Transcript Comparing and Ordering Fraction and Mixed Numbers

4-8
6th grade math
Comparing and Ordering Fraction
and
Mixed Numbers
Objective
• To compare and order fractions and mixed
numbers
• Why? To understand the value of all types of
fractions.
California State Standards
NS 1.1 : Compare and order positive …
fractions … and mixed numbers, and place
them on a number line.
Vocabulary
• Mixed Numbers
– A number written as a whole number and a fraction
• 2½
• Improper Fractions
– A fraction in which the numerator is greater than or
equal to the denominator
• 12
6
23
5
How to Compare Fractions
Q,
Which is larger: or
1) Find the LCD
2) Write equivalent fractions,
using the LCD
3) Compare the fractions by
looking at the numerators.
Do NOT simplify
LCD = 40
7·5= 35 4·8 = 32
8·5 = 40 5·8 = 40
35 is larger than 32
35 > 32 or
40 40
>
Another Way to Compare Fractions
Which is larger: or
1) Cross multiply each
fraction
2) Write the answer on the
top of each crossing
multiplication
3) Compare the fractions by
looking at the
multiplication. The
larger number indicates
the larger fraction
35
32
7↖↗ 4
8↗↖ 5
35 is larger than 32
7 > 4
8
5
Still Another Way to Compare Fractions
1) Check the first fraction
to see if the numerator
is more or less than half
the denominator.
2) Check the other fraction
if its numerator is less or
more than half the
denominator.
3) Perhaps one or the
other is less or more
than half.
1) 5
7
3
8
½ of 7 = 3.5; 5 > 3.5
½ of 8 = 4; 3 < 4
So ….
5 > 3
7
8
(You can also change the fractions into decimals
and compare. ~ 0.71 > ~0.38)
Change a Mixed Number to an
Improper Fraction
2¼
1) Multiply the
denominator to the
whole number.
2) Add the numerator.
3) Write the answer as
the numerator.
4) Keep the denominator
the same
2¼
4·2=8
8+1=
9
9
4
To Change an Improper to a Mixed Number
9
4
1) Divide the denominator
into the numerator.
2) The whole number is the
quotient.
3) The remainder is the new
numerator.
4) Keep the denominator
the same.
9
4
2
4 9
r1
2¼
Ordering Fractions
1 ¾, 17 , 3 , 7
8 2 8
1) Rewrite improper-s as
mixed numbers.
2) Separate the mixed
numbers. Look at the
whole numbers to
order the fractions.
3) Write equivalent
fractions or use the
cross multiplication
method.
1 ¾, 17 , 3 , 7
8 2 8
1 ¾, 2 , 1 ½,
= , 1 ¾, 1 ½, 2
6
>
4
1¾ 1½
, 1 ½, 1 ¾, 2
Try It!
1)
7
3
r 12
3 7
=2
Write improper to mixed
or mixed to improper.
1)
7
3
2) 22
3
3) 9 4
7
4) 10 3
5
2) 22
3
=7
7
3 22 r 1
3) 9 4
7
7·9+4=
=67
7
4) 10 3
5
5 · 10 + 3 =
53
5
Try Some More!
5) 3 > 1
4 4
Compare. Use < > or =
5)
6) 7 2
9 3
7 6
9 9
7 > 6
9 9
6) 7 2
9 3
7) 3 4
5
33
4
8) 1 7 1 3
8 16
7) 3 4
5
16
3 4
5
(same denominators)
8) 1 7 1 3
8 16
1 14
16
3 3
4
15
3 3
4
3 4 > 3 3
5
4
1 3
16
1 14 > 1 3
16
16
Objective Review
• To compare and order
fractions and mixed
numbers
• Why? You can now
understand the value of
all types of fractions.
Independent Practice
• Complete problems 1021
• Copy original problem
first.
• Show all work!
• If time, complete Mixed
Review: 22-31
• If still more time, work
on Accelerated Math.