8.1 Fractions review

Convert the improper fraction $\dfrac{23}{4}$ to a mixed numeral.

Convert the mixed numeral $3\tfrac{5}{6}$ to an improper fraction.

Simplify the fraction $\dfrac{28}{42}$ to its simplest form.

Write $\dfrac{2}{5}$ as an equivalent fraction with denominator 30.

Calculate $\dfrac{3}{12} + \dfrac{5}{12}$ and simplify if possible.

Calculate $\dfrac{2}{5} + \dfrac{1}{2}$. Give your answer in simplest form.

Calculate $\dfrac{4}{5} \times \dfrac{5}{6}$. Give your answer in simplest form.

Calculate $\dfrac{5}{6} \div \dfrac{5}{12}$. Give your answer in simplest form.

Write 65% as (a) a decimal and (b) a fraction in its simplest form.

Write $\dfrac{7}{20}$ as a decimal and as a percentage.

Calculate $\dfrac{7}{10} - \dfrac{2}{5}$. Give your answer in simplest form.

Calculate $3\tfrac{1}{4} + 2\tfrac{1}{2}$.

Find $\dfrac{2}{3}$ of 450 g.

Calculate $\dfrac{5}{9} \times 27$ where $n$ is a whole number. Give the answer in simplest form.

Calculate $\dfrac{9}{10} \div 6$.

Order from smallest to largest: $\dfrac{2}{3}$, $\dfrac{5}{8}$, $\dfrac{7}{12}$.

Convert the recurring decimal $0.\overline{6}$ to a fraction in its simplest form.

Calculate $\dfrac{3}{4} + \dfrac{1}{6} - \dfrac{1}{12}$.

Write 0.625 as a fraction in its simplest form.

Calculate $3\tfrac{1}{3} \times \dfrac{3}{4}$.

A pizza is cut into 8 equal slices. Tomás eats $\tfrac{3}{8}$, and his sister eats $\tfrac{1}{4}$ of the whole pizza. What fraction of the pizza is left?

A bottle holds 800 ml. Joëlle drinks $\tfrac{2}{5}$ of it on the way to school and $\tfrac{1}{4}$ of the remainder at break. How many ml are left?

Find $25\%$ of $\dfrac{2}{5}$ of 400 chf.

Calculate $\dfrac{3}{5} \div \dfrac{6}{25} + \dfrac{1}{4}$.

In a school survey, $\tfrac{2}{5}$ of the students chose Maths and 30% chose English. The rest chose Science. What fraction chose Science? Give your answer as a fraction in simplest form.

Calculate $6\tfrac{1}{3} - 3\tfrac{5}{6}$.

Order from smallest to largest: 0.6, $\tfrac{5}{8}$, 62%.

A recipe for 8 pancakes uses $\tfrac{3}{4}$ cup of flour. How much flour is needed for 12 pancakes? Give the answer as a mixed numeral if possible.

Calculate $\left(\dfrac{1}{4} + \dfrac{1}{6}\right) \times \dfrac{12}{5}$.

Write 87.5% as a fraction in its simplest form.

Calculate $\dfrac{\tfrac{2}{3} + \tfrac{1}{4}}{\tfrac{5}{6} - \tfrac{1}{3}}$.

A jug is $\tfrac{2}{3}$ full of juice. After pouring out 600 ml, it is $\tfrac{1}{4}$ full. How many ml does the jug hold when full?

Convert the recurring decimal $0.\overline{45}$ to a fraction in its simplest form.

A test has 60 questions. Léa answered $\tfrac{3}{5}$ of them correctly. Of the remainder, $\tfrac{1}{4}$ were left blank and the rest were wrong. How many were wrong?

Show that $0.\overline{9} = 1$ by an algebraic argument.

A pile of marbles is shared among three children. Anna takes $\tfrac{1}{4}$, Ben takes $\tfrac{2}{5}$ of what is left, and Carla takes the remaining 18. How many marbles were in the pile?

Two fractions $\tfrac{a}{b}$ and $\tfrac{c}{d}$ are equivalent if $ad = bc$. Determine whether $\tfrac{12}{18}$ and $\tfrac{20}{30}$ are equivalent, and explain.

Find a fraction $\tfrac{p}{q}$ between $\tfrac{3}{8}$ and $\tfrac{1}{2}$ with a denominator less than 10.

A fraction $\tfrac{n}{n+5}$ simplifies to $\tfrac{3}{4}$. Find $n$.

Show that the sum $1 + \tfrac{1}{2} + \tfrac{1}{4} + \tfrac{1}{8}$ can be written as a single improper fraction, and explain whether the pattern $1 + \tfrac{1}{2} + \tfrac{1}{4} + \ldots + \tfrac{1}{2^n}$ ever reaches 2.