Expressions with fractions questions with answers

Questions

1. Question 1Letters over numbers

   Express $\dfrac{3x}{2} - \dfrac{x}{5}$ as a single fraction in its simplest form.

   Show the worked solution

   1. Step 1: Find the LCM of the denominators$\text{LCM of } 2 \text{ and } 5 =$ $10$
   2. Step 2: Write each fraction over the LCM (multiply its top and bottom by the same number)$\dfrac{3x}{2} - \dfrac{x}{5} = \dfrac{15x}{10} - \dfrac{2x}{10}$
   3. Step 3: Add or subtract the tops$= \dfrac{13x}{10}$
2. Question 2Letters over numbers

   Express $\dfrac{4x}{3} - \dfrac{x}{2}$ as a single fraction in its simplest form.

   Show the worked solution

   1. Step 1: Find the LCM of the denominators$\text{LCM of } 3 \text{ and } 2 =$ $6$
   2. Step 2: Write each fraction over the LCM (multiply its top and bottom by the same number)$\dfrac{4x}{3} - \dfrac{x}{2} = \dfrac{8x}{6} - \dfrac{3x}{6}$
   3. Step 3: Add or subtract the tops$= \dfrac{5x}{6}$
3. Question 3Adding fractions with two terms on top

   Express $\dfrac{4x + 6}{5} + \dfrac{4x - 3}{3}$ as a single fraction in its simplest form.

   Show the worked solution

   1. Step 1: Find the LCM of the denominators$\text{LCM of } 5 \text{ and } 3 =$ $15$
   2. Step 2: Write each fraction over the LCM (multiply its top and bottom by the same number)$\dfrac{4x + 6}{5} + \dfrac{4x - 3}{3} = \dfrac{3(4x + 6) + 5(4x - 3)}{15}$
   3. Step 3: Expand the tops$= \dfrac{12x + 18 + 20x - 15}{15}$
   4. Step 4: Collect like terms$= \dfrac{32x + 3}{15}$
4. Question 4Adding fractions with two terms on top

   Express $\dfrac{2x + 5}{4} + \dfrac{x - 3}{6}$ as a single fraction in its simplest form.

   Show the worked solution

   1. Step 1: Find the LCM of the denominators$\text{LCM of } 4 \text{ and } 6 =$ $12$
   2. Step 2: Write each fraction over the LCM (multiply its top and bottom by the same number)$\dfrac{2x + 5}{4} + \dfrac{x - 3}{6} = \dfrac{3(2x + 5) + 2(x - 3)}{12}$
   3. Step 3: Expand the tops$= \dfrac{6x + 15 + 2x - 6}{12}$
   4. Step 4: Collect like terms$= \dfrac{8x + 9}{12}$
5. Question 5Subtracting a fraction

   Express $\dfrac{4x - 4}{3} - \dfrac{2x - 5}{4}$ as a single fraction in its simplest form.

   Show the worked solution

   1. Step 1: Find the LCM of the denominators$\text{LCM of } 3 \text{ and } 4 =$ $12$
   2. Step 2: Write each fraction over the LCM (multiply its top and bottom by the same number)$\dfrac{4x - 4}{3} - \dfrac{2x - 5}{4} = \dfrac{4(4x - 4) - 3(2x - 5)}{12}$
   3. Step 3: Expand the tops (the minus reaches every term of the second top)$= \dfrac{16x - 16 - 6x + 15}{12}$
   4. Step 4: Collect like terms$= \dfrac{10x - 1}{12}$
6. Question 6Subtracting a fraction

   Express $\dfrac{4x - 3}{4} - \dfrac{x + 2}{3}$ as a single fraction in its simplest form.

   Show the worked solution

   1. Step 1: Find the LCM of the denominators$\text{LCM of } 4 \text{ and } 3 =$ $12$
   2. Step 2: Write each fraction over the LCM (multiply its top and bottom by the same number)$\dfrac{4x - 3}{4} - \dfrac{x + 2}{3} = \dfrac{3(4x - 3) - 4(x + 2)}{12}$
   3. Step 3: Expand the tops (the minus reaches every term of the second top)$= \dfrac{12x - 9 - 4x - 8}{12}$
   4. Step 4: Collect like terms$= \dfrac{8x - 17}{12}$