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Chapter 2: Problem 5

Multiply. $$ \frac{7}{8} \cdot \frac{7}{8} $$

Short Answer

Expert verified
\[ \frac{49}{64} \]

Step by step solution

01

- Multiply the Numerators

To multiply fractions, first multiply the numerators (the top numbers) together. For the fractions \(\frac{7}{8} \) and \(\frac{7}{8}\), the numerators are 7 and 7. Multiply these together: \[ 7 \times 7 = 49 \]
02

- Multiply the Denominators

Next, multiply the denominators (the bottom numbers) together. For the fractions \(\frac{7}{8} \) and \(\frac{7}{8} \), the denominators are 8 and 8. Multiply these together: \[ 8 \times 8 = 64 \]
03

- Write the Result as a Fraction

Now that you have the product of the numerators and denominators, write the result as a fraction: \[ \frac{49}{64} \]

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Key Concepts

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

Numerators and Denominators
When working with fractions, it's important to understand the parts that make up a fraction: the numerator and the denominator. The numerator is the top number in a fraction, and it represents how many parts we have. The denominator is the bottom number, and it shows how many equal parts the whole is divided into.

For example, in the fraction \(\frac{7}{8}\), 7 is the numerator, and 8 is the denominator. Knowing these terms helps you follow the steps in fraction multiplication, adding, subtracting, or dividing fractions more easily.
Fraction Multiplication
Fraction multiplication might seem tricky, but it's straightforward if you follow the steps. To multiply two fractions like \(\frac{7}{8}\) and \(\frac{7}{8}\), you need to multiply the numerators (top numbers) and then the denominators (bottom numbers) separately.

  • Step 1: Multiply the numerators together: \(7 \times 7 = 49\)

  • Step 2: Multiply the denominators together: \(8 \times 8 = 64\)
Once you have both products, write them as a new fraction: \(\frac{49}{64}\). That's your final answer!
Basic Arithmetic
Basic arithmetic, like addition, subtraction, multiplication, and division, is foundational for math. When dealing with fractions, these operations are applied in specific ways. For the multiplication exercise we discussed, you're mainly focusing on multiplying two numbers together.

Here, the arithmetic operation is multiplication. When you multiply two numbers, you're essentially adding one of the numbers to itself as many times as the other number specifies.

Understanding basic arithmetic ensures you can solve more complex problems by breaking them into simpler, manageable parts.

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Most popular questions from this chapter

Determine whether the second number is a factor of the first. $$ 625 ; 25 $$

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