Decoding Ratios: Solve the Equation for 2x : (7y : 4x)

Question

$2x:(7y:4x)=\text{?}$

00:00 Solve

00:03 Let's write division as a fraction

00:09 Division is also multiplication by the reciprocal

00:14 Make sure to multiply numerator by numerator and denominator by denominator

00:19 Convert from fraction to whole number and remainder

00:23 And this is the solution to the question

To solve this problem, we'll simplify the expression $2x : (7y : 4x)$ using properties of division:

Step 1: Recognize $a : (b : c) = a \times \frac{c}{b}$ . This changes the nested division into a singular operation.
Step 2: Substitute into our expression: $2x : (7y : 4x) = 2x \times \frac{4x}{7y}$ .
Step 3: Simplify the expression $= 2 \times \frac{4x^2}{7y}$ .
Step 4: Calculate the product: $= \frac{8x^2}{7y}$ .
Step 5: Convert to a mixed number if necessary: $= 1\frac{1}{7}\frac{x^2}{y}$ .

Therefore, the solution to the problem is $\frac{8x^2}{7y}$ , which can be expressed as a mixed number $1\frac{1}{7}\frac{x^2}{y}$ .

$1\frac{1}{7}\frac{x^2}{y}$