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Math Made Easy: Simple tricks and tips to memorise formulae

The Butterfly method is an easy way to learn how to add, subtract, multiply and divide fractions, says this Apeejay School, Noida Math teacher

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Editor’s Note: Math Made Easy is a new series by Apeejay Newsroom where experts share study tips and fun ways to learn the subject. This is part IV of the series. Read part III here; part II here and part I here.

Almost all of us have struggled with Math more often than not. The most common issue that students face is how to remember all the formulae that each topic has. Add to this are at least 12-14 chapters for each class, and there is a daunting task in front of the child. The worst part is that one has to remember these formulae as long as one is studying the subject.

While the adage: Practice makes a person perfect is apt for Math; sadly to remember hundreds of formulae is a tough ask. And it gets tougher as the child is unable to cope with the subject and starts to lag and the subject starts to look like a mountain that is impossible to scale.

So why is Math easy for some and difficult for others? The reason is simple says Rinki Verma, a Math teacher at Apeejay School, Noida in Uttar Pradesh. “Not everyone can be good in all subjects. Children have preferences. Some excel in Music, Sports, Social Studies, and or Science and even cooking,” Verma opined.

Also, Math is a wide subject and there are so many domains that as one progresses with class, the topics become more complex and become harder to understand for many. Take an example. It is not possible for everyone to easily understand abstract algebra. Who can understand the permutations of the Rubik’s Cube learn (a + b)3 = a3 + 3a2b + 3ab2 + b3 ; (a + b)3 = a3 + b3 + 3ab(a + b)?

“Math also appears to be difficult because it takes time and energy. Most students shy away from the most basic principle of Math – practice. The result is that the student falls behind the class while the teacher has moved ahead. This means that the student has a shaky foundation that can collapse at any time,” Verma warned and shares the most basic tricks for students to learn how to add, subtract, multiply and divide fractions.

“The butterfly method for adding, subtracting, comparing, multiplying, and dividing two fractions is a fun way that students can use. Not only does the student remember it for life, but the best part is also that the steps involved at simple and easy to understand,” Verma said.


How to add?

Take an example.

4/5   +    2/3

Draw the ovals and antennae of the butterfly. Multiply the numbers in one oval and put the answer in antennae over the oval. Repeat with the other side. Add the numbers written in the antenna that will give the numerator. Multiply the denominators of both fractions to get the denominator.

We get the sum of the two fractions. The same method can be used to subtract two fractions

How to compare (which is greater)?

4/5 or   2/3

Draw the ovals and antennae of the butterfly. Multiply the numbers in one oval and put the answer in antennae over the oval. Repeat with the other side. Multiply the denominators of both fractions to get the denominator.

4×3= 12

5×2= 10

The denominator is 15. For this is follows: 12/15 is greater than 10/15/

How to divide?

4/5 ÷ ½

The product in the left antennae gives the numerator and the product is right the antennae gives the denominator.                

How to multiply?

4/7 × 35/18        

Take any of the ovals drawn first and divide both the numbers of that oval by that greatest number which divides both the numbers of that oval completely.

Repeat the same for another oval drawn. Multiply the numerator by the numerator to get the numerator and the denominator by the denominator to get the denominator of the required fraction. 

Divide 4 by 2 and 18 by 2. The answer is 2 and 9 respectively. Do the same with the other oval. The answer in the numerator is 2×5 and the denominator is 1×9. Multiplying the numerators the answer is 10 and for the denominators, the answer is 9. The final answer is 10/9.


“Math also appears to be difficult because it takes time and energy. Most students shy away from the most basic principle of Math – practice. The result is that the student falls behind the class while the teacher has moved ahead”  

Rinki Verma, Math teacher, Apeejay School, Noida

Shalini is an Executive Editor with Apeejay Newsroom. With a PG Diploma in Business Management and Industrial Administration and an MA in Mass Communication, she was a former Associate Editor with News9live. She has worked on varied topics - from news-based to feature articles.

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