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Chapter 1: Problem 43

Write a problem for a classmate to solve for which fractions must be multiplied in order to get the answer.

Short Answer

Expert verified
\(\frac{8}{15}\)

Step by step solution

01

Identify the Fractions

Determine which fractions need to be multiplied. For example, let's consider two fractions: \(\frac{2}{3}\) and \(\frac{4}{5}\).
02

Multiply the Numerators

Multiply the numerators (top numbers) of the fractions together. In this case, \(2 \times 4 = 8\).
03

Multiply the Denominators

Multiply the denominators (bottom numbers) of the fractions together. In this case, \(3 \times 5 = 15\).
04

Form the New Fraction

Combine the results from the previous steps to form a new fraction. The product will be \(\frac{8}{15}\).
05

Simplify the Fraction (if possible)

Check if the resulting fraction can be simplified. Since 8 and 15 have no common factors other than 1, \(\frac{8}{15}\) is already in its simplest form.

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Key Concepts

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

fraction multiplication
Multiplying fractions is a fundamental skill in math. It involves two main steps: multiplying the numerators and multiplying the denominators. Let's say we have the fractions \(\frac{2}{3}\) and \(\frac{4}{5}\). Here's how you multiply them:
  • Multiply the Numerators: The numerator is the top number of a fraction. Multiply \(2\) (the numerator of the first fraction) by \(4\) (the numerator of the second fraction). This gives you \(2 \times 4 = 8\).
  • Multiply the Denominators: The denominator is the bottom number of a fraction. Multiply \(3\) (the denominator of the first fraction) by \(5\) (the denominator of the second fraction). This gives you \(3 \times 5 = 15\).
  • Form the New Fraction: Now you have a new fraction formed by the products of the numerators and the denominators. So, \(\frac{8}{15}\) is the result.
As you can see, fraction multiplication is straightforward. The key is to handle the numerators and denominators separately.
simplifying fractions
Simplifying fractions makes them easier to understand. Simplification means reducing the fraction to its simplest form. Here's how you can simplify a fraction:
  • Find the Greatest Common Factor (GCF): Look for the largest number that divides both the numerator and the denominator.
  • Divide Both Terms by the GCF: Once you know the GCF, divide both the numerator and the denominator by this number.
  • Get the Simplified Fraction: The result is the fraction in its simplest form.
For instance, suppose we multiply the fractions \(\frac{6}{9}\) and \(\frac{3}{4}\). First, we perform the multiplication: \(6 \times 3 = 18\) and \(9 \times 4 = 36\), leading to the fraction \(\frac{18}{36}\). Since the GCF of \18\ and \36\ is \18,\ dividing both the numerator and denominator by \18\ gives us \(\frac{1}{2}\). Therefore, \(\frac{1}{2}\) is the simplified version of \(\frac{18}{36}\). Always check for the GCF before finalizing your answer.
numerator and denominator
Understanding the numerator and denominator is crucial when working with fractions. A fraction consists of two parts:
  • Numerator: This is the top number of a fraction. It represents how many parts of the whole are being considered.
  • Denominator: This is the bottom number of a fraction. It indicates the total number of equal parts the whole is divided into.For example, in the fraction \(.... \).
In the fraction \(\frac{2}{3}\), \(2\) is the numerator, and it shows the parts we are taking. The \3\ is the denominator, representing the three equal parts in the whole. When multiplying fractions, it's crucial to handle the numerators and denominators separately. Multiply the numerators first to get the new numerator, and then multiply the denominators to find the new denominator. After you've formed your new fraction, check if it needs simplification. This separation ensures clarity and accuracy in fraction problems.

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