Ethan used (17)/(5) cups of flour for bread and 2(3)/(10) cups for muffins. To add these two quantities, we first convert the mixed number 2(3)/(10) into an improper fraction. Multiplying the whole number 2 by the denominator 10 and adding the numerator 3 gives (23)/(10).

Ethan used (17)/(5) cups of flour for bread and 2(3)/(10) cups for muffins. To add these two quantities, we first convert the mixed number 2(3)/(10) into an improper fraction. Multiplying the whole number 2 by the denominator 10 and adding the numerator 3 gives (23)/(10).

The denominators are 5 and 10. The least common multiple (LCM) of 5 and 10 is 10. We convert (17)/(5) into an equivalent fraction with a denominator of 10 by multiplying both the numerator and the denominator by 2, giving (34)/(10).

The denominators are 5 and 10. The least common multiple (LCM) of 5 and 10 is 10. We convert (17)/(5) into an equivalent fraction with a denominator of 10 by multiplying both the numerator and the denominator by 2, giving (34)/(10).

Ethan used (17/5) cups of flour for bread and 2 (3/10) cups for muffins. Written as a mixed number, how many cups of flour did he use altogether?

Answer: $5\frac{7}{10}$ cups

Step-by-step solution

Step 1: Convert mixed number to an improper fraction

Ethan used $\frac{17}{5}$ cups of flour for bread and $2\frac{3}{10}$ cups for muffins. To add these two quantities, we first convert the mixed number $2\frac{3}{10}$ into an improper fraction. Multiplying the whole number $2$ by the denominator $10$ and adding the numerator $3$ gives $\frac{23}{10}$ .

Step 2: Find a common denominator for the fractions

The denominators are $5$ and $10$ . The least common multiple (LCM) of $5$ and $10$ is $10$ . We convert $\frac{17}{5}$ into an equivalent fraction with a denominator of $10$ by multiplying both the numerator and the denominator by $2$ , giving $\frac{34}{10}$ .

Step 3: Add the fractions to find the total flour

Now that both fractions have the same denominator, we add their numerators together: $34 + 23 = 57$ . The total amount of flour used is $\frac{57}{10}$ cups.

Step 4: Convert the improper fraction to a mixed number

Dividing $57$ by $10$ yields a quotient of $5$ with a remainder of $7$ . Therefore, the total amount of flour written as a mixed number is $5\frac{7}{10}$ cups.

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