Procedure: Dividing a Whole Number by a Non-Unit Fraction
Dividing a whole number by a non-unit fraction in Grade 6 is done by multiplying the whole number by the reciprocal of the fraction. From enVision Mathematics, Grade 6, to divide 6 ÷ (2/3), multiply by the reciprocal: 6 × (3/2) = 9. This works because dividing by 2/3 asks how many two-thirds fit in 6 — and multiplying by the reciprocal gives that count. This procedure applies to all whole-number-divided-by-fraction problems and builds the foundational understanding for fraction division throughout middle school algebra.
Key Concepts
To divide a whole number by a non unit fraction , we can use a two step process or simply multiply by the reciprocal . The reciprocal of a fraction $\frac{b}{c}$ is $\frac{c}{b}$ (flipping the numerator and denominator). $$a \div \frac{b}{c} = a \times \frac{c}{b}$$.
Common Questions
How do you divide a whole number by a fraction?
Multiply the whole number by the reciprocal of the fraction. For example, 6 ÷ (2/3) = 6 × (3/2) = 18/2 = 9.
What is the reciprocal of a fraction?
The reciprocal is the fraction flipped — numerator and denominator swapped. The reciprocal of 2/3 is 3/2.
Why does multiplying by the reciprocal work for division?
Division asks how many of the divisor fit in the dividend. Multiplying by the reciprocal computes this count algebraically, and it is equivalent to dividing by the original fraction.
How is dividing by a non-unit fraction different from dividing by a unit fraction?
A unit fraction has numerator 1 (like 1/3). Dividing by a non-unit fraction (like 2/3) involves the same reciprocal step but the reciprocal is not a whole number.
Where is this procedure taught in enVision Mathematics?
Dividing a whole number by a non-unit fraction is covered in enVision Mathematics, Grade 6, as part of fraction division and operations.
Can you show another example?
4 ÷ (3/5) = 4 × (5/3) = 20/3 = 6⅔. This means 4 contains 6 and two-thirds groups of 3/5.
What mistakes do students make when dividing by a fraction?
Students often multiply by the fraction itself instead of its reciprocal, or forget to convert the whole number to a fraction (over 1) before multiplying.