Question

Find three fractions equivalent to each given fraction. \(\frac{14}{5}\)

Short answer

\[ \frac{28}{10}, \frac{42}{15}, \frac{56}{20} \]

Step-by-step solution

- Understanding Equivalent Fractions

Equivalent fractions represent the same value, even though they have different numerators and denominators. To find equivalent fractions, multiply or divide both the numerator and denominator of the original fraction by the same non-zero number.

- Finding the First Equivalent Fraction

Multiply both the numerator and the denominator of \(\frac{14}{5}\) by 2.\[ \frac{14 \times 2}{5 \times 2} = \frac{28}{10} \]

- Finding the Second Equivalent Fraction

Multiply both the numerator and the denominator of \(\frac{14}{5}\) by 3.\[ \frac{14 \times 3}{5 \times 3} = \frac{42}{15} \]

- Finding the Third Equivalent Fraction

Multiply both the numerator and the denominator of \(\frac{14}{5}\) by 4.\[ \frac{14 \times 4}{5 \times 4} = \frac{56}{20} \]

Key concepts

Numerator and Denominator

To understand fractions, it's essential to first grasp what the numerator and denominator are. In any fraction, the top number is called the numerator. This number represents how many parts we have out of the total number of parts. The bottom number is called the denominator. It tells us into how many equal parts the whole is divided.

For example, in the fraction \(\frac{3}{8}\), 3 is the numerator, indicating that we have 3 parts out of 8 total parts. The denominator, 8, shows that the whole is divided into 8 equal parts.

Knowing the roles of the numerator and denominator can help you understand fractions better and how to work with them.

Multiplication of Fractions

Multiplication of fractions is a crucial concept for finding equivalent fractions. To create an equivalent fraction, multiply both the numerator and the denominator by the same number. This does not change the value of the fraction, just its form. For example, if we have the fraction \(\frac{14}{5}\), and we want to find an equivalent fraction, we can multiply the top (numerator) and bottom (denominator) by the same number.

Let's multiply \(\frac{14}{5}\) by 2:

• Numerator: 14 x 2 = 28
• Denominator: 5 x 2 = 10

This gives us the equivalent fraction \(\frac{28}{10}\). By following the same method, we can multiply by any number to find as many equivalent fractions as we need.

Finding Equivalent Fractions

Finding equivalent fractions involves multiplying or dividing the numerator and the denominator by the same number. For example, to find three equivalents for \(\frac{14}{5}\), we can follow these steps:

• First, multiply by 2: \(\frac{14 \times 2}{5 \times 2} = \frac{28}{10}\).
• Next, multiply by 3: \(\frac{14 \times 3}{5 \times 3} = \frac{42}{15}\).
• Finally, multiply by 4: \(\frac{14 \times 4}{5 \times 4} = \frac{56}{20}\).

Each fraction we get (\(\frac{28}{10}\), \(\frac{42}{15}\), and \(\frac{56}{20}\)) is equivalent to the original fraction \(\frac{14}{5}\). They all represent the same value but look different. This method makes it easy to find as many equivalent fractions as you need.