dividing a whole number by a mixed number requires converting the mixed number to an improper fraction, then multiplying the whole number by the reciprocal. For example, 6 divided by 1 and 1/2: convert to 6 / (3/2) = 6 x 2/3 = 12/3 = 4. This 6th grade skill from enVision Mathematics Grade 6 connects fraction division to real-world problems like splitting a length of rope into sections of a given mixed number length, and builds the operational fluency with fractions needed for pre-algebra.
Key Concepts
Property To divide a whole number by a mixed number, write the whole number as a fraction with a denominator of 1 and the mixed number as an improper fraction. Then, multiply by the reciprocal of the improper fraction.
Examples $6 \div 1\frac{1}{2} = \frac{6}{1} \div \frac{3}{2} = \frac{6}{1} \times \frac{2}{3} = \frac{12}{3} = 4$ $5 \div 2\frac{1}{4} = \frac{5}{1} \div \frac{9}{4} = \frac{5}{1} \times \frac{4}{9} = \frac{20}{9} = 2\frac{2}{9}$.
Explanation This skill combines two key concepts from the lesson. First, convert the whole number into a fraction by placing it over 1. Second, convert the mixed number divisor into an improper fraction. Once both numbers are in fraction form, you can perform the division by multiplying the first fraction by the reciprocal of the second. The final answer can be simplified or converted back to a mixed number if necessary.
Common Questions
How do you divide a whole number by a mixed number?
Convert the mixed number to an improper fraction, then multiply the whole number by the reciprocal. For 6 divided by 1 and 1/2: 6 / (3/2) = 6 x 2/3 = 4.
Why do you convert a mixed number to an improper fraction before dividing?
You cannot directly flip a mixed number to find its reciprocal. Converting to an improper fraction gives a single fraction that can be flipped and multiplied.
What is the reciprocal of a mixed number?
First convert the mixed number to an improper fraction. The reciprocal is that fraction flipped. The reciprocal of 1 and 1/2 (= 3/2) is 2/3.
What grade covers dividing a whole number by a mixed number?
This is a 6th grade skill in enVision Mathematics Grade 6, extending fraction division to include mixed numbers in the divisor.
How can you check your answer when dividing by a mixed number?
Multiply your answer by the original mixed number. The result should equal the original whole number. For 4 x 1.5 = 6, confirming the division was correct.
When would you divide a whole number by a mixed number in real life?
Any time you split a total into groups of a fractional size: 9 feet of rope cut into pieces of 1 and 1/2 feet each gives 9 / 1.5 = 6 pieces.