Solving Division Word Problems and Fractions

11 Questions

What is the first step in solving a division word problem?

Read the problem carefully

In the example with Priscilla and the cheese, what is the total weight of the cheese she bought?

⅔ pound

What is the portion size that Priscilla wants to make with the cheese?

¼ pound

What is the first step in dividing fractions?

Divide the numerator of the first fraction by the denominator of the second fraction

What is the purpose of simplifying the answer when solving a division word problem?

To make the answer easier to understand

In the example with Priscilla and the cheese, how many portions can she make?

6 portions

What is the second step in the process of dividing fractions?

Take the reciprocal of both the numerator and denominator of the quotient

In the example $\frac{1}{2} / \frac{1}{3}$, what is the result after the first two steps?

$\frac{3}{1} / \frac{1}{2} = \frac{3}{2}$

What is the purpose of the 'cross cancel' step in dividing fractions?

To simplify the fraction by eliminating common factors between the numerator and denominator

What is the purpose of the final 'check' step in dividing fractions?

To check if the resulting equation balances

What is the simplified result of the example $\frac{1}{2} / \frac{1}{3}$?

$\frac{3}{2}$

Study Notes

Solving Division Word Problems and the Division of Fractions

Division problems involve splitting a quantity evenly among parts. This concept can sometimes seem tricky when dealing with fractions. However, by understanding the process and practicing with examples, you can become proficient in solving these types of problems. In this article, we'll discuss techniques for handling division word problems and dividing fractions.

Divison Word Problems

To solve division word problems, follow these steps:

Read the problem carefully: Make sure you understand the quantities involved, such as weight or length.
Think about what it asks: Determine the unknown variable you need to calculate.
Identify the details needed: Figure out the given values, like the total amount or the number of parts.
Carry out the division operation: Divide the total amount by the part size to determine the number of parts.
Simplify: If possible, reduce the answer to its simplest form.
Check: Ensure the answer makes sense in context.

For instance, if Priscilla buys cheese weighing ⅔ pound and wants to make portions that are each ¼ pound, you would calculate how many portions she can make using dividing fractions:

Total weight / Portion size = Number of portions
⅔ pound / ¼ pound = _______ portions

The result would indicate that Priscilla could make 6 portions.

Dividing Fractions

When dividing fractions, follow these procedures:

Multiply: Multiply the numerator of the dividend by the denominator of the divisor.
Invert: Take the reciprocal of both the numerator and denominator of the quotient.
Cross cancel: Eliminate common factors between the top and bottom.
Check: See if the resulting equation balances.

Consider the following example:

\(\frac{1}{2}\) / \(\frac{1}{3}\) = ?

First, multiply and invert:

\(\frac{1}{2} * \frac{3}{1} = \frac{1}{2} \times 3 = \frac{3}{2}\)
\(\frac{3}{1} / \frac{1}{2} = \frac{3}{1} \times \frac{2}{1} = \frac{3}{2}\)

Next, cross cancel:

\(\frac{3}{2}\)

Finally, the result checks out:

\(\frac{3}{2}\) is the simplified result.

By utilizing these strategies, you can successfully tackle division word problems and the division of fractions. Remember to practice regularly to improve your skills in solving these types of mathematical challenges.