(a) To convert from gallons to quarts, multiply by what? 7 gallons = 28 quarts Multiply by 4 (b) Write down an equation y = k * x expressing the relationship between gallons (G) and quarts (Q). The equation is Q = 4G (c) To convert from pounds to kilograms, multiply by what? 4.4 pounds = 2 kilograms Multiply by 0.45 (Round to two decimal places as needed) (d) Write down an equation y = k * X expressing the relationship between pounds (P) and kilograms. The equation is K = 0.45P (Round to two decimal places as needed) (e) To convert from furlongs to miles, multiply by what? 24 furlongs = 3 miles Multiply by 0.125 Write down an equation y = k * X expressing the relationship between furlongs (F) and miles (M). The equation is M = 0.125F
The Correct Answer and Explanation is:
Let’s go through each part of the conversion step-by-step.
(a) Converting Gallons to Quarts
To convert gallons to quarts, we use the fact that there are 4 quarts in 1 gallon. This means that to convert any number of gallons into quarts, we multiply by 4.
- Example: For 7 gallons, the conversion would be: 7 gallons×4=28 quarts7 \, \text{gallons} \times 4 = 28 \, \text{quarts}7gallons×4=28quarts
Thus, multiplying by 4 gives the correct number of quarts for any number of gallons.
(b) Equation for Gallons to Quarts
The equation that expresses the relationship between gallons (G) and quarts (Q) is:Q=4GQ = 4GQ=4G
This equation tells us that the number of quarts is 4 times the number of gallons.
(c) Converting Pounds to Kilograms
To convert pounds to kilograms, we know that 1 pound is approximately equal to 0.45 kilograms. This is the constant multiplier between pounds and kilograms.
- Example: For 4.4 pounds, the conversion would be: 4.4 pounds×0.45=2 kilograms4.4 \, \text{pounds} \times 0.45 = 2 \, \text{kilograms}4.4pounds×0.45=2kilograms
Thus, to convert from pounds to kilograms, we multiply by 0.45.
(d) Equation for Pounds to Kilograms
The equation that expresses the relationship between pounds (P) and kilograms (K) is:K=0.45PK = 0.45PK=0.45P
This equation tells us that the number of kilograms is 0.45 times the number of pounds.
(e) Converting Furlongs to Miles
To convert furlongs to miles, we know that 1 mile is equal to 8 furlongs. Therefore, to convert furlongs into miles, we multiply by 0.125 (since 1 mile ÷ 8 furlongs = 0.125).
- Example: For 24 furlongs, the conversion would be: 24 furlongs×0.125=3 miles24 \, \text{furlongs} \times 0.125 = 3 \, \text{miles}24furlongs×0.125=3miles
Thus, multiplying by 0.125 gives the correct number of miles for any number of furlongs.
(f) Equation for Furlongs to Miles
The equation that expresses the relationship between furlongs (F) and miles (M) is:M=0.125FM = 0.125FM=0.125F
This equation tells us that the number of miles is 0.125 times the number of furlongs.
Conclusion:
To summarize, the conversion factors and equations are:
- Gallons to Quarts: Multiply by 4 → Q=4GQ = 4GQ=4G
- Pounds to Kilograms: Multiply by 0.45 → K=0.45PK = 0.45PK=0.45P
- Furlongs to Miles: Multiply by 0.125 → M=0.125FM = 0.125FM=0.125F
These equations provide a simple and efficient way to perform these conversions accurately.
