Question

emily uses 1 2/3 cups od sugar and 3 1/4 cups of flour to make muffins
she says she has 1 2/3 more cups of flour than sugar do you agree explain

Answer 1

To determine if Emily's statement is correct, let's break down the quantities she used.

1. Emily uses **1 2/3 cups of sugar** and **3 1/4 cups of flour**.

First, convert the mixed numbers to improper fractions:

- **Sugar:**
\[
1 \frac{2}{3} = \frac{3 \times 1 + 2}{3} = \frac{5}{3}
\]

- **Flour:**
\[
3 \frac{1}{4} = \frac{4 \times 3 + 1}{4} = \frac{13}{4}
\]

2. Next, we need to compare the amount of flour to the amount of sugar to see if she has **1 2/3** more cups of flour than sugar.

Let's find out how much more flour she claims to have than sugar by calculating:
\[
\text{Flour} - \text{Sugar} = \frac{13}{4} - \frac{5}{3}
\]

To subtract these fractions, we need a common denominator, which is 12:
- Convert \(\frac{13}{4}\) to twelfths:
\[
\frac{13}{4} = \frac{13 \times 3}{4 \times 3} = \frac{39}{12}
\]

- Convert \(\frac{5}{3}\) to twelfths:
\[
\frac{5}{3} = \frac{5 \times 4}{3 \times 4} = \frac{20}{12}
\]

Now, perform the subtraction:
\[
\frac{39}{12} - \frac{20}{12} = \frac{19}{12}
\]

3. Now convert \(\frac{19}{12}\) to a mixed number:
\[
\frac{19}{12} = 1 \frac{7}{12}
\]

4. Conclusion:
Emily claims to have **1 2/3** cups more flour than sugar, which is equivalent to \(1 \frac{2}{3} = \frac{5}{3}\). However, she actually has **1 7/12** cups more flour than sugar.

Since \(\frac{5}{3}\) equates to approximately **1.6667**, and \(\frac{19}{12}\) equates to approximately **1.5833**, we find:

\[
1 \frac{7}{12} < 1 \frac{2}{3}
\]

Thus, Emily's statement that she has \(1 \frac{2}{3}\) more cups of flour than sugar is incorrect.