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Year 6 Maths Chance

Represent probabilities as fractions / decimals / percentages

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Theory

A probability can be written as a fraction, a decimal or a percentage: \(\dfrac{7}{10} = 0.7 = 70\%\). This Year 6 maths page shows how to change between the three forms, especially by making a denominator of \(100\), and how to compare probabilities written in different ways.

When outcomes are equally likely, the probability of an event is \(\dfrac{\text{outcomes in the event}}{\text{total outcomes}}\).

Fraction to percentage: make the denominator \(100\). \(\dfrac{3}{20} = \dfrac{15}{100} = 15\%\).

Decimal to percentage: multiply by \(100\). \(0.7 = 70\%\). Percentage to decimal: divide by \(100\). \(64\%= 0.64\).

Percentage to fraction: write it over \(100\) and simplify. \(35\% = \dfrac{35}{100} = \dfrac{7}{20}\).

Hundred grid with 35 squares shaded A 10 by 10 grid with 35 of the 100 squares shaded.
\(35\) out of \(100\): \(\dfrac{35}{100} = \dfrac{7}{20} = 0.35 = 35\%\).
Matching fractions, decimals and percentages Three parallel number lines from 0 to 1, labelled fraction, decimal and percent. The ticks line up: 0, 1/4, 1/2, 3/4 and 1 match 0, 0.25, 0.5, 0.75 and 1 and 0%, 25%, 50%, 75% and 100%. fraction 0 1/4 1/2 3/4 1 decimal 0 0.25 0.5 0.75 1 percent 0% 25% 50% 75% 100%
Each column of labels names the same probability in three ways.
Spinner with two green, one red and one blue sector A spinner with four equal sectors: green, red, green and blue. green red green blue
\(P(\text{green}) = \dfrac{2}{4} = 0.5 = 50\%\). \(P(\text{red}) = \dfrac{1}{4} = 0.25 = 25\%\).

Converting probabilities:

\[ \dfrac{35}{100} = 0.35 = 35\% \]
35/100=0.35=35
\[ \text{decimal} \times 100 = \text{percentage} \]
decimal ×100= percentage
FractionDecimalPercentage
\(\dfrac{1}{10}\)\(0.1\)\(10\%\)
\(\dfrac{1}{5}\)\(0.2\)\(20\%\)
\(\dfrac{1}{4}\)\(0.25\)\(25\%\)
\(\dfrac{1}{2}\)\(0.5\)\(50\%\)
\(\dfrac{3}{4}\)\(0.75\)\(75\%\)
\(1\)\(1\)\(100\%\)
Denominator 100. Any fraction you can rename with denominator \(100\) turns straight into a percentage.
Same form to compare. Change every probability to a percentage (or every one to a decimal) before ordering.

Fraction to decimal and percentage

  1. Rename the fraction with denominator \(100\) (or \(1000\)) if you can.
  2. Write the hundredths as a decimal.
  3. Write the number of hundredths as a percentage.

Percentage to fraction

  1. Write the percentage over \(100\).
  2. Simplify by dividing the top and bottom by the same number.
Example 1 — Fraction to all forms
A bag has \(10\) marbles and \(7\) are blue. Write the probability of blue as a fraction, a decimal and a percentage.
Solution

\(\dfrac{7}{10} = 0.7 = 70\%\).

Example 2 — Make a denominator of 100
Write \(\dfrac{3}{20}\) as a percentage and as a decimal.
Solution
\(\dfrac{3}{20}\)\(=\)\(\dfrac{15}{100}\)
3/20=15/100

\(15\%\), which is \(0.15\).

Example 3 — Eighths
The probability of an event is \(\dfrac{3}{8}\). Write it as a decimal and a percentage.
Solution
\(\dfrac{3}{8}\)\(=\)\(\dfrac{375}{1000}\)
3/8=375/1000=0.375

\(0.375 = 37.5\%\).

Example 4 — Percentage to fraction
Write each as a fraction in lowest terms.
(i) \(35\%\)
(ii) \(0.64\)
Solution
\(\dfrac{35}{100}\)\(=\)\(\dfrac{7}{20}\)
\(\dfrac{64}{100}\)\(=\)\(\dfrac{16}{25}\)
35/100=7/2064/100=16/25

(i) \(\dfrac{7}{20}\)
(ii) \(\dfrac{16}{25}\)

Example 5 — Counters
A jar holds \(25\) counters and \(6\) are red. What is the probability of red, as a percentage?
Solution
\(\dfrac{6}{25}\)\(=\)\(\dfrac{24}{100}\)
6/25=24/100=24

\(24\%\) (or \(0.24\)).

Example 6 — Spinner
Use the spinner with green, red and blue.
(i) Write \(P(\text{green})\) as a percentage.
(ii) Write \(P(\text{blue})\) as a decimal.
Solution

(i) \(\dfrac{2}{4} = 50\%\)
(ii) \(\dfrac{1}{4} = 0.25\)

Example 7 — Order
Order from least to most likely: \(\dfrac{7}{10}\), \(0.66\), \(72\%\).
Solution

As percentages: \(70\%\), \(66\%\), \(72\%\).

\(0.66\), \(\dfrac{7}{10}\), \(72\%\).

Example 8 — Not happening
The probability that a seed sprouts is \(0.22\). What is the chance, as a percentage, that it does not sprout?
Solution
\(100 - 22\)\(=\)\(78\)
100−22=78

\(0.22 = 22\%\), so the chance it does not sprout is \(78\%\).

Example 9 — Find the mistake
Mia says a probability of \(\dfrac{1}{20}\) is \(120\%\). What is right?
Solution
\(\dfrac{1}{20}\)\(=\)\(\dfrac{5}{100}\)
1/20=5/100

Mia just wrote the digits together. One twentieth is \(5\) hundredths, so it is \(5\%\).

Common pitfalls

Joining the digits. \(\dfrac{1}{20}\) is not \(120\%\); it is \(5\%\).
Moving the point the wrong way. \(0.7\) is \(70\%\), not \(7\%\) or \(0.007\%\).
Comparing different forms. Change \(\dfrac{7}{10}\) to \(70\%\) before comparing with \(72\%\).
Not simplifying. \(\dfrac{35}{100}\) in lowest terms is \(\dfrac{7}{20}\).

Frequently asked questions

How do I change a fraction to a percentage?

Rename it with denominator \(100\): \(\dfrac{3}{20} = \dfrac{15}{100} = 15\%\).

How do I change a decimal to a percentage?

Multiply by \(100\): \(0.7 = 70\%\).

How do I change a percentage to a fraction?

Write it over \(100\) and simplify: \(35\% = \dfrac{7}{20}\).

How do I compare 7/10 and 72%?

Change \(\dfrac{7}{10}\) to \(70\%\); \(72\%\) is larger.

What is 9/10 as a percentage?

\(90\%\).

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