Types of Fractions and Equivalent Fractions

In short: A proper fraction is less than 1, an improper fraction is 1 or more, and a mixed number has a whole part and a fraction part, like $2 \frac{1}{3}$ . Equivalent fractions are equal fractions, made by multiplying or dividing the top and bottom by the same number.

Before you start

A fraction has a numerator (top: how many parts you have) and a denominator (bottom: how many equal parts make a whole).
Times tables and division with remainders, like $13 \div 4 = 3$ remainder 1.
Factors of a number divide it exactly. Factors of 12: 1, 2, 3, 4, 6, 12.

Three types of fraction

Seven quarters make one whole and three quarters more.

Type	What it means	Examples
Proper fraction	top is smaller than bottom, so less than 1	$\frac{2}{5}$ , $\frac{3}{10}$ , $\frac{1}{7}$
Improper fraction	top is bigger than (or equal to) bottom, so 1 or more	$\frac{13}{10}$ , $\frac{7}{4}$ , $\frac{29}{12}$
Mixed number	a whole number and a proper fraction	$1 \frac{1}{3}$ , $2 \frac{7}{8}$ , $6 \frac{1}{10}$

Improper fraction to mixed number

Mixed number to improper fraction

Equivalent fractions

Equivalent fractions look different but have the same value.

$\frac{2}{5} = \frac{4}{10} = \frac{8}{20}$

Lowest terms

A fraction is in lowest terms (or simplest form) when no number except 1 divides both the top and bottom.

To simplify, divide top and bottom by their highest common factor (HCF), the biggest number that divides both.

Fractions

Types

Proper: top smaller
Improper: top bigger
Mixed: whole + fraction

Improper to mixed

Divide top by bottom
Remainder over bottom

Mixed to improper

Whole x bottom + top

Equivalent

Same to top and bottom
$\frac{2}{5} = \frac{8}{20}$

Lowest terms

Divide by the HCF

Quick summary

Proper fractions are less than 1. Improper fractions are 1 or more. Mixed numbers have a whole part and a fraction part.
Improper to mixed: divide top by bottom, and the remainder goes over the bottom.
Mixed to improper: whole times bottom, plus top, over the bottom.
Equivalent fractions: multiply or divide top and bottom by the same number.
Lowest terms: divide top and bottom by their highest common factor.

Quiz

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Try 3 questions now

Which is an improper fraction?
1. A $\frac{3}{10}$
2. B $\frac{13}{10}$
3. C $1 \frac{3}{10}$
4. D $\frac{1}{7}$
Show answer
B: $\frac{13}{10}$
The top (13) is bigger than the bottom (10).
$\frac{13}{4} =$
1. A $3 \frac{1}{4}$
2. B $4 \frac{1}{3}$
3. C $3 \frac{3}{4}$
4. D $13 \frac{1}{4}$
Show answer
A: $3 \frac{1}{4}$
$13 \div 4 = 3$ remainder 1.
$2 \frac{3}{5} =$
1. A $\frac{6}{5}$
2. B $\frac{23}{5}$
3. C $\frac{13}{5}$
4. D $\frac{11}{5}$
Show answer
C: $\frac{13}{5}$
$2 \times 5 + 3 = 13$ , so $\frac{13}{5}$ .

Types of Fractions and Equivalent Fractions

Before you start

Three types of fraction

Improper fraction to mixed number

Mixed number to improper fraction

Equivalent fractions

Lowest terms

Quick summary

Quiz

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