Question

use these numbers to form another facts.

1. (5) \\(\frac{2 cdot 3 cdot 2 cdot 5 cdot 2 cdot 5}{2 cdot 5 cdot 2 cdot 5}\\)
2. (42) \\(\frac{5}{6} = \frac{?}{24}\\)
3. (29) represent copy this rectangle

Explanation:

Step1: Simplify the numerator and denominator

$$\begin{align*} \text{Numerator}&=2\times3\times2\times5\times2\times5\\ &=(2\times2\times2)\times(3)\times(5\times5)\\ &=8\times3\times25\\ & = 600 \end{align*}$$

$$\begin{align*} \text{Denominator}&=2\times5\times2\times5\\ &=(2\times2)\times(5\times5)\\ &=4\times25\\ &=100 \end{align*}$$

Step2: Calculate the fraction

$$\frac{600}{100} = 6$$

Step3: Solve $\frac{5}{6}=\frac{?}{24}$

Let the unknown number be \(x\). Using the property of equivalent fractions \(\frac{a}{b}=\frac{c}{d}\Rightarrow ad = bc\). Here \(a = 5\), \(b=6\), \(c=x\), \(d = 24\). So \(6x=5\times24\).
First, calculate \(5\times24=120\). Then \(x=\frac{120}{6}\).
Since \(120\div6 = 20\), \(x = 20\).

Answer:

For problem 24: \(6\); For problem 25: \(20\)