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Chapter 4: Problem 170

Portions Don purchased a bulk package of candy that weighs 5 pounds. He wants to sell the candy in little bags that hold \(\frac{1}{4}\) pound. How many little bags of candy can he fill from the bulk package?

Short Answer

Expert verified
Don can fill 20 little bags.

Step by step solution

01

Understand the Problem

Identify the details given in the problem and the requirement. Don has 5 pounds of candy, and each small bag should hold \(\frac{1}{4}\) pound. The problem asks for the number of small bags.
02

Set Up the Division

Recognize that you need to divide the total weight by the weight per little bag. Thus, you need to compute \(\frac{5}{\frac{1}{4}}\).
03

Simplify the Division

Divide 5 by \(\frac{1}{4}\) by multiplying by the reciprocal of \(\frac{1}{4}\). This is given by: \(\frac{5}{\frac{1}{4}} = 5 \times 4\).
04

Perform the Multiplication

Multiply 5 by 4 to find the total number of little bags: \(5 \times 4 = 20\).
05

Conclude the Solution

After computing the multiplication, conclude that Don can fill 20 little bags with the bulk candy.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

fractions
Fractions are a way to represent parts of a whole. They consist of a numerator and a denominator. The numerator is the top number and shows how many parts we have. The denominator is the bottom number and shows how many equal parts make up a whole. For example, in the fraction \(\frac{1}{4}\), 1 is the numerator and 4 is the denominator. This fraction means we have one part out of four equal parts.
Fractions are handy in everyday life for measurements, cooking, and many other tasks that involve portions. Understanding fractions is vital for more advanced math concepts like division and multiplication of fractions.
division
Division is the process of splitting a number into equal parts. When we divide, we ask how many times a number (the divisor) fits into another number (the dividend).
In our candy example, Don has 5 pounds of candy (the dividend) and wants to divide it into small bags of \(\frac{1}{4}\) pound each (the divisor).
The division of fractions looks slightly different than whole number division. To divide by a fraction, we multiply by its reciprocal.
The reciprocal of a fraction is just flipping the numerator and the denominator. So, the reciprocal of \(\frac{1}{4}\) is \(\frac{4}{1}\) (which is just 4). Thus, dividing by \(\frac{1}{4}\) is the same as multiplying by 4.
multiplication of fractions
Multiplication of fractions involves multiplying the numerators together and the denominators together. For instance, \(\frac{A}{B} \times \frac{C}{D} = \frac{A \times C}{B \times D}\).
In our example, we need to multiply 5 by the reciprocal of \(\frac{1}{4}\), which is 4. So, we calculate: \(\frac{5}{1} \times \frac{4}{1} = \frac{20}{1} = 20\).
This tells us that 5 pounds of candy can be divided into 20 small bags, each weighing \(\frac{1}{4}\) pound.
Multiplying by the reciprocal makes division with fractions easier to understand and perform.
problem-solving
Problem-solving in math often involves breaking down the problem into smaller, manageable steps.
Let's see how we tackled the candy problem:
  • First, we understood what was given and what we needed to find. Don has 5 pounds of candy and wants to know how many \(\frac{1}{4}\) pound bags he can fill.
  • Next, we set up the division problem: 5 divided by \(\frac{1}{4}\).
  • We then simplified this by multiplying 5 by the reciprocal of \(\frac{1}{4}\), which is 4.
  • Finally, we performed the multiplication and concluded that Don could fill 20 small bags with the candy.

Following these steps ensures you understand each part of the problem before solving it. Taking it step-by-step helps avoid mistakes and makes complex problems easier to solve.

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Most popular questions from this chapter

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