Problem 441 Subtract. $$ \frac{5 y}{8}-\... [FREE SOLUTION]

Chapter 1: Problem 441

Subtract. $$ \frac{5 y}{8}-\frac{7}{8} $$

Short Answer

Expert verified

\[ \frac{5y - 7}{8} \]

Step by step solution

Common Denominator Check

Identify the denominators in the given fractions: $ \frac{5y}{8} $ and $ \frac{7}{8} $. Both denominators are 8, so they are the same.

Subtract the Numerators

Since the denominators are the same, subtract the numerators: $ 5y - 7 $. Therefore, the subtraction problem becomes: \[ \frac{5y - 7}{8} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Common Denominator

When you subtract fractions, the first step is to make sure they have a common denominator. This means the bottom numbers of both fractions must be the same. If they are already the same, like in our example with $ \frac{5y}{8} $ and $ \frac{7}{8} $, then you can proceed to the next step directly. Having a common denominator allows us to directly subtract the numerators. Otherwise, you'll need to find a common denominator by determining the least common multiple (LCM) of the different denominators.

Fraction Simplification

Simplifying fractions means making the fraction as simple as possible. This can involve reducing the numerator and the denominator to their smallest possible values. In the given exercise $ \frac{5y - 7}{8} $, our already calculated fraction doesn't need further simplification since the numerator and the denominator are as simple as they can get. However, always remember to check for common factors between the numerator and the denominator to simplify your fraction. For instance, if you had something like $ \frac{10}{20} $, you would simplify it to $ \frac{1}{2} $ by dividing both the numerator and the denominator by their greatest common divisor, which is 10 in this case.

Algebraic Subtraction

Algebraic subtraction involves subtracting polynomials or algebraic expressions. In our exercise, an algebraic term $5y$ and a constant $7$ are subtracted. Before the subtraction in algebra, ensure that the terms you are subtracting are like terms (they have the same variables raised to the same power). If you have $ \frac{5y}{8} $ and $ \frac{7}{8} $, these fractions have a common denominator of 8, so we only need to subtract the numerators. The subtraction is performed as follows: $ 5y - 7 $. Now, the new numerator is placed over the original common denominator, giving us $ \frac{5y - 7}{8} $. Always ensure your final expression is in its simplest form.

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91影视

Subtract. $$ \frac{5 y}{8}-\frac{7}{8} $$

Short Answer

Step by step solution

Common Denominator Check

Subtract the Numerators

Key Concepts

Common Denominator

Fraction Simplification

Algebraic Subtraction

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