Problem 42 - Prealgebra

Question

Express each rate as a unit rate. Round to the nearest tenth, if necessary. \(\$ 5\) for 4 loaves of bread

Step-by-Step Solution

Answer

The unit rate is $1.25 per loaf of bread.

Step 1: Understanding the Problem

To express the rate as a unit rate, we need to determine how much money is spent per single loaf of bread. This is done by dividing the total cost by the number of items.

Step 2: Setting Up the Division

We have a total cost of $5 for 4 loaves of bread. We set up the division as follows: divide 5 by 4.

Step 3: Performing the Division

Perform the calculation: \[\frac{5}{4} = 1.25\]This indicates that the cost per loaf of bread is $1.25.

Step 4: Rounding if Necessary

Check if the unit rate needs rounding. Since $1.25 is already rounded to the nearest tenth, no further rounding is necessary.

Key Concepts

Division in Math

Division in math is a fundamental operation, much like addition, subtraction, and multiplication. It's used to determine how many times one number, called the divisor, fits into another number, known as the dividend. In our example, dividing \(5 by 4 helps us find the cost per single loaf of bread.
To perform division:

• Identify the dividend: the total amount, which is \)5 in this case.
• Identify the divisor: the number of equal parts you need, here it’s 4 loaves.

The result of the division is called the quotient. Thus, \(\frac{5}{4} = 1.25\) tells us that each loaf costs $1.25. Division reduces a large total into smaller, more manageable units, like individual loaf costs.

Problem-Solving Steps

Problem-solving in math involves understanding the problem, devising a plan, carrying out the plan, and reviewing/rounding the answer. For unit rate calculations, these steps help break down the problem.

• Understanding the Problem: Identify what you need – the cost per loaf for this example.
• Setting Up the Division: Organize the information clearly, knowing that the total cost is divided by the number of loaves.
• Performing the Division: Execute the calculation carefully to avoid errors, leading to the answer: $1.25 in our case.
• Rounding: Analyze if the result needs adjustment for precision, especially if asked to round to the nearest tenth.

These steps ensure that each part of the problem is approached methodically, making the process clear and manageable.

Rounding Numbers

Rounding numbers is a technique used to simplify numbers, making them easier to work with, especially for approximations or when dealing with decimals. The main idea is to replace a number with another that is approximately equal but has fewer digits.
When rounding to the nearest tenth:

• Identify the tenths place and the digit immediately following it (hundredths place).
• If the hundredths digit is 5 or more, increase the tenths digit by 1.
• If the hundredths digit is less than 5, leave the tenths digit unchanged.

In our exercise, we didn't need additional rounding because $1.25 was already rounded to the nearest tenth. Rounding helps in presenting cleaner, more straightforward figures in practical scenarios.