Which expression is equal to 7/8?

Understand the Problem

The question is asking for equivalent expressions or fractions that can represent the value of 7/8. This may involve understanding fractions and their equivalents.

Answer

The equivalent fractions for $\frac{7}{8}$ are $\frac{14}{16}$, $\frac{21}{24}$, and $\frac{28}{32}$.

Steps to Solve

Identify Equivalent Fractions

To find equivalent fractions for $\frac{7}{8}$, we can multiply both the numerator (7) and the denominator (8) by the same non-zero integer.

Calculate Multiples of the Fraction

Let's choose a few integers to multiply by, such as 2, 3, and 4.

For multiplying by 2: $$ \frac{7 \times 2}{8 \times 2} = \frac{14}{16} $$

For multiplying by 3: $$ \frac{7 \times 3}{8 \times 3} = \frac{21}{24} $$

For multiplying by 4: $$ \frac{7 \times 4}{8 \times 4} = \frac{28}{32} $$

List Out the Equivalent Fractions

Now we can list the equivalent fractions we found:

$\frac{14}{16}$
$\frac{21}{24}$
$\frac{28}{32}$

Check the Equivalency

Finally, we can verify that each of the fractions listed above is equivalent to $\frac{7}{8}$ by simplifying them back to their lowest terms or cross-multiplying.

For example, for $\frac{14}{16}$: $$ 7 \times 16 = 112 $$ $$ 14 \times 8 = 112 $$ Since both products are equal, $\frac{14}{16}$ is indeed equivalent to $\frac{7}{8}$.

The equivalent fractions for $\frac{7}{8}$ include:

$\frac{14}{16}$
$\frac{21}{24}$
$\frac{28}{32}$

More Information

Equivalent fractions are fractions that represent the same value. Understanding how to create them by multiplying the numerator and denominator can help simplify and compare fractions in various mathematical situations.

Tips

Forgetting to use the same integer: When creating equivalent fractions, it's crucial to multiply both the numerator and the denominator by the same number to maintain the value.
Miscalculating products: Double-check multiplication to ensure that the equivalent fractions produced are correct.

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