Connecting Division by a Unit Fraction to Multiplication
Dividing a whole number by a unit fraction (like 1/2 or 1/3) produces the same result as multiplying the whole number by the denominator, because the problem asks how many fractional pieces fit in the whole number. This Grade 5 math skill from Eureka Math Chapter 25 covers division of fractions and the relationship between division and multiplication.
Key Concepts
We noticed in the previous visual models that dividing by a unit fraction ($\frac{1}{b}$) produces the same result as multiplying by the denominator ($b$). To solve $a \div \frac{1}{b}$, you can ask: "$a$ is $\frac{1}{b}$ of what number?". The shortcut is to multiply the whole number by the denominator : $$a \div \frac{1}{b} = a \times b$$.
Common Questions
What is the rule for dividing a whole number by a unit fraction?
Dividing a whole number by a unit fraction 1/b equals multiplying the whole number by b. For example, 2 divided by 1/3 equals 2 times 3 equals 6.
Why does dividing by a unit fraction equal multiplying by its denominator?
Division by 1/b asks how many 1/b-sized pieces are in the whole number. Since there are b pieces of size 1/b in each whole, multiplying by b gives the total number of pieces.
What is an example of dividing by a unit fraction?
To solve 4 divided by 1/5, ask: 4 is 1/5 of what number? Since 4 is one-fifth of the total, the total must be 4 times 5 equals 20.
How does this connect division to multiplication?
Division by a unit fraction is equivalent to multiplication by the denominator, showing that division and multiplication are inverse operations even when fractions are involved.