Jorge has a recipe that calls for $$ 2 \frac{1}{3} $$ cups of flour. He plans to make $$ 1 \frac{1}{2} $$ times the recipe. Will the amount of flour Jorge needs be equal to, greater than, or less than the amount of flour his recipe calls for?

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UpStudy AI · Accepted Answer

1. Convert mixed numbers to improper fractions.

- Given recipe calls for $$ 2 \frac{1}{3} $$ cups of flour. Express it as:
     $$
     2 \frac{1}{3} = \frac{3 \times 2 + 1}{3} = \frac{7}{3}.
     $$

- The multiplier is $$ 1 \frac{1}{2} $$, which is:
     $$
     1 \frac{1}{2} = \frac{2 \times 1 + 1}{2} = \frac{3}{2}.
     $$

2. Multiply the amount of flour by the multiplier to get the new amount:

$$
   \frac{7}{3} \times \frac{3}{2} = \frac{7 \times 3}{3 \times 2}.
   $$

3. Simplify the multiplication by cancelling common factors:

The $$3$$ in the numerator and denominator cancels out:
   $$
   \frac{7 \times \cancel{3}}{\cancel{3} \times 2} = \frac{7}{2}.
   $$

4. Convert the result back to a mixed number if needed:

$$
   \frac{7}{2} = 3 \frac{1}{2}.
   $$

5. Compare the new amount to the original recipe amount:

- The original recipe calls for $$ 2 \frac{1}{3} $$ cups, which is approximately $$ 2.33 $$ cups.
   - The new amount is $$ 3 \frac{1}{2} $$ cups, which is $$ 3.5 $$ cups.

Since $$ 3.5 > 2.33 $$, Jorge needs more flour for the multiplied recipe.

Thus, the amount of flour Jorge needs is **greater than** the amount required by his original recipe.
Jorge needs more flour, so the amount is greater than what the recipe calls for.

Jorge has a recipe that calls for \( 2 \frac{1}{3} \) cups of flour. He plans to make \( 1 \frac{1}{2} \) times the recipe. Will the amount of flour Jorge needs be equal to, greater than, or less than the amount of flour his recipe calls for?

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