One number is 3/8 of another number

General
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one number is 3/8 of another number

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LectureNotes said one number is ( \frac{3}{8} ) of another number.

Understanding Fractional Relationships:

When we say that one number is (\frac{3}{8}) of another number, we are expressing a proportional relationship between two quantities. This statement can be translated into an equation for clarity and ease of calculation.

Mathematical Representation:

Let’s denote the larger number by ( y ) and the smaller number by ( x ). According to the given relationship, ( x ) is (\frac{3}{8}) of ( y ). This relationship can be written as:

x = \frac{3}{8} y

Example Calculation:

Let’s consider a practical example to illustrate this concept. Say we know the value of ( y ) and we need to find ( x ).

Example 1:

Suppose ( y = 80 ). To find ( x ):

x = \frac{3}{8} \times 80

Perform the multiplication:

x = 30

Therefore, ( x = 30 ) when ( y = 80 ).

Example 2:

If ( x = 18 ), we can also find ( y ) by rearranging the equation:

x = \frac{3}{8} y \\ 18 = \frac{3}{8} y

To solve for ( y ), multiply both sides by the reciprocal of (\frac{3}{8}), which is (\frac{8}{3}):

y = 18 \times \frac{8}{3} \\ y = 48

Therefore, ( y = 48 ) when ( x = 18 ).

General Approach:

  1. If given ( y ), multiply by (\frac{3}{8}) to find ( x ):
x = \frac{3}{8} y
  1. If given ( x ) and need to find ( y ), divide ( x ) by (\frac{3}{8}) or multiply by its reciprocal:
y = x \times \frac{8}{3}

Conceptual Insight:

Understanding the relationship between numbers and their fractions is crucial for various applications in mathematics, such as solving algebraic equations, analyzing proportions in statistics, and working with ratios in real-world scenarios.

By breaking down the process this way, students can better grasp how to work with fractional relationships and apply them in different contexts.