Use the double number line to convert
gallons to quarts. Gallons 0
1
2
3
4
5
6 Quarts 0 2 4 6 8 10 12 14 16 18 20 22 24
gallons = quarts
The Correct Answer and Explanation is:
Correct Answer:
314 gallons=13 quarts3\frac{1}{4} \text{ gallons} = 13 \text{ quarts}341 gallons=13 quarts
Explanation
The problem asks us to convert 3143\frac{1}{4}341 gallons into quarts using the provided double number line. First, let’s understand the relationship between gallons and quarts:
1 gallon = 4 quarts
This means each tick mark for gallons corresponds to 4 quarts on the quarts line. The number line is labeled incrementally for gallons and quarts, showing fractional gallons and their equivalent in quarts.
On the top number line, gallons are marked in quarters:
- 0,14,12,34,1,54,32,…0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1, \frac{5}{4}, \frac{3}{2}, \ldots0,41,21,43,1,45,23,…
On the bottom number line, quarts are marked at intervals of 2:
- 0,2,4,6,8,10,12,14,16,…0, 2, 4, 6, 8, 10, 12, 14, 16, \ldots0,2,4,6,8,10,12,14,16,…
To solve the problem, we find where 3143\frac{1}{4}341 gallons is located on the top number line, then trace directly downward to the matching point on the quarts line.
- 3143\frac{1}{4}341 gallons is one tick past 3 gallons.
- At 3 gallons, the quarts line reads 12 quarts.
- Each quarter gallon is 1 quart (since 1 gallon = 4 quarts, 14\frac{1}{4}41 gallon = 1 quart).
- So, 3143\frac{1}{4}341 gallons = 12+1=1312 + 1 = 1312+1=13 quarts.
The box in the image mistakenly shows 2625, which is incorrect. That appears to be a typographical or input error.
Final Conversion:
314 gallons=13 quarts3\frac{1}{4} \text{ gallons} = 13 \text{ quarts}341 gallons=13 quarts
This solution demonstrates how to use proportional reasoning and visual aids like double number lines to perform unit conversions accurately.
