Step by step adding fractions

When the cards played have different denominators we must find a hand that gives the same result but with fractions of the same denominator.

The steps are:

1. Change to the division form of fraction;
2. Find the prime factors of each of the denominators;
3. Find the HCF of the denominators;
4. Factorise the denominators using the HCF as one factor;
5. Calculate the LCM of the denominators;
6. Find the multipliers to make each denominator into the LCM;
7. Work out the fractions that are equivalent to the ones you started with.

Example



1. Change to the division form of fraction.



2. Find the prime factors of each of the denominators.





Arrange the denominators with their prime factors in numerical order




3. Find the HCF (highest common factor) of the denominators
Rearrange the prime factors and pair those in common to the denominators




The matching pairs of factors give the HCF = 2 x 3 = 6

4. Factorise the denominators using the HCF as one factor



5. Calculate the LCM of the denominators
Push the overlapping HCF cards into one pile





Take the factors that are still showing and multiply to form the LCM

LCM = 6 x 2 x 5 = 60

This will form the new denominator for each fraction.
That is the number of boards to use that will work with both fractions.

6. Find the multipliers to make each denominator into the LCM

Remove the HCF from the arrangement below and swap the other factors over.




This gives



Turn the factor cards in holders and put with card they are next to.




7. Work out the fractions that are equivalent to the ones you started with by putting the holders with the numerator as well as the denominator.



gives the same result as



and gives the same result as



Here we have a game played over sixty boards with Twenty Five and Fourteen to be added in the game giving Thirty Nine in the game over sixty boards.

which gives the same result as
which gives the same results as

and as

Working Out Factorise denominators and circle primes Write denominators as product of prime factors and pair those in common, these give HCF Find LCM by multiplying the HCF by the other factors,those not paired off Factorise the LCM in two ways using a denominator as one factor

Record

Maths