Question

Evaluate each expression. $$\frac{14}{19} \cdot \frac{38}{77}$$

Short answer

\(\frac{532}{1463}\)

Step-by-step solution

Multiply the Numerators

To evaluate \(\frac{14}{19} \cdot \frac{38}{77}\), begin by multiplying the numerators together. This means multiplying 14 by 38. \[ 14 \cdot 38 = 532 \]

Multiply the Denominators

Next, multiply the denominators together. This means multiplying 19 by 77. \[ 19 \cdot 77 = 1463 \]

Combine the Results

Combine the results of the numerators and denominators to form the new fraction: \(\frac{532}{1463}\). This is already in its simplest form.

Key concepts

Numerator

The numerator is the top number of a fraction. In our exercise, \(\frac{14}{19} \cdot \frac{38}{77}\), the numerators are 14 and 38. To multiply fractions, we start by multiplying the numerators together. For this example, we multiply 14 by 38, which equals 532. Understanding the role of the numerator is crucial, as it represents how many parts of the whole we are considering. When performing operations with fractions, always handle the numerators separately from the denominators before combining.

Denominator

The denominator is the bottom number of a fraction. It shows the total number of parts that make up a whole. In our problem, the denominators are 19 and 77. To complete the multiplication of fractions, we multiply these denominators together. For instance, when multiplying 19 by 77, we get 1463. Remember, the denominator helps us understand into how many equal parts the whole is divided. Like with numerators, when performing fraction operations, handle denominators separately and carefully follow the arithmetic rules.

Simplifying Fractions

Simplifying fractions means reducing them to their simplest form, where the numerator and denominator have no common factors other than 1. In the step-by-step solution provided, combining our results gives \(\frac{532}{1463}\). We check if 532 and 1463 share any common factors. Since they do not, \(\frac{532}{1463}\) is already simplified. To simplify other fractions, find the greatest common divisor (GCD) of the numerator and denominator, then divide them both by this number. This process makes working with fractions easier and more understandable.

Math Homework Help

When working on math homework, especially with fractions, understanding the basics is key. Use these tips to help with your assignments:

• Break problems into smaller steps, such as multiplying numerators and denominators separately.
• Always simplify fractions to their lowest terms.
• Practice regularly to strengthen your understanding and skills.
• Ask for help from teachers, peers, or online resources when stuck.

Remember, consistent practice and a clear understanding of core concepts, like numerators and denominators, will make math homework more manageable and less stressful.