Fractions and mixed numbers questions with answers

Questions

1. Question 1Mixed number to improper fraction

   Express $2\dfrac{3}{5}$ as an improper fraction.

   Show the worked solution

   1. Step 1: Whole number × denominator + numerator, over the same denominator$2\dfrac{3}{5}$$= \dfrac{2 \times 5 + 3}{5}$$= \dfrac{13}{5}$
2. Question 2Add and subtract fractions

   Calculate $\dfrac{5}{8} + \dfrac{3}{5}$, giving your answer in its simplest form.

   Show the worked solution

   1. Step 1: Use the LCM of the denominators as the common denominator$\dfrac{5}{8} + \dfrac{3}{5}$$= \dfrac{25}{40} + \dfrac{24}{40}$
   2. Step 2: Add or subtract the numerators (the denominator stays the same)$= \dfrac{49}{40}$$= 1\dfrac{9}{40}$
3. Question 3Add and subtract mixed numbers

   Calculate $2\dfrac{1}{3} + 2\dfrac{3}{4}$, giving your answer in its simplest form.

   Show the worked solution

   1. Step 1: Change each mixed number to an improper fraction$2\dfrac{1}{3} + 2\dfrac{3}{4}$$= \dfrac{7}{3} + \dfrac{11}{4}$
   2. Step 2: Use the LCM of the denominators as the common denominator$= \dfrac{28}{12} + \dfrac{33}{12}$
   3. Step 3: Add or subtract the numerators (the denominator stays the same)$= \dfrac{61}{12}$$= 5\dfrac{1}{12}$
4. Question 4Multiply fractions and mixed numbers

   Calculate $\dfrac{5}{6} \times 3\dfrac{3}{4}$, giving your answer in its simplest form.

   Show the worked solution

   1. Step 1: Change each mixed number to an improper fraction$\dfrac{5}{6} \times 3\dfrac{3}{4}$$= \dfrac{5}{6} \times \dfrac{15}{4}$
   2. Step 2: Multiply the numerators and multiply the denominators, then simplify$= \dfrac{75}{24}$$= \dfrac{25}{8}$$= 3\dfrac{1}{8}$
5. Question 5Divide fractions and mixed numbers

   Calculate $3\dfrac{2}{3} \div 2\dfrac{2}{3}$, giving your answer in its simplest form.

   Show the worked solution

   1. Step 1: Change each mixed number to an improper fraction$3\dfrac{2}{3} \div 2\dfrac{2}{3}$$= \dfrac{11}{3} \div \dfrac{8}{3}$
   2. Step 2: To divide by a fraction, multiply by its reciprocal (turn it upside down)$= \dfrac{11}{3} \times \dfrac{3}{8}$
   3. Step 3: Multiply the numerators and multiply the denominators, then simplify$= \dfrac{33}{24}$$= \dfrac{11}{8}$$= 1\dfrac{3}{8}$
6. Question 6Fractions of the rest: find the whole

   Nur Aisyah spends $\dfrac{1}{5}$ of her savings on a pair of shoes and $\dfrac{2}{5}$ of the whole on a book. She has $\$20$ left. Find the amount of money she had at first.

   Show the worked solution

   1. Step 1: Both fractions are of the whole: take both away from 1$1 - \dfrac{1}{5} - \dfrac{2}{5} = \dfrac{2}{5}$
   2. Step 2: That fraction of the whole is the amount left: find 1 part, then the whole$\text{Whole} = 20 \div \dfrac{2}{5}$$\phantom{\text{Whole}} = 20 \times \dfrac{5}{2}$$\phantom{\text{Whole}} = 50$She had $\$50$ at first.