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Year 5 Maths Percentages

Benchmark fraction / decimal / percentage equivalence

20 practice questions 0 video lessons Theory + worked examples
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Theory

Percent means out of 100, and \(100\%\) is the whole amount. A few amounts are used so often that they are worth knowing by heart: one half is \(0.5\) and \(50\%\), one quarter is \(0.25\) and \(25\%\), three quarters is \(0.75\) and \(75\%\), one tenth is \(0.1\) and \(10\%\), and one fifth is \(0.2\) and \(20\%\). This Year 5 maths page shows where these come from and how to use them.

Percent (\(\%\)) means out of 100. \(30\%\) means \(30\) out of \(100\), which is \(\dfrac{30}{100}\) or \(0.3\).

\(100\%\) is the whole amount. If \(30\%\) of a group has a pet, the other \(70\%\) do not, because \(30\% + 70\% = 100\%\).

To change a fraction to a percentage, write it with a denominator of \(100\): \(\dfrac{2}{5} = \dfrac{40}{100} = 40\%\).

A decimal to two places is a number of hundredths: \(0.4 = 0.40 = \dfrac{40}{100} = 40\%\).

A hundred grid with 25 squares shaded A 10 by 10 grid of 100 squares with 25 squares shaded: one quarter, 0.25 or 25 percent of the grid.
\(25\) of \(100\) squares: \(\dfrac{1}{4} = 0.25 = 25\%\).
A hundred grid with 30 squares shaded A 10 by 10 grid of 100 squares with three full columns of 10 shaded: 30 squares, which is 3 tenths, 0.3 or 30 percent.
\(3\) columns of \(10\): \(\dfrac{3}{10} = 0.3 = 30\%\).
Matching number lines for fractions, decimals and percentages Three parallel number lines from 0 to 1. The ticks line up: 0, 1/4, 1/2, 3/4 and 1 on the fraction line; 0, 0.25, 0.5, 0.75 and 1 on the decimal line; 0%, 25%, 50%, 75% and 100% on the percent line. Fraction 0 1/4 1/2 3/4 1 Decimal 0 0.25 0.5 0.75 1 Percent 0% 25% 50% 75% 100%
The same points named as fractions, decimals and percentages.

Benchmark amounts to know:

FractionDecimal   Percent
\(\dfrac{1}{2}\)\(=\)\(0.5\)   \(50\%\)
\(\dfrac{1}{4}\)\(=\)\(0.25\)   \(25\%\)
\(\dfrac{3}{4}\)\(=\)\(0.75\)   \(75\%\)
\(\dfrac{1}{10}\)\(=\)\(0.1\)   \(10\%\)
\(\dfrac{1}{5}\)\(=\)\(0.2\)   \(20\%\)
\(1\)\(=\)\(1\)   \(100\%\)
\[ \dfrac{2}{5} = \dfrac{40}{100} = 0.4 = 40\% \]
2/5=40/100=0.4=40
Percent means hundredths. A percentage is a number of hundredths: \(40\%\) is \(0.40\), not \(0.040\).
The whole is 100%. The part that is left is \(100\%\) minus the part you know.

Fraction to percentage

  1. Make the denominator 100 with an equivalent fraction.
  2. The numerator is the percentage.

Decimal to percentage

  1. Write the decimal with two decimal places (hundredths).
  2. Read the number of hundredths as the percentage: \(0.6 = 0.60 = 60\%\).

Percentage to decimal

  1. Write the percentage as hundredths: \(35\% = \dfrac{35}{100} = 0.35\).
Example 1 — Tenths
Write \(\dfrac{3}{10}\) as a decimal and as a percentage.
Solution
\(\dfrac{3}{10}\)\(=\)\(\dfrac{30}{100}\)
\(\dfrac{30}{100}\)\(=\)\(0.3 = 30\%\)
3/10=0.3=30

\(0.3\) and \(30\%\).

Example 2 — Fifths
Write \(\dfrac{2}{5}\) as a percentage.
Solution
\(\dfrac{2 \times 20}{5 \times 20}\)\(=\)\(\dfrac{40}{100} = 40\%\)
2/5=40

\(40\%\).

Example 3 — Decimal to percent
Write each decimal as a percentage.
(i) \(0.9\)
(ii) \(0.05\)
Solution
\(0.90\)\(=\)\(\dfrac{90}{100} = 90\%\)
\(0.05\)\(=\)\(\dfrac{5}{100} = 5\%\)
0.9=90,0.05=5

(i) \(90\%\)
(ii) \(5\%\)

Example 4 — Percent to decimal
Write \(60\%\) as a decimal and as a fraction in simplest form.
Solution
\(60\%\)\(=\)\(\dfrac{60}{100} = 0.6\)
\(\dfrac{60}{100}\)\(=\)\(\dfrac{3}{5}\)
60=0.6=3/5

\(0.6\) and \(\dfrac{3}{5}\).

Example 5 — The rest of the whole
In a class, \(30\%\) of students have a pet.
(i) What percentage do not have a pet?
(ii) Write the part with a pet as a fraction.
Solution
\(100\% - 30\%\)\(=\)\(70\%\)
100−30=70

(i) \(70\%\)
(ii) \(\dfrac{30}{100} = \dfrac{3}{10}\)

Example 6 — Compare
Order \(0.6\), \(\dfrac{1}{4}\) and \(45\%\) from smallest to largest.
Solution

Change each to a percentage.

\(0.6\)\(=\)\(60\%\)
\(\dfrac{1}{4}\)\(=\)\(25\%\)
25<45<60

\(\dfrac{1}{4},\ 45\%,\ 0.6\).

Example 7 — Find the mistake
Mai says \(0.4\) is the same as \(4\%\). Explain why she is wrong.
Solution
\(0.4\)\(=\)\(0.40 = \dfrac{40}{100} = 40\%\)
0.4=40

\(0.4\) is \(4\) tenths, which is \(40\) hundredths, so \(0.4 = 40\%\). \(4\%\) is \(0.04\).

Common pitfalls

Reading tenths as hundredths. \(0.4\) is \(40\%\), not \(4\%\).
Treating 100% as part of something. \(100\%\) is the whole amount, not a part of it.
Mixing up 1/4 and 4%. \(\dfrac{1}{4} = 25\%\); the digits of a fraction are not the percentage.
Comparing different forms directly. Change everything to percentages (or decimals) before comparing \(0.6\), \(\dfrac{1}{4}\) and \(45\%\).

Frequently asked questions

What does percent mean?

Out of \(100\). \(30\%\) means \(30\) out of every \(100\).

What does 100% mean?

The whole amount. All of it.

What is three tenths as a percentage?

\(30\%\), because \(\dfrac{3}{10} = \dfrac{30}{100}\). As a decimal it is \(0.3\).

How do you change a decimal to a percentage?

Write it as hundredths: \(0.9 = 0.90 = 90\%\).

How do you change a fraction to a percentage?

Make the denominator \(100\): \(\dfrac{2}{5} = \dfrac{40}{100} = 40\%\).

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