0:00
Simplifying and Equivalent Fractions
Select the skills to practice, and then click Go!
Foundational skills
List factors of a number
\[ \text{Factors of } 12 \]
List all the factors of a given number.
Identify common factors of two numbers
\[ \text{Common: } 12 \text{ and } 18 \]
Find all factors that two numbers share.
Find the HCF when one number is a multiple of the other
\[ \text{HCF}(6, 18) \]
HCF where one divides into the other.
Find the HCF when numbers are coprime
\[ \text{HCF}(8, 15) \]
HCF of numbers with no common factors.
Find the HCF when numbers share a common factor
\[ \text{HCF}(12, 18) \]
HCF of numbers sharing common factors.
Identify if a fraction is in simplest form
\[ \text{Is } \frac{3}{8} \text{ simplest?} \]
Decide if a fraction is fully simplified.
Identify the common factor to simplify by
\[ 8 \text{ and } 12 \div \text{?} \]
Find a common factor to simplify with.
Recognising equivalent fractions
Recognise if two fractions are equivalent
\[ \frac{2}{3} = \frac{8}{12} \text{?} \]
Decide if two fractions are equivalent.
Match equivalent fractions
\[ \frac{3}{4} = \text{which?} \]
Select equivalent from a list.
Find the scale factor between equivalent fractions
\[ \frac{2}{5} = \frac{6}{15}, \; \times\text{?} \]
Find the multiplier between fractions.
Creating equivalent fractions
Create equivalent fraction — given scale factor
\[ \frac{2}{5} = \frac{?}{15} \]
Create equivalent with target denominator.
Find missing numerator
\[ \frac{3}{4} = \frac{?}{12} \]
Find the missing numerator.
Find missing denominator
\[ \frac{2}{3} = \frac{8}{?} \]
Find the missing denominator.
Write a fraction in higher terms
\[ \frac{3}{5} \to \text{den } 20 \]
Rewrite with a larger denominator.
Find equivalent fraction with given numerator
\[ \frac{4}{5} = \frac{12}{?} \]
Scale to achieve target numerator.
Simplifying proper fractions
Simplify by dividing by 2 or 3 or 4 or 5
\[ \frac{6}{9} \to \frac{2}{3} \]
Simplify where HCF is 2, 3, 4, or 5.
Simplify by dividing by 6 or 7 or 8 or 9 or 12
\[ \frac{24}{36} \to \frac{2}{3} \]
Simplify where HCF is 6, 7, 8, 9, or 12.
Simplifying fractions — to integers
Simplify to a whole number
\[ \frac{12}{4} = 3 \]
Simplify where numerator is a multiple of denominator.
Recognise when a fraction equals a whole number
\[ \frac{15}{5} = \text{whole?} \]
Identify if fraction equals whole number.
Simplifying improper fractions
Simplify an improper fraction — result improper
\[ \frac{14}{6} \to \frac{7}{3} \]
Simplify improper, stays improper.
Simplify an improper fraction — result whole number
\[ \frac{18}{6} = 3 \]
Simplify improper to whole number.
Simplify and convert to mixed number
\[ \frac{20}{8} = 2\frac{1}{2} \]
Simplify and convert to mixed number.
Simplifying mixed numbers
Simplify the fractional part of a mixed number
\[ 3\frac{4}{6} = 3\frac{2}{3} \]
Simplify fractional part only.
Simplify fractional part — requires regrouping
\[ 3\frac{6}{4} = 4\frac{1}{2} \]
Simplify with regrouping required.
Special cases
Fraction already in simplest form
\[ \frac{5}{8} = \frac{5}{8} \]
Recognise already simplified fractions.
Unit fraction simplification
\[ \frac{1}{4} = \frac{1}{4} \]
Unit fractions are always simplest.
Simplify where numerator equals denominator
\[ \frac{8}{8} = 1 \]
Simplify when num = den.
Simplify to a unit fraction
\[ \frac{5}{15} = \frac{1}{3} \]
Simplify to unit fraction.
Express a decimal as a simplified fraction
\[ 0.6 = \frac{3}{5} \]
Convert decimal to simplified fraction.
Timer (Optional)
0:00
Question