Question

1. alyssa usó $1\frac{2}{3}$ galones de pintura blanca para pintar el cielorraso de su habitación. usó $3\frac{1}{3}$ galones de pintura verde para las paredes de la habitación. ¿cuánta pintura verde más que pintura blanca usó alyssa?

a $1\frac{1}{3}$ galones
b $1\frac{2}{3}$ galones
c 2 galones
d $2\frac{1}{3}$ galones

Explanation:

Step1: Identify the operation

To find how much more green paint than white paint was used, we subtract the amount of white paint from the amount of green paint. The amounts are \( 3\frac{1}{3} \) gallons (green) and \( 1\frac{2}{3} \) gallons (white).

Step2: Subtract the mixed numbers

First, convert the mixed numbers to improper fractions (or subtract the whole numbers and fractions separately).
Subtract the whole numbers: \( 3 - 1 = 2 \)
Subtract the fractions: \( \frac{1}{3} - \frac{2}{3} \). Wait, that would be negative, so we borrow 1 from the whole number part of the green paint.
\( 3\frac{1}{3} = 2 + 1 + \frac{1}{3} = 2 + \frac{3}{3} + \frac{1}{3} = 2\frac{4}{3} \)
Now subtract: \( 2\frac{4}{3} - 1\frac{2}{3} = (2 - 1) + (\frac{4}{3} - \frac{2}{3}) = 1 + \frac{2}{3} = 1\frac{2}{3} \)? Wait, no, wait. Wait, original numbers: \( 3\frac{1}{3} - 1\frac{2}{3} \). Let's do it as improper fractions:
\( 3\frac{1}{3} = \frac{10}{3} \), \( 1\frac{2}{3} = \frac{5}{3} \)
Subtract: \( \frac{10}{3} - \frac{5}{3} = \frac{5}{3} = 1\frac{2}{3} \)? Wait, no, that's not right. Wait, \( 3\frac{1}{3} \) is \( \frac{10}{3} \), \( 1\frac{2}{3} \) is \( \frac{5}{3} \). \( \frac{10}{3} - \frac{5}{3} = \frac{5}{3} = 1\frac{2}{3} \). Wait, but let's check again. Wait, the green paint is \( 3\frac{1}{3} \), white is \( 1\frac{2}{3} \). So \( 3\frac{1}{3} - 1\frac{2}{3} \). Let's subtract the whole numbers: 3 - 1 = 2, then fractions: \( \frac{1}{3} - \frac{2}{3} = -\frac{1}{3} \). So we have 2 - \( \frac{1}{3} \)? No, that's wrong. Wait, no, when subtracting mixed numbers, if the fraction part of the subtrahend is larger than the minuend's fraction, we borrow 1 from the whole number. So \( 3\frac{1}{3} = 2 + 1 + \frac{1}{3} = 2 + \frac{3}{3} + \frac{1}{3} = 2\frac{4}{3} \). Now subtract \( 1\frac{2}{3} \): \( 2\frac{4}{3} - 1\frac{2}{3} = (2 - 1) + (\frac{4}{3} - \frac{2}{3}) = 1 + \frac{2}{3} = 1\frac{2}{3} \). Wait, but that's option B. Wait, but let's check with improper fractions: \( 3\frac{1}{3} = \frac{10}{3} \), \( 1\frac{2}{3} = \frac{5}{3} \). \( \frac{10}{3} - \frac{5}{3} = \frac{5}{3} = 1\frac{2}{3} \). Yes, that's correct. So the answer is \( 1\frac{2}{3} \) gallons, which is option B.

Answer:

B. \( 1\frac{2}{3} \) galones