To complete the table, we will first write the

fractions as decimals, then write the decimals as percentages. Because a fraction bar means division, to convert a fraction to a decimal, we divide the numerator

by the denominator. So for the fractions

3/8, 3/8 is equivalent to three divided by eight. Let’s show the division on the right. Three eighths is equal to .375, however, we normally place a zero

on the one’s place value, and write the decimal as 0.375. Next we have the fraction 7/4. 7/4 is equivalent to

seven divided by four. Again, let’s show the

division on the right. 7/4 equals 1.75. For the last one notice

how we have a mixed number. We have two and 3/5. One option would be to

convert 3/5 to a decimal by dividing three by

five and then adding two, but let’s write the mixed

number as an improper fraction where the denominator remains five, and the numerator is five times

two plus three which is 13, and 13/5 is equivalent

to 13 divided by five. Again, let’s show the

division on the right. Two and 3/5 equals 2.6 as a decimal, and now let’s convert the

decimals to percentages. We will show two methods for doing this. For the first method, we

will write the decimal as a fraction, then if the denominator of the fraction is not 100,

we rewrite the fraction as a equivalent fraction

with the denominator of 100. This is important because

remember that percent is a number compared to

100, and then step three, we rewrite the ratio or fraction with a denominator of 100 as a percent. The second method is the

shortcut method in which we begin with the decimal, move

the decimal point two places to the right, and then add a percent sign. We will show both methods

for these three examples. Beginning with 0.375, we can write this as a fraction two ways. If we know our place values, we read this decimal as 375/1000. In this form, we need to

write a equivalent fraction with the denominator of 100, and because 1000 divided

by ten is equal to 100, we divide the numerator

and the denominator by ten. 375 divided by ten equals 37.5. 1000 divided by ten is equal to 100. Now that we have a fraction,

our ratio with a denominator of 100, the numerator

indicates the percentage. This is equal to 37.5%. Another way to write

0.375 as a fraction is to just write 0.375/1,

and now in this form, try an equivalent fraction

with a denominator of 100, we need to multiply the numerator and the denominator by 100. 0.375 times 100 is 37.5,

and of course one times 100 is equal to 100, giving us

the same result of 37.5%. So this is the percent. Let’s also take a look at

the shortcut method where I can bring the decimal to a percent. Beginning with the decimal,

the shortcut is to move the decimal point two places

to the right, so one two. The decimal point is now here, and then we add a percent sign, and of course we can now

remove the old decimal, and notice how this also gives us 37.5%. Now let’s look at the decimal 1.75. 1.75 is equivalent to one

and 75/100 using place value. Notice how the denominator is already 100, but we need to write the mixed number as an improper fraction to

determine the percentage. The denominator remains 100, and the numerator is 100 times

one plus 75, which is 175. Because the denominator is 100, the numerator indicates the percentage, this is equal to 175%, or another

way is to start with 1.75, and write the decimal as a

fraction with a denominator of one, and now to write

an equivalent fraction with a denominator of 100, we multiply the numerator and denominator by 100. 1.75 times 100 is equal to

175, one times 100 is equal to 100, giving us the

same percentage at 175%, and for the shortcut

method beginning with 175, move the decimal point two

places to the right, one two. The decimal point is now

here, add a percent sign. We can now remove the old decimal which of course also gives us 175%, and now let’s look at

the last decimal of 2.6. 2.6 is equal to two and 6/10. Now we right the mixed number

as an improper fraction, the denominator remains ten, the numerator is ten times

two plus six, which is 26. Now we write an equivalent fraction with the denominator of 100,

which means we now multiply the numerator and denominator by ten, because ten times ten is 100. 26 times ten is equal to

260, ten times ten is 100. Because we have a denominator of 100, the numerator indicates

this is equal to 260%, or we can also write

2.6 as a fraction with the denominator of one, and now to write an equivalent fraction

with the denominator of 100 we multiply the numerator

and denominator by 100. 2.6 times 100 is 260, one times

100 is 100, giving us 260%, and let’s show the shortcut one last time. Beginning with 2.6, move

the decimal point two places to the right, so one and two. The new decimal point is here. Notice how we are missing a digit here. We always replace

missing digits with zeros and then add a percent

sign, and of course now we can remove the old decimal point, which does give us 260%. I hope you found this helpful.

Thank you, you helped me do my hard test from school.

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