Question

express the ratio below in its simplest form 5:2 1/2

Answer 1

Step-by-step explanation:

Change values to whole numbers.

Convert any mixed numbers to fractions.

Convert 3 1/8

3 1/8 = 25/8

We now have:

5 : 3 1/8 = 5 : 25/8

Convert the whole number 5 to a fraction with 1 in the denominator.

We then have:

5 : 3 1/8 = 5/1 : 25/8

Convert fractions to integers by eliminating the denominators.

Our two fractions have unlike denominators so we find the Least Common Denominator and rewrite our fractions as necessary with the common denominator

LCD(5/1, 25/8) = 8

We now have:

5 : 3 1/8 = 40/8 : 25/8

Our two fractions now have like denominators so we can multiply both by 8 to eliminate the denominators.

We then have:

5 : 3 1/8 = 40 : 25

Try to reduce the ratio further with the greatest common factor (GCF).

The GCF of 40 and 25 is 5

Divide both terms by the GCF, 5:

40 ÷ 5 = 8

25 ÷ 5 = 5

The ratio 40 : 25 can be reduced to lowest terms by dividing both terms by the GCF = 5 :

40 : 25 = 8 : 5

Therefore:

5 : 3 1/8 = 8 : 5

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Answer 2

SOLUTION

TO DETERMINE

To express the ratio below in its simplest form

$\displaystyle \sf{5 : 2 \frac{1}{2} }$

EVALUATION

Here the given ratio is

$\displaystyle \sf{ = 5 : 2 \frac{1}{2} }$

Now

$\displaystyle \sf{5 : 2 \frac{1}{2} }$

$\displaystyle \sf{ = 5 : \frac{5}{2} }$

$\displaystyle \sf{ = (5 \times 2) : \bigg(\frac{5}{2} \times 2 \bigg) }$

$\displaystyle \sf{ = 10 : 5 }$

$\displaystyle \sf{ = \frac{10}{5} : \frac{5}{5} }$

$\displaystyle \sf{ = 2 : 1 }$

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