Question

Give two fractions that are equivalent to each given fraction. $$\frac{5}{8}$$

Short answer

Two fractions equivalent to \( \frac{5}{8} \) are \( \frac{10}{16} \) and \( \frac{15}{24} \).

Step-by-step solution

- Understand Equivalent Fractions

Equivalent fractions are different fractions that represent the same part of a whole. To find equivalent fractions, multiply both the numerator (top number) and the denominator (bottom number) of the given fraction by the same non-zero number.

- Choose a Number to Multiply

Choose a number to multiply both the numerator and the denominator of the fraction \( \frac{5}{8} \). For simplicity, let’s start with 2.

- Calculate the First Equivalent Fraction

Multiply the numerator and the denominator of \( \frac{5}{8} \) by 2: \[ \frac{5 \times 2}{8 \times 2} = \frac{10}{16} \] So, \( \frac{10}{16} \) is an equivalent fraction to \( \frac{5}{8} \).

- Choose Another Number to Multiply

Choose another number to multiply both the numerator and the denominator of the fraction \( \frac{5}{8} \). This time, let’s use 3.

- Calculate the Second Equivalent Fraction

Multiply the numerator and the denominator of \( \frac{5}{8} \) by 3: \[ \frac{5 \times 3}{8 \times 3} = \frac{15}{24} \] So, \( \frac{15}{24} \) is another equivalent fraction to \( \frac{5}{8} \).

Key concepts

fractions

A fraction represents a part of a whole. It's composed of two parts: the numerator and the denominator. The numerator is the top number and indicates how many parts we have. The denominator is the bottom number and shows the total number of parts the whole is divided into. For instance, in the fraction \(\frac{5}{8}\), 5 is the numerator, and 8 is the denominator. Fractions are essential in math as they help us describe quantities that aren't whole numbers. They are used in everyday situations like cooking, measuring, and splitting items fairly. Equivalent fractions are different fractions that represent the same value. For example, \(\frac{5}{8}\) is equivalent to both \(\frac{10}{16}\) and \(\frac{15}{24}\).

numerator and denominator

Understanding the numerator and denominator is crucial for working with fractions. As mentioned, the numerator is the top number. It tells you how many parts of the whole you are dealing with. The denominator is the bottom number, and it tells you into how many equal parts the whole is divided. So, in \(\frac{5}{8}\), the whole is divided into 8 parts, and we are considering 5 of those parts. When creating equivalent fractions, you multiply both the numerator and the denominator by the same number. This process doesn't change the overall value of the fraction. For example:

• Multiplying \(\frac{5}{8}\) by 2 gives \(\frac{10}{16}\)
• Multiplying \(\frac{5}{8}\) by 3 gives \(\frac{15}{24}\)

Both new fractions have the same value as \(\frac{5}{8}\).

multiplication in fractions

Multiplication in fractions is straightforward when creating equivalent fractions. You simply multiply the numerator and the denominator by the same non-zero number. This keeps the ratio the same, and the fractions remain equivalent. Let's look at \(\frac{5}{8}\) again.

If we multiply the numerator and the denominator by 2, we get: \(\frac{5 \times 2}{8 \times 2} = \frac{10}{16}\).

This means \(\frac{10}{16}\) has the same value as \(\frac{5}{8}\). To find another equivalent fraction, we multiply by 3: \(\frac{5 \times 3}{8 \times 3} = \frac{15}{24}\).

• Step-by-step, it's important to keep the fraction balanced by multiplying both numbers equally.
• This principle is vital for accurately working with and comparing fractions in various mathematical scenarios.