How do you determine which fraction is greater 3/7 or 4/9?

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How do you determine which fraction is greater 3/7 or 4/9?

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Answer 1 · 2016-01-13T21:49:50

Divide one into the other. The resulting value will indicate which is the greater: $color(white)(....)4/9>3/7$

Explanation:

Consider $4/9-:3/7$ giving:

$4/9xx7/3 =28/27$ which is greater than 1 so

$4/9>3/7$

Answer 2 · 2016-09-19T09:31:30

$3/7 < 4/9$

Explanation:

A quick method is to cross multiply the fractions.

However, this only works if you multiply in the same direction every time. $color(red)("Red x Red")$ first as shown below:

$color(red)(3)/color(blue)(7) and color(blue)(4)/color(red)(9)$

$color(red)(3xx9) and color(blue)(7xx4)$

$color(red)(27) < color(red)(28)$

$color(red)(3/7) < color(blue)(4/9)$

An alternative method is to get rid of the denominators

$xx LCD" "$ which in this case is 63

$cancel63^9/1 xx3/cancel7 and cancel63^7/1xx4/cancel9$

$27 < 28$

$3/7 < 4/9$

Worst method - use a calculator!

Use a calculator to change them into decimals, then compare.

$3/7 = 0.42857...." "larr$ smaller

$4/9 = 0.44444..." "larr$ larger

You can also use a calculator to subtract the two fractions.
If you get a positive answer, then the first fraction was bigger.
If you get a negative answer then the first fraction was smaller.

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How do you determine which fraction is greater 3/7 or 4/9?

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