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Chapter 1: Problem 93

Determine whether the given number is a solution of the equation. $$w-\frac{2}{3}=\frac{3}{4} ; 1 \frac{5}{12}$$

Short Answer

Expert verified
Yes, 1 5/12 is a solution to the given equation.

Step by step solution

01

Convert the Mixed Number

Convert the given mixed number 1 5/12 into an improper fraction or decimal number. An improper fraction is created by multiplying the denominator by the whole number and then adding the numerator. Here, (12*1) + 5 = 17, so the improper fraction is 17/12.
02

Substitute into the Equation

Now substitute the improper fraction for the variable 'w' in the equation. Therefore, the equation becomes 17/12 - 2/3 = 3/4. In order to perform the subtraction, first convert all fractions to have the common denominator, which is 12 in our case.
03

Simplify the Equation

After converting into fractions with common denominator, the equation becomes 17/12 - 8/12 = 9/12. By simplifying the left side, we get 9/12 = 9/12.
04

Verifying the Equality

The left and right sides are now both equal to 9/12, so the equation is balanced. Therefore, the given mixed number is indeed a solution to the equation.

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