Lesson 8

How Much for One?

Let’s use ratios to describe how much things cost.

8.1: Number Talk: Remainders in Division

Find the quotient mentally.

\(246\div 12\)

8.2: Grocery Shopping

Answer each question and explain or show your reasoning. 

  1. Eight avocados cost $4.

    1. How much do 16 avocados cost?
    2. How much do 20 avocados cost?
    3. How much do 9 avocados cost?
  2. Twelve large bottles of water cost $9.

    1. How many bottles can you buy for $3?
    2. What is the cost per bottle of water?
    3. How much would 7 bottles of water cost?
  3. A 10-pound sack of flour costs $8.

    1. How much does 40 pounds of flour cost?
    2. What is the cost per pound of flour?

Here is an applet you can use if you choose to.



It is commonly thought that buying larger packages or containers, sometimes called buying in bulk, is a great way to save money. For example, a 6-pack of soda might cost $3 while a 12-pack of the same brand costs $5.

Find 3 different cases where it is not true that buying in bulk saves money. You may use the internet or go to a local grocery store and take photographs of the cases you find. Make sure the products are the same brand. For each example that you find, give the quantity or size of each, and describe how you know that the larger size is not a better deal.

8.3: More Shopping

  1. Four bags of chips cost $6.

    1. What is the cost per bag?

    2. At this rate, how much will 7 bags of chips cost?

  2. At a used book sale, 5 books cost $15.
    1. What is the cost per book?

    2. At this rate, how many books can you buy for $21?

  3. Neon bracelets cost $1 for 4.
    1. What is the cost per bracelet?

    2. At this rate, how much will 11 neon bracelets cost? 

    Pause here so your teacher can review your work.

  4. Your teacher will assign you one of the problems. Create a visual display that shows your solution to the problem. Be prepared to share your solution with the class.

Here is an applet you may use if you choose to.

Summary

The unit price is the price of 1 thing—for example, the price of 1 ticket, 1 slice of pizza, or 1 kilogram of peaches.

If 4 movie tickets cost $28, then the unit price would be the cost per ticket. We can create a double number line to find the unit price.

Double number line. Cost in dollars. Number of tickets.

This double number line shows that the cost for 1 ticket is $7. We can also find the unit price by dividing, \(28 \div 4 = 7\), or by multiplying, \(28 \boldcdot \frac14 = 7\).

Glossary Entries

  • double number line diagram

    A double number line diagram uses a pair of parallel number lines to represent equivalent ratios. The locations of the tick marks match on both number lines. The tick marks labeled 0 line up, but the other numbers are usually different.

    A double number line for teaspoons of red paint: 0, 3, 6, 9, 12 and teaspoons of yellow paint: 0, 5, 10, 15, 20.
  • per

    The word per means “for each.” For example, if the price is $5 per ticket, that means you will pay $5 for each ticket. Buying 4 tickets would cost $20, because \(4 \boldcdot 5 = 20\).

  • unit price

    The unit price is the cost for one item or for one unit of measure. For example, if 10 feet of chain link fencing cost $150, then the unit price is \(150 \div 10\), or $15 per foot.