Find y. 1 1/2 y = 2 3/4

Convert to Improper Fractions: First, we need to convert the mixed numbers to improper fractions to make the calculation easier. 1 1/2 is the same as 3/2 because 1 1/2 = 1 + 1/2 = 2/2 + 1/2 = 3/2. 2 3/4 is the same as 11/4 because 2 3/4 = 2 + 3/4 = 8/4 + 3/4 = 11/4. Now we can rewrite the equation as (3/2)y = 11/4.Isolate and Solve for y: Next, we need to isolate y by dividing both sides of the equation by 3/2. To divide by a fraction, we multiply by its reciprocal. The reciprocal of 3/2 is 2/3. So we multiply both sides of the equation by 2/3 to find y. y = (11/4) * (2/3)Perform Multiplication: Now we perform the multiplication of the two fractions. y = (11 * 2) / (4 * 3) y = 22 / 12Simplify Fraction: We can simplify the fraction 22/12 by dividing both the numerator and the denominator by their greatest common divisor, which is 2. y = (22 ÷ 2) / (12 ÷ 2) y = 11 / 6Convert to Mixed Number: Finally, we can convert the improper fraction back to a mixed number if necessary. 11/6 is the same as 1 5/6 because 11/6 = 6/6 + 5/6 = 1 + 5/6. So, y = 1 5/6.

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Find $y$ . $\frac{3}{2}y = \frac{11}{4}$

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Grade 7

Add and subtract fractions

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Q. Find

y

\frac{3}{2}y = \frac{11}{4}

Convert to Improper Fractions: First, we need to convert the mixed numbers to improper fractions to make the calculation easier. $\newline$ $1\frac{1}{2}$ is the same as $\frac{3}{2}$ because $1\frac{1}{2} = 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2}$ . $\newline$ $2\frac{3}{4}$ is the same as $\frac{11}{4}$ because $2\frac{3}{4} = 2 + \frac{3}{4} = \frac{8}{4} + \frac{3}{4} = \frac{11}{4}$ . $\newline$ Now we can rewrite the equation as $(\frac{3}{2})y = \frac{11}{4}$ .
Isolate and Solve for y: Next, we need to isolate $y$ by dividing both sides of the equation by $\frac{3}{2}$ . To divide by a fraction, we multiply by its reciprocal. $\newline$ The reciprocal of $\frac{3}{2}$ is $\frac{2}{3}$ . $\newline$ So we multiply both sides of the equation by $\frac{2}{3}$ to find $y$ . $\newline$ $y = \left(\frac{11}{4}\right) * \left(\frac{2}{3}\right)$
Perform Multiplication: Now we perform the multiplication of the two fractions. $\newline$ $y = \frac{11 \times 2}{4 \times 3}$ $\newline$ $y = \frac{22}{12}$
Simplify Fraction: We can simplify the fraction $\frac{22}{12}$ by dividing both the numerator and the denominator by their greatest common divisor, which is $2$ . $\newline$ $y = \left(\frac{22 \div 2}{12 \div 2}\right)$ $\newline$ $y = \frac{11}{6}$
Convert to Mixed Number: Finally, we can convert the improper fraction back to a mixed number if necessary. $\newline$ $\frac{11}{6}$ is the same as $1 \frac{5}{6}$ because $\frac{11}{6} = \frac{6}{6} + \frac{5}{6} = 1 + \frac{5}{6}$ . $\newline$ So, $y = 1 \frac{5}{6}$ .