Comparing Quantities by Dividing
Comparing Quantities by Dividing is a Grade 6-7 math skill that teaches students to use division to compare two quantities and express their relationship as a ratio or rate. This approach is used to find unit rates, compare prices, and analyze proportional relationships.
Key Concepts
Property To estimate how many times larger one quantity is than another, divide their estimated values in scientific notation. Divide the coefficients and subtract the exponents of 10:$$\frac{a \times 10^m}{b \times 10^n} = \left(\frac{a}{b}\right) \times 10^{m n}$$.
Examples Example 1: Compare 9 x 10^ 7 and 3 x 10^ 3. (9 x 10^ 7) / (3 x 10^ 3) = (9 / 3) x 10^( 7 ( 3)) = 3 x 10^ 4 Example 2: A large city has a budget of about 7.5 x 10^5 dollars for parks, and a small town has 3 x 10^2 dollars. How many times larger is the city's budget? (7.5 x 10^5) / (3 x 10^2) = (7.5 / 3) x 10^(5 2) = 2.5 x 10^3 The city's budget is 2.5 x 10^3 (or 2,500) times larger.
Explanation Often in science and finance, we don't just want to know a number; we want to compare it to something else! To find out "how many times bigger" something is, we use division. This is a simple two part process. First, divide the front numbers (the coefficients). Then, use your Quotient of Powers property to subtract the bottom exponent from the top exponent.
Common Questions
How do you compare quantities by dividing?
Divide one quantity by the other to find how many times larger or smaller one is. The result can be expressed as a ratio or unit rate.
What is the difference between comparing by subtracting and comparing by dividing?
Subtracting gives the difference; dividing gives the ratio or how many times one quantity is compared to the other.
What is a unit rate?
A unit rate compares a quantity to 1 unit of another quantity by dividing. For example, 60 miles in 2 hours gives a unit rate of 30 miles per hour.
How do you find the best value using division?
Divide the total price by the number of units to find the price per unit, then compare the unit prices.
What grade covers comparing quantities by dividing?
Comparing quantities by dividing and unit rates are taught in Grade 6 and Grade 7 math.