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Glacius
FoundationsConcept reference

Fractions

A fraction denotes its numerator divided by its nonzero denominator.

1 min read1 figureSources & further reading
On this page 8 sections
  1. Overview
  2. A fraction is one number written as a quotient
  3. Check your understanding
  4. Check your understanding
  5. Key takeaway
  6. Further questions
  7. Sources & further reading
  8. Concept connections

01A fraction is one number written as a quotient#

A fraction is one number written as a quotient. In 34\dfrac{3}{4}, the numerator 33 is divided by the denominator 44. One whole split into four equal pieces has three of those pieces selected.

One whole is divided into four equal parts, with three selected: three quarters.One whole is divided into four equal parts, with three selected: three quarters.
Figure 1One whole is divided into four equal parts, with three selected: three quarters.
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The fraction bar means divide. It can represent a value between whole numbers, a whole number, or a negative value.

63=6÷3=2\frac{6}{3}=6\div3=2

The denominator must be nonzero. A zero numerator is allowed: 05=0\dfrac{0}{5}=0. For 50\dfrac{5}{0}, division by zero is undefined. A numerator larger than the denominator is also allowed: 52\dfrac{5}{2} exceeds one whole.

Check your reasoning

Calculate −124\dfrac{-12}{4}.

Show answer and explanation
-3

The bar means divide: −12÷4=−3-12\div4=-3.

02Check your understanding#

Check your reasoning

Which is undefined?

  1. A03\dfrac{0}{3}
  2. B30\dfrac{3}{0}
  3. C31\dfrac{3}{1}
Show answer and explanation
30\dfrac{3}{0}

A denominator cannot be zero.

03Check your understanding#

Check your reasoning

Three metres, five equal shares. Each gets:

  1. A53\dfrac{5}{3} metres
  2. B35\dfrac{3}{5} metres
  3. C88 metres
Show answer and explanation
35\dfrac{3}{5} metres

Divide 33 by 55: 3/53/5 metres.

Key takeaway

The fraction bar means numerator divided by denominator.

  • Interpret a fraction as a quotient with a nonzero denominator

Further questions

Can a fraction be larger than one?
Yes. Five halves means five divided by two, which is two whole units and one half.

Sources & further reading

  1. [1]

Reference this concept

Link to this page, a section, or an individual figure.

Glacius. “Fractions.” Math behind ML. /learn/f-fractions