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3 years ago

Add. Write your answer as a fraction in simplest form. 1 5 + 9 9

Mathematics

1 answer:

Sladkaya [172]3 years ago

7 0

Answer:

57/5

Step-by-step explanation:

what is that supposed to be ?

1.5 + 9.9 ?

I base my answer in that assumption.

1.5 = 3/2

9.9 = 99/10

so, we need 3/2 + 99/10.

how do we do that ?

by bringing both fractions to the same denominator (bottom parts) but without changing the value of the fractions. that means we need to multiply numerator and denominator (top and bottom parts) by the same factor. and that factor is determined by what is needed to transform the denominator.

we have denominators 2 and 10. what is the smallest common multiple ?

I think it is plainly visible : 10. as 2 also cleanly divides 10.

in other examples, if you don't see that right away, the simplest approach is to just multiply both denominators (in our case 2×10 = 20) and work with that result.

so, we are trying to bring both fractions to denominators of 10 (or, as mentioned 20), so that we can easily add the fractions.

let's start with 3/2.

what multiplication do we need to do to turn 2 into 10 ?

right, by multiplying by 5.

remember, we need to do the same thing to numerator and denominator to keep the value of the fraction unchanged.

so, we do the following

3/2 × 5/5

as you can see, multiplying something by 5/5 does not change any value, as it means we are just multiply by 1. but we can use that little trick to change the appearance of the original fraction.

so,

3/2 × 5/5 = (3×5) / (2×5) = 15/10

by the way, if we had wanted to change the denominator to 20, our factor would have been 10/10, and we would have gotten 30/20.

now to 99/10.

well, the denominator is already 10, so we don't need any transformation.

but if we had not seen that and went for 20 as desired denominator, we would have had to multiply by 2/2 giving us

198/20.

so, for the final sum :

15/10 + 99/10 = 114/10 = 57/5

and in case of 1/20th :

30/20 + 198/20 = 228/20 = 114/10 = 57/5

now, should that original problem have been

1/5 + 9/9 ?

the same principles apply.

bring both fractions to the same denominator.

9/9 = 1

and that can be transformed easily into any other denominator expression - like 5/5.

and then we have

1/5 + 5/5 = 6/5

but if we had not seen that simple approach, we could have turned both into fractions with denominator 5×9 = 45.

9/45 + 45/45 = 54/45 = 6/5

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