☰ Year plan · Mathematics

Adding and subtracting fractions with unlike denominators

Week 17 · Adding and subtracting fractions with unlike denominators · 3 lessons
1

Adding fractions with unlike denominators

Discover Mathematics P5: Term 2, Unit 7, Lessons 4–6
GoalAdd two fractions with different denominators by finding a common denominator, adding the numerators and simplifying.
New words
numerator · the top number: how many parts we havesimplest form · a fraction that cannot be written with smaller whole numbersimproper fraction · a fraction whose numerator is bigger than or equal to its denominator, such as 8/6
Explanation

To add fractions with unlike denominators follow four steps. One: find the LCM of the denominators. Two: rewrite each fraction as an equivalent fraction with that denominator. Three: add the numerators and keep the denominator. Four: simplify the answer by dividing the top and the bottom by the same number, and if the answer is an improper fraction, write it as a mixed number. For example 1/2 + 5/6 = 3/6 + 5/6 = 8/6. Divide top and bottom by 2: 4/3, which is 1 1/3. Estimate first with benchmarks to be sure the answer is sensible.

StepWhat to do
1Find the LCM of the denominators
2Rewrite both fractions
3Add the numerators
4Simplify
Worked examples
3/122/125/12
Add 1/4 + 1/6. The LCM of 4 and 6 is 12. 1/4 = 3/12 and 1/6 = 2/12. 3/12 + 2/12 = 5/12, which cannot be simplified.
Add 3/4 + 1/6. In twelfths: 9/12 + 2/12 = 11/12. Estimate: 3/4 is close to 1 and 1/6 is close to 0, so about 1. The answer 11/12 is close to 1.
Add 1/2 + 5/6. In sixths: 3/6 + 5/6 = 8/6. Simplify: 8/6 = 4/3 = 1 1/3.
Class activity

Four-step cards. Write the four steps on four cards. The grown-up writes two fractions with different denominators (for example 3/8 and 1/6). The child lays down the cards one at a time and writes what happens at each step. Do three sums and always estimate first.

Practice
1
Work out 2/3 + 1/4.
2
Work out 3/10 + 2/5.
3
Work out 5/8 + 1/6.
4
Work out 1/6 + 1/3 and simplify.
5
Work out 3/4 + 5/6 and write the answer as a mixed number.