4
13

=
4×10
13×10

=
40
130

53
8
=
53
×
5
8
×
5
=
265
40
8
53

=
8×5
53×5

=
40
265

7
5
=
7
×
8
5
×
8
=
56
40
5
7

=
5×8
7×8

=
40
56

How did you get the 53 × 5 and 7×8

The expressions \( 53 \times 5 \) and \( 7 \times 8 \) come from cross-multiplying to compare two fractions. Let's break this down.

When you compare two fractions, for example:

\[
\frac{a}{b} = \frac{c}{d}
\]

You can cross-multiply to verify the equality:

\[
a \times d = b \times c
\]

Now, let’s apply this to your example.

### Example 1: 
Given the fraction \(\frac{53}{8}\), to compare it with \(\frac{8}{53}\), you would:

1. Cross-multiply the numerators and denominators:
   - Multiply the numerator of the first fraction by the denominator of the second fraction: \(53 \times 5\).
   - Multiply the denominator of the first fraction by the numerator of the second fraction: \(8 \times 5\).

So, you get \(53 \times 5\) and \(8 \times 5\).

### Example 2:
Similarly, for the fraction \(\frac{7}{5}\) compared to \(\frac{5}{7}\):

1. Cross-multiply the numerators and denominators:
   - Multiply the numerator of the first fraction by the denominator of the second fraction: \(7 \times 8\).
   - Multiply the denominator of the first fraction by the numerator of the second fraction: \(5 \times 8\).

So, you get \(7 \times 8\) and \(5 \times 8\).

In both cases, the multiplication arises because you're checking if the two fractions are equivalent or simplifying them by ensuring their products match.

---

Would you like a more detailed explanation or have any questions?

Here are some related questions:
1. What does it mean to cross-multiply in fraction comparisons?
2. How can you simplify fractions after cross-multiplying?
3. What are other methods to compare fractions?
4. How can you use cross-multiplication to solve proportion problems?
5. What role does cross-multiplication play in solving equations with fractions?

**Tip:** Cross-multiplication is a powerful tool for comparing fractions, but remember it’s only valid when equating or comparing two fractions directly.

Explore how to compare fractions using cross-multiplication with detailed examples. Learn why cross-multiplying helps verify or simplify fractions, illustrated with examples like 53 × 5 and 7 × 8. Suitable for high school students studying algebra and fraction operations.

Math Problem Statement

53 8

53 × 5 8 × 5

7 5

7 × 8 5 × 8

Solution

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