How to Calculate 2/3 of a Number

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Knowing how to find a fraction of a number is a handy skill for home project measurements, reducing recipes or calculating discounts. You can find two-thirds of a number using either fractions or decimals. Remember that “of” in a math sentence means to multiply, and that the bottom numbers are denominators and top numbers numerators on top. When we look at fractions, these are rational numbers, where the fraction simply represents a ratio of two numbers.

Fractional Findings

Multiply two-thirds and your number. If you have a whole number, convert it to a fraction by putting it over a denominator of one. When multiplying fractions, calculate numerator times numerator, then denominator times denominator. For example, to find two-thirds of 18:

\frac{2}{3} \times \frac{18}{1} = \frac{2\times18}{3} = \frac{36}{3} = 12.

Mixed Fraction Math

When working with a mixed number/fraction, or a whole number and a fraction, first change it to an improper fraction: Multiply the denominator and the whole number. Add that to the numerator. Write the sum over the original denominator. For example, to convert:

2 \frac{5}{6}: 6 \times 2 = 12 \rightarrow 12 + 5 = 17 \rightarrow \text{ The improper fraction is } \frac{17}{6}

Decimal Doings

Change two-thirds to a decimal number and then multiply the decimal and your number. To convert two-thirds to decimal, divide the numerator by the denominator:

\frac{2}{3} \approx 0.666667 \text{ round to the hundredths place } 0.67

For example, to find two-thirds of twenty-one:

\frac{2}{3}\times 21 \approx 0.67 \times 21 = 14.07 \text{ round to } 14

All fractions can have a decimal representation (either a finite decimal or an infinitely repeating decimal) that is exact. The fraction form of a decimal is simply an alternate way of representing a real number. Not all numbers on the number line are rational however; this means they can not be represented with a fraction. One such number is pi, which cannot be represented exactly by a ratio of numbers.

Arithmetic Approach

We can also view two-thirds as a combination of multiple terms. So if finding two-thirds of a number seems difficult, we can find one-third of that number (simply equivalent to dividing by three) and then multiply by two:

\frac{2}{3}x = \frac{x}{3} \times 2

Alternatively we can look at subtracting fractions by equating two-thirds to one minus one-third.

\frac{2}{3}x = 1x - \frac{1}{3}x = x - \frac{x}{3}

This can look more complicated, so it is up to you to choose the best method for you, but they are all equivalent!

Reducing Fractions

When we are working with fractions, it can sometimes be difficult when they involve very large numbers. However, a ratio of numbers can often be reduced to its simplest form. This simplified fraction is known as the lowest term.

In this process we will simplify a fraction by finding the greatest common factor (GCF) of the numerator and the denominator. We then factor out this GCF from the top and the bottom. The new numerator and the new denominator will still have the same ratio (relationship) to one another, but they will likely be easier to work with multiplying and dividing fractions.

Here is an example of simplifying 24 divided 36 to two-thirds.

\frac{24}{36} \rightarrow GCF = 12 \rightarrow \frac{24 \div 12}{36 \div 12} = \frac{2}{3}