Convert Customary Weights Using Equivalent Ratios
Converting customary weights using equivalent ratios means setting up a proportion with a known conversion rate and solving for the unknown quantity. For example, since 1 pound = 16 ounces, to convert 3.5 pounds to ounces, set up 1 lb / 16 oz = 3.5 lb / x oz and solve: x = 3.5 x 16 = 56 ounces. This 6th grade measurement skill from enVision Mathematics Grade 6 connects ratio and proportion reasoning to the practical task of unit conversion within the US customary system.
Key Concepts
Property The standard customary units of weight can be expressed as ratios: $$\frac{1 \text{ pound}}{16 \text{ ounces}} \quad \text{and} \quad \frac{1 \text{ ton}}{2,000 \text{ pounds}}$$ These ratios are used to set up equivalent rates for conversion.
Examples To convert 5 pounds to ounces, find an equivalent rate: $$\frac{1 \text{ lb}}{16 \text{ oz}} = \frac{1 \times 5}{16 \times 5} = \frac{5 \text{ lb}}{80 \text{ oz}}$$ So, 5 pounds is equal to 80 ounces. To convert 3 tons to pounds, find an equivalent rate: $$\frac{1 \text{ T}}{2,000 \text{ lb}} = \frac{1 \times 3}{2,000 \times 3} = \frac{3 \text{ T}}{6,000 \text{ lb}}$$ So, 3 tons is equal to 6,000 pounds.
Explanation To convert customary units of weight, you can use ratio reasoning. Start by writing the known conversion as a rate, such as $\frac{1 \text{ lb}}{16 \text{ oz}}$. To find an equivalent measure, multiply the numerator and denominator by the same number to create an equivalent rate. This method allows you to convert between ounces, pounds, and tons by scaling the base conversion rate up or down.
Common Questions
How do you convert customary weights using equivalent ratios?
Set up a proportion using the conversion factor as one ratio. For pounds to ounces (1 lb = 16 oz): to convert 3.5 lb, solve 1/16 = 3.5/x, giving x = 56 ounces.
What are the common customary weight conversions?
16 ounces = 1 pound; 2000 pounds = 1 ton. These are the key conversions within the US customary weight system.
How is unit conversion the same as solving a proportion?
A conversion factor is a ratio (like 16 oz : 1 lb). Setting equal this ratio to an unknown ratio and solving is exactly solving a proportion by cross multiplication.
What grade converts customary weights using ratios?
Converting customary weights using equivalent ratios is a 6th grade skill in enVision Mathematics Grade 6, applying proportional reasoning to measurement contexts.
How do you convert tons to pounds?
Multiply by 2000, since 1 ton = 2000 pounds. For 1.5 tons: 1.5 x 2000 = 3000 pounds. Or set up the proportion 1/2000 = 1.5/x.
When would you convert ounces to pounds in real life?
Grocery shopping (buying 48 oz of nuts is 3 lb), cooking (converting recipe amounts), shipping (packages charged by pounds when weight is given in ounces).