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Chapter 4: Problem 101

Multiply, and write the answer in simplified form. \(\frac{3}{4} \cdot \frac{9}{10}\)

Short Answer

Expert verified
\( \frac{27}{40} \)

Step by step solution

01

Multiply the Numerators

To multiply fractions, start by multiplying the numerators (the top numbers) together. Here, multiply 3 by 9: \[ 3 \times 9 = 27 \]
02

Multiply the Denominators

Next, multiply the denominators (the bottom numbers) together. Here, multiply 4 by 10: \[ 4 \times 10 = 40 \]
03

Write the Fraction

Now, write the new fraction from the results of the previous steps. The new fraction is: \[ \frac{27}{40} \]
04

Simplify the Fraction

Check if the fraction can be simplified. The greatest common divisor (GCD) of 27 and 40 is 1. Since there are no common factors other than 1, the fraction is already in its simplest form: \[ \frac{27}{40} \]

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Key Concepts

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

Numerators
When we talk about fractions, the numerator is the number above the fraction line. Think of it as the top number. The numerator shows how many parts of a whole we have. For example, in the fraction \( \frac{3}{4} \), the numerator is 3.

In our exercise, we had to multiply two numerators together. We took the numerators from each fraction, 3 and 9, then simply multiplied them: 3 x 9 = 27. This step is crucial, as the result (27 in this case) becomes the new numerator of our resulting fraction.
Denominators
The denominator is the number below the fraction line. It shows how many equal parts the whole is divided into. For instance, in \( \frac{3}{4} \), the denominator is 4, meaning the whole is split into 4 equal parts.

In our example problem, we also need to multiply the denominators. We took the denominators from each fraction, 4 and 10, then multiplied them: 4 x 10 = 40. This step ensures the new fraction correctly reflects the division of the whole into parts. So, 40 becomes our new denominator.
Simplifying Fractions
Simplifying fractions means making them as simple as possible. We find the greatest common divisor (GCD) of the numerator and the denominator. This number is the highest number that divides both the numerator and denominator without leaving a remainder.

In this exercise, our new fraction was \( \frac{27}{40} \). To simplify, we looked for the GCD of 27 and 40. Since their only common factor is 1, the fraction is already in its simplest form: \( \frac{27}{40} \).

Simplifying makes it easier to understand and work with fractions. Always check if your fraction can be simplified to make your math easier!

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Most popular questions from this chapter

In the following exercises, perform the indicated operations and simplify. $$\frac{4}{11} \div \frac{2}{7 d}$$

In the following exercises, solve the equation. $$ -\frac{2}{3} c=18 $$

In the following exercises, simplify. $$12 \left(\frac{9}{20}-\frac{4}{15}\right)$$

In the following exercises, simplify. $$ \frac{\frac{p}{2}}{\frac{q}{5}} $$

In the following exercises, simplify. $$ \frac{5}{20} $$
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