If Five Sevenths of a Number is 15 What is the number?
If five sevenths of a number is 15, we can solve for the number by setting up the equation:
(5/7) * x = 15
To find x, we multiply both sides by the reciprocal of (5/7), which is (7/5):
x = 15 * (7/5)
x = 21
So, the number is 21.
Solving Problems Involving Fractions of a Number
Word problems commonly involve determining an unknown original number based on a clue involving a fractional amount of that number. For example, if you know 5/7 of a number is 15, you can algebraically determine the full number. Let’s look at the step-by-step process.
Understand the Relationship
The first step is to analyze what we know:
- 5/7 of the number is 15
- We want to find the original number
So we’re looking for the number that gives 15 when 5/7 of it is taken.
Set Up an Equation with a Variable
Using a variable like x to represent the unknown number, we can express the relationship mathematically:
(5/7)x = 15
The fraction 5/7 multiplied by x gives the fractional amount 15.
Isolate the Variable
To isolate x, we multiply both sides by 7/
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