aspifsGak5u

2021-12-26

To solve:
The proportion $\frac{y}{10}=\frac{13}{4}$.

godsrvnt0706

Approach:
The quotient of two numbers is called a ratio.
Ex. $\frac{2}{3}$.
The ratio is no different from a fraction, except that a ratio is sometimes written using notation other than fractional notation.
Ex. The ratio of 5 to 7 can be written as fractional notation $\frac{5}{7}$ or colon notation $5:7$.
If a ratio contains decimal numbers or mixed numbers, then the ratio can be written only by the ratio of whole numbers.
Ex. $5.7:3$ can be written as $\frac{57}{30}$.
A proportion is a statement that two ratios or rates are equal.
Ex. If are two ratios, then $\frac{a}{b}=\frac{c}{d}$ is a proportion.
If the cross product are equal, the proportion is true.
Ex. If $a\cdot d=b\cdot c$, then it is true.
If the cross products are not equal, the proportion is false.
Ex. If $a\cdot d\ne b\cdot c$, then it is false.
When one number of proportion is unknown, then use cross product to find the unknown number.
Ex. Find the unknown number x in the proportion $\frac{4}{2}=\frac{20}{x}$. It can be found by cross product. That is, $x=10$.
Calculation:
Determine the value of y in the proportion $\frac{y}{10}=\frac{13}{4}$ by using the cross product.
$\frac{y}{10}=\frac{13}{4}$
$y\cdot 4=13\cdot 10$
$y=\frac{130}{4}$
$y=32.5$
Therefore, the value is $y=32.5$.
The final Statement:
The value of y in the proportion

Jordan Mitchell

Step 1
$\frac{y}{10}=\frac{13}{4}$
Multiply both sides by 10
$y=\frac{13}{4}×10$
Express $\frac{13}{4}×10$ as a single fraction
$y=\frac{12×10}{4}$
Multiply 13 and 10 to get 130
$y=\frac{130}{4}$
Reduce the fraction $\frac{130}{4}$ to lowest terms by extracting and canceling out 2.
$y=\frac{65}{2}$

karton

$\begin{array}{}\text{Step 1}\\ \text{Cross Multiplication}\\ \text{the equation}\\ \frac{y}{10}=\frac{13}{4}\\ \text{Cross product:}\\ y×4=10×13\\ \text{Solving:}\\ y=\frac{10×13}{4}\\ \text{reducing:}\\ y=32.5\\ \text{Step 2}\\ \text{The proportion}\\ 10÷4=2.5\\ \text{Then:}\\ y÷13=2.5\\ \text{Solving}\\ y=13×2.5\\ y=32.5\end{array}$