Key points
Fractions can be added in different ways:
- When fractions have the same Number written on the bottom of a fraction. The denominator is the number of equal parts. Eg, for 1⁄3, the denominator is 3, the Number written at the top of a fraction. The numerator is the number of parts used. Eg, for 1⁄3, the numerator is 1 are added to give the total.
- When fractions have different denominators, A fraction with the same value as another. are used that have the same denominator. The denominator of the equivalent fractions will be the The lowest multiple that is common to two or more numbers. The LCM of 15 and 12 is 60 because it is the lowest value in both of their multiplication tables. Also known as the least common multiple., which is found by listing the multiples of each number and circling any common multiples to find the lowest.
- A fraction where the numerator is greater than the denominator, eg 9⁄4 can be added as fractions or they can be converted to A number that is written using a whole number and a fraction, eg 3 4⁄5 and then added.
- To add mixed numbers, add the Integers are numbers with no fraction or decimal part. They can be positive, negative or zero. 42, 8, and 10000 are examples of integers. parts and fractions separately.
- Learning about equivalent fractions and converting between improper fractions and mixed numbers is useful when adding fractions.
Adding fractions with the same denominators
When the denominators are the same, add the numerators.
Sometimes the final answer can be To reduce a fraction to its simplest form, also known as its lowest terms.
If the final answer is an A fraction where the numerator is greater than the denominator, eg 9⁄4, the answer can be left as an improper fraction or it could be written as a A number that is written using a whole number and a fraction, eg 3 4⁄5
Examples
Image caption, Add these fractions with the same denominators.
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Question
Add the fractions.
\( \frac{8}{15} + \frac{11}{15} = \) ?
- The denominators are the same - the answer will be in fifteenths.
- Add the numerators. 8 + 11 = 19
- The sum is \( \frac{19}{15} \). This is \( 1 \frac{4}{15} \) as a mixed number.
Adding fractions with different denominators
Find the The lowest multiple that is common to two or more numbers. The LCM of 15 and 12 is 60 because it is the lowest value in both of their multiplication tables. Also known as the least common multiple. of the denominators.
Rewrite the fractions as A fraction with the same value as another. with the same denominator.
Add the numerators.
To reduce a fraction to its simplest form, also known as its lowest terms. where possible.
If the The answer to an addition calculation is an A fraction where the numerator is greater than the denominator, eg 9⁄4, the answer can be left as an improper fraction or it can be written as a mixed number.
Any common An integer that is in the multiplication table of a specific number. Eg, 20 is a multiple of ten because 20 is in the ten times table. of the denominators can be used as the A denominator that is the same for two or more fractions. . However, the most efficient way of adding fractions with different denominators is to use the LCM.
Examples
Image caption, What is 3⁄5 + 1⁄10?
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Question
Add the fractions \( \frac{2}{5} + \frac{3}{8} = \) ?
Find the LCM. The LCM of 5 and 8 is 40
Create equivalent fractions with a denominator of 40. \( \frac{2}{5} \) is equivalent to \( \frac{16}{40} \) and \( \frac{3}{8} \) is equivalent to \( \frac{15}{40} \)
Add the numerators. 16 + 15 = 31
The fractions add up to \( \frac{31}{40} \)
\( \frac{2}{5} + \frac{3}{8} = \frac{31}{40} \)
How to add improper fractions and mixed numbers
To add improper fractions:
The simplest approach is to add the improper fractions using a A denominator that is the same for two or more fractions.
Alternatively, convert the improper fractions into mixed numbers by dividing the numerator by the denominator. The whole is the Integers are numbers with no fraction or decimal part. They can be positive, negative or zero. 42, 8, and 10000 are examples of integers. for the mixed number and the remainder is the numerator for the fraction.
The improper fractions are now mixed numbers. To add these, follow the steps below for adding mixed numbers.
To add mixed numbers:
Add the integers.
Use the LCM of the denominators to rewrite the fractions as equivalent fractions with the same denominator
Add the fractions.
Simplify the answer if possible.
Alternatively change the mixed numbers to improper fractions first and add the improper fractions using a common denominator.
Examples
Image caption, Add 5⁄4 and 8⁄3
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Question
Add the mixed numbers. \( 4 \frac{2}{9} + 1 \frac{5}{12} + 2 \frac{1}{18} = \) ?
- Add the integers.
- The fractions have different denominators.
- The LCM of 9, 12 and 18 is 36. Rewrite the fractional parts with a denominator of 36. \( \frac{2}{9} \) is equivalent to \( \frac{8}{36} \), \( \frac{5}{12} \) is equivalent to \( \frac{15}{36} \) and \( \frac{1}{18} \) is equivalent to \( \frac{2}{36} \)
- Add the fractions.
\( 4 \frac{2}{9} + 1 \frac{5}{12} + 2 \frac{1}{18} = 7 \frac{25}{36} \)
Question
Add the mixed numbers \( 2 \frac{3}{4} + 1 \frac{7}{8} = \) ?
- If the sum of two fractions gives an answer over 1 (an improper fraction), the calculation is completed by changing the improper fraction to a mixed number and adding the integers.
- Add the integers.
- Write the fractions with the same common denominator.
- Add the fractions.
- The answer is \( 3 + \frac{13}{8} = 3 + 1 \frac{5}{8} \)
- The fractions add to over 1. Complete the calculation by adding \( 3 + 1 \frac{5}{8} \) to give \( 4 \frac{5}{8} \)
Practise adding fractions
Try this quiz to practise adding fractions. You may need a pen and paper to solve some of these problems.
Real-world maths
Adding fractions can be used to combine measurements. This can be useful if, for example, you want to add a border to a photograph.
A wide or narrow border can affect the look of a photo. These measurements may involve mixed numbers.
For a picture measuring 24 \( \frac{1}{2} \) cm by 24 \( \frac{1}{2} \) cm with a border of 18 \( \frac{3}{8} \) cm on each side, the total dimensions will be 18 \( \frac{3}{8} \) + 24 \( \frac{1}{2} \) +18 \( \frac{3}{8} \) which is 61 \( \frac{1}{4} \) cm by 61 \( \frac{1}{4} \) cm.
Game - Divided Islands
Play the Divided Islands game! game
Using your maths skills, help to build bridges and bring light back to the islands in this free game from ý Bitesize.
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