A fraction describes equal parts of a whole or a collection. In 3/4, the denominator 4 tells us that the whole is divided into four equal parts. The numerator 3 tells us that three of those parts are being considered. Always identify the whole before comparing fractions.
Equivalent fractions
Multiplying the numerator and denominator by the same non-zero whole number gives an equivalent fraction. For example, 1/2 = 2/4 = 3/6. The number of pieces changes, but the proportion of the whole stays the same.
To simplify 6/8, divide both numbers by their common factor 2. The result is 3/4. Never change only the numerator or only the denominator when making an equivalent fraction.
Compare and add
When denominators are equal, compare numerators. When numerators are equal and positive, the fraction with the smaller positive denominator is larger. For other cases, rewrite the fractions with a common denominator.
To add fractions with the same denominator, add the numerators and keep that denominator. For different denominators, first find equivalent fractions with a common denominator.
- 1/5 + 2/5 = 3/5.
- 1/2 + 1/4 = 2/4 + 1/4 = 3/4.
Put it into practice
A worked example
Which is larger: 2/3 or 3/4?
- Use the common denominator 12.
- 2/3 = 8/12 and 3/4 = 9/12.
- Nine twelfths is larger than eight twelfths.
Answer: 3/4 is larger.
Try it yourself
Have a go before revealing the answer.
Simplify 9/12.
Show answer
3/4, by dividing the numerator and denominator by 3.
Answer: 3/4, by dividing the numerator and denominator by 3.
Find 2/5 + 1/10.
Show answer
4/10 + 1/10 = 5/10 = 1/2.
Answer: 4/10 + 1/10 = 5/10 = 1/2.
Watch out for these
- Adding 1/2 and 1/3 does not give 2/5; the correct answer is 5/6.
- Equal-sized pieces matter: two unequal pieces are not automatically halves.
Continue with official resources
Match these concept notes to your current textbook and syllabus. They are independent explanations, not official board publications.
