Transcript Equivalent Fractions and Ordering Fractions

Equivalent Fractions and
Ordering Fractions
What Are Equivalent Fractions ?
A fraction can have many versions or “forms” BUT
can still be the same number !
1/4 multiplied top & bottom by 3 = 3/12
1/4 and 3/12 are called Equivalent Fractions
Different numbers top & bottom BUT the SAME
NUMBER or VALUE as a whole.
Why Use Equivalent Fractions ?
Test Question
1 Compare the sizes of the fractions 1/4 , 2/3 and 3/5.
Before we compare we must find a common
denominator for all three fractions.
Denominators 4, 3 and 5 are all factors of 60 so
adjust all three fractions to have new denominators
of 60, how do we do this ?
Make sure that 60 is the new denominator then
adjust the numerators with the same multiplication
1/4 , to get 60 on bottom multiply by 15, then multiply
the top number by the SAME number 15 = 15/60
2/3, to get 60 on bottom multiply by ?, then multiply
the top number by the SAME number ? = ?
3/5, to get 60 on bottom multiply by ? then multiply
the top number by the SAME number ? = ?
Make sure that 60 is the new denominator then adjust
the numerators with the same multiplication
1/4 , to get 60 on bottom multiply by 15, then multiply
the top number by the SAME number 15 = 15/60
2/3, to get 60 on bottom multiply by 20, then multiply
the top number by the SAME number 20 = 40/60
3/5, to get 60 on bottom multiply by ? then multiply the
top number by the SAME number ? = ?
Make sure that 60 is the new denominator then adjust
the numerators with the same multiplication
1/4 , to get 60 on bottom multiply by 15, then multiply
the top number by the SAME number 15 = 15/60
2/3, to get 60 on bottom multiply by 20, then multiply
the top number by the SAME number 20 = 40/60
3/5, to get 60 on bottom multiply by 12 then multiply the
top number by the SAME number 12 = 36/60
NOW WE CAN COMPARE THE FRACTIONS !!
Fractions We CAN Compare
Now we can use the Equivalent Fractions we
just worked out to compare them in the same
fraction language (Denominator = 60)
1/4 = 15/60 , 2/3 = 40/60, 3/5 = 36/60
40 > 36 > 15
2/3 is the biggest, then 3/5 and smallest is 1/4
Biggest first order is 2/3, 3/5, 1/4
(Exam Questions sometimes want smallest first)
Quick Test
1) Write three Equivalent Fractions of 1/5
2) 1/4, 2/5, 3/4, 8/20, 15/20, 6/24 Find the
three pairs of Equivalent Fractions
3) Rewrite 21/49 with the lowest possible
equivalent fraction numbers top and bottom
HINT: What is the Common Factor ?
Quick Test Answers
1) Write three Equivalent Fractions of 1/5
2/10 (x2), 3/15 (x3), 7/35 (x7), 9/45 (x9) ....
2) 1/4, 2/5, 3/4, 8/20, 15/20, 6/24 Find the
three pairs of Equivalent Fractions
1/4, 6/24 (x6) 2/5, 8/20 (x4) 3/4, 15/20 (x5)
3) Rewrite 21/49 with the lowest possible
equivalent fraction numbers top and bottom
HINT: What is the Common Factor ? (7) 3/7
Finding Equivalent Fractions and Ordering Them
• One fraction can many versions or “forms”
e.g. 1/4 , 2/8, 4/16 are all the same number.
• Make sure you multiply top AND bottom by
the same number or it won’t work !
• Successful fraction ordering needs conversion
to common denominators before comparing.