Solve for b 5/6b=1 7/8

Solution:

Step 1: Simplify the equation's left-hand side.

• Combine the fraction $\frac{5}{6}$ with the variable $b$ to get $\frac{5b}{6} = 1 \frac{7}{8}$.

Step 2: Convert the mixed number on the right-hand side to an improper fraction.

• Recognize that a mixed number is the sum of its integer and fractional parts: $\frac{5b}{6} = 1 + \frac{7}{8}$.

• Express the integer 1 as a fraction with a denominator of 8: $\frac{5b}{6} = \frac{8}{8} + \frac{7}{8}$.

• Add the fractions by combining the numerators: $\frac{5b}{6} = \frac{8 + 7}{8}$.

• Perform the addition to get $\frac{5b}{6} = \frac{15}{8}$.

Step 3: Eliminate the fraction on the left-hand side by multiplying both sides by $\frac{6}{5}$.

• Multiply the equation by $\frac{6}{5}$ to get $\frac{6}{5} \cdot \frac{5b}{6} = \frac{6}{5} \cdot \frac{15}{8}$.

Step 4: Simplify both sides of the equation.

• On the left side, cancel the 6 in the numerator with the 6 in the denominator: $\frac{\cancel{6}}{5} \cdot \frac{5b}{\cancel{6}} = b$.

• On the right side, simplify the multiplication: $\frac{6}{5} \cdot \frac{15}{8}$.

• Cancel any common factors: $\frac{3}{5} \cdot \frac{15}{4}$.

• Multiply the fractions to find the value of $b$: $b = \frac{9}{4}$.

Step 5: Present the solution in various forms.

• Exact form: $b = \frac{9}{4}$
• Decimal form: $b = 2.25$
• Mixed number form: $b = 2 \frac{1}{4}$

Knowledge Notes:

To solve the equation $\frac{5}{6}b = 1 \frac{7}{8}$, we follow these steps:

1. Combining Fractions and Variables: When a fraction is multiplied by a variable, it is written as the numerator times the variable over the denominator.

2. Converting Mixed Numbers to Improper Fractions: A mixed number is converted to an improper fraction by multiplying the whole number by the denominator of the fractional part, adding the numerator, and placing the result over the original denominator.

3. Simplifying Equations: To isolate the variable, we can multiply both sides of the equation by the reciprocal of the coefficient of the variable.

4. Canceling Common Factors: When a common factor appears in both the numerator and the denominator, it can be canceled out to simplify the expression.

5. Multiplying Fractions: To multiply fractions, multiply the numerators together and the denominators together. If possible, simplify the result by canceling out any common factors before multiplying.

6. Presenting Results in Different Forms: The solution to an equation can be expressed in exact form (as a fraction), decimal form, or as a mixed number, depending on the context or preference.