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One half

One half is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand One half rather than just read about it. In short: One half is the multiplicative inverse of 2. It is an irreducible fraction with a numerator of 1 and a denominator of 2.

One half — main illustration
One half — illustration

Key takeaways

  • One half belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect One half to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of One half from memory before moving on to harder problems.

Reference excerpt

One half is the multiplicative inverse of 2. It is an irreducible fraction with a numerator of 1 and a denominator of 2. It often appears in mathematical equations, recipes and measurements.

As a word One half is one of the few fractions which are commonly expressed in natural languages by suppletion rather than regular derivation: the word for "half" in various languages is etymologically unrelated to their word for "two". In English, for example, other small fractions, such as "sixth" and "eleventh", are derived from the corresponding number word. A half can also be said to be one part of something divided into two equal parts. It is acceptable to write one half as a hyphenated word, one-half.

Mathematics One half is the rational number that lies midway between 0 and 1 on the number line. Multiplication by one half is equivalent to division by two, or "halving"; conversely, division by one half is equivalent to multiplication by two, or "doubling".

A number raised to the power of one half is equal to its square root. This follows from the fact that when multiplying powers, the exponents add. So, a 1 / 2 {\displaystyle a^{1/2}} times itself is a 1 / 2 + 1 / 2 {\displaystyle a^{1/2+1/2}} which is a 1 {\displaystyle a^{1}} , which equals a {\displaystyle a} .

The area of a triangle is one half its base and its height, also known as its altitude. The gamma function evaluated at one half is the square root of pi. It has two different decimal representations in base ten, the familiar 0.5 {\displaystyle 0.5} and the recurring 0.4 9 ¯ {\displaystyle 0.4{\overline {9}}} , with a similar pair of expansions in any even base; while in odd bases, one half has no terminating representation. The Bernoulli number B 1 {\displaystyle B_{1}} has the value ± 1 2 {\displaystyle \pm {\tfrac {1}{2}}} (its sign depending on competing conventions). The Riemann hypothesis is the conjecture that every nontrivial complex root of the Riemann zeta function has a real part equal to 1 2 {\displaystyle {\tfrac {1}{2}}} .

Computer characters

The "one-half" symbol has its own code point as a precomposed character in the Latin-1 Supplement block of Unicode, rendering as ½. The reduced size of this symbol may make it illegible to readers with relatively mild visual impairment; consequently the decomposed forms 1⁄2 or ⁠1/2⁠ may be more appropriate.

See also

Division by two.

References

Illustrations

One half: Fundamental region of the modular j-invariant in the upper half-plane (shaded gray), with modular discriminant | τ | ≥ 1 {\displaystyle |\tau |\geq 1} and − 1 2 < R ( τ ) ≤ 1 2 {\displaystyle -{\tfrac {1}{2}}<{\mathfrak {R}}(\tau )\leq {\tfrac {1}{2}}} , where − 1 2 < R ( τ ) < 0 ⇒ | τ | > 1 {\displaystyle -{\tfrac {1}{2}}<{\mathfrak {R}}(\tau )<0\Rightarrow |\tau |>1}
Fundamental region of the modular j-invariant in the upper half-plane (shaded gray), with modular discriminant | τ | ≥ 1 {\displaystyle |\tau |\geq 1} and − 1 2 < R ( τ ) ≤ 1 2 {\displaystyle -{\tfrac {1}{2}}<{\mathfrak {R}}(\tau )\leq {\tfrac {1}{2}}} , where − 1 2 < R ( τ ) < 0 ⇒ | τ | > 1 {\displaystyle -{\tfrac {1}{2}}<{\mathfrak {R}}(\tau )<0\Rightarrow |\tau |>1}
One half: Postal stamp, Ireland, 1940: one halfpenny postage due
Postal stamp, Ireland, 1940: one halfpenny postage due

Worked examples

Example 1 — a first encounter with One half

Start with the simplest possible case. Write down what One half claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to One half before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about One half ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of One half

In research
One half appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses One half in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
One half is common in secondary-school and first-year university syllabi. It links to neighbouring topics Fractions (mathematics), so understanding it makes those chapters shorter.
In everyday life
Look for One half outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study One half in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what One half means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain One half out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is One half in simple terms?

One half is the multiplicative inverse of 2. It is an irreducible fraction with a numerator of 1 and a denominator of 2.

Why does One half matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study One half?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on One half.

Tags

  • Fractions (mathematics)

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