6.NS.1 - Division of Whole Number by Fraction Word Problem - Free Printable

We are told that Benjamin has 9 cups of sugar, and that this amount is $\frac{3}{4}$ of the total amount he *needs* to make the cake.

So, we’re being asked:
> If 9 cups = $\frac{3}{4}$ of the total needed, what is the whole (i.e., 100% or $\frac{4}{4}$) amount?

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Step-by-step Solution:

Let’s call the total amount of sugar Ben needs $x$ cups.

According to the problem:

$$
\frac{3}{4} \cdot x = 9
$$

To solve for $x$, divide both sides by $\frac{3}{4}$:

$$
x = 9 \div \frac{3}{4}
$$

Remember: dividing by a fraction is the same as multiplying by its reciprocal.

$$
x = 9 \times \frac{4}{3}
$$

Now compute:

$$
9 \times \frac{4}{3} = \frac{9 \times 4}{3} = \frac{36}{3} = 12
$$

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Visual Explanation (using the bar model shown):

The bar is divided into 4 equal parts (since we’re dealing with quarters).
We’re told that 3 of those parts = 9 cups.
So, each part = $9 \div 3 = 3$ cups.
Therefore, the whole bar (4 parts) = $4 \times 3 = 12$ cups.

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Final Answer:

✔ Ben needs 12 cups.

Fill in the blanks:

- $9 \div \frac{3}{4} = \boxed{12}$
- Ben needs $\boxed{12}$ cups.