Download 9. [Fraction +,−]

[Fraction +,−]
9.
Skill 9.1
continues on page 40
Simplifying a fraction
Changing an improper
fraction to a mixed number
Hint: If the numbers are
both even then you can start
with dividing by 2.
4
16
•
MMBlue 1 1 2 2 3 3 4 4
MMGreen 1 1 2 2 3 3 4 4
Adding fractions with the same denominator (1).
numerator
(even)
4 ÷ 2 2÷ 2 1
=
=
16 ÷ 2 8 ÷ 2 4
MIXED NUMBER
numerator
7
3
denominator
Divide the numerator by
the denominator.
7
= 7 ÷ 3 = 2 remainder 1
3
•
Write the result as the
whole number and the
remainder over the
denominator.
7
1
=7÷3=2
3
3
•
Multiply the whole number
by the denominator and
then add the result to the
numerator.
2
3 + 3 × 5 + 2 = 17
× 5
•
Rewrite the total over the
denominator.
2 17
3 =
5 5
•
•
•
Add the numerators (top numbers of the fractions).
Do not change the denominators.
Simplify the resulting fraction and/or change it to a mixed number if necessary.
Q.
3 4
+ =
5 5
A.
3 4
+
5 5
3+ 4
=
5
7
=
5
=1
5
4
+
=
12 12
a)
Add the numerators
(top numbers) only
5+4
9 ÷3
=
=
=
12
12 ÷ 3
.........................................
2 4
+ =
7 7
d)
=
=
page 39
4
5
7
5
=
=
=
www.mathsmate.net
=
1
2
5
=
.........................................
4 1
+ =
9 9
f)
.........................................
7
5
3
5
+
=
11 11
c)
2
8
+
=
13 13
=
=
.........................................
=
+
=
=
2
5
=
e)
.........................................
+
3
5
2 2
+ =
5 5
b)
3
4
Add the numerators
(top numbers) only
7 ÷ 5 = 1 remainder 2
proper
fraction
32
5
whole
number
IMPROPER FRACTION
•
denominator
(even)
Divide both the numerator
and the denominator by
the same number.
Changing a mixed number
to an improper fraction
=
=
.........................................
© Math’s Mate Blue/Green Skill Builder 9
continued from page 39
Skill 9.1
Adding fractions with the same denominator (2).
4 4
5 4
g)
h)
+ =
+ =
5 5
7 7
=
4+ 4 8
Change to
=
mixed number
5
5
...........................................................
=8÷5
= 1
.........................................
=
=
10 1
+ =
3 3
k)
=
5 7
+ =
8 8
9 11
+ =
13 13
l)
=
...........................................................
=
=
...........................................................
=
=
.........................................
3 3
+ =
4 4
n)
5 + 7 12 ÷ 4 Simplify
=
=
8 ÷4
8
...........................................................
=
.........................................
5 5
+ =
6 6
o)
=
=
...........................................................
3
=3÷2=
2
.........................................
=
.........................................
=
.........................................
.........................................
=
...........................................................
.........................................
...........................................................
m)
=
...........................................................
=
=
7 7
+ =
9 9
i)
=
3
5
7
9
+
=
11 11
j)
MMBlue 1 1 2 2 3 3 4 4
MMGreen 1 1 2 2 3 3 4 4
=
...........................................................
=
=
.........................................
=
.........................................
Change to
mixed number
p)
1 5
+ =
8 8
1+ 5 6 ÷2
=
=
=
8 ÷2
8
.........................................
s)
1
2
+
=
15 15
q)
3
2
+
=
10 10
=
=
5
3
+
=
12 12
=
1 3
+ =
8 8
=
page 40
u)
7
1
+
=
10 10
=
.........................................
w)
.........................................
=
.........................................
=
.........................................
v)
=
.........................................
t)
1 1
+ =
6 6
r)
5
5
+
=
12 12
.........................................
x)
=
.........................................
www.mathsmate.net
2 10
+
=
15 15
=
.........................................
© Math’s Mate Blue/Green Skill Builder 9
Skill 9.2
•
•
•
MMBlue 1 1 2 2 3 3 4 4
MMGreen 1 1 2 2 3 3 4 4
Subtracting fractions with the same denominator.
Subtract the numerators (top numbers of the fractions).
Do not change the denominators.
Simplify the resulting fraction and/or change it to a mixed number if necessary.
(see skill 9.1, page 39)
Q.
5 1
− =
8 8
A.
5 1
−
8 8
5− 1
=
8
4 ÷4
=
8 ÷4
=
7
2
a)
−
=
11 11
=
Subtract the numerators
(top numbers) only
7−2
=
11
.........................................
11 2
− =
5 5
d)
=
.........................................
7
5
−
=
12 12
g)
=
Simplify
4
5
11 7
−
=
18 18
=
=
page 41
=
5 1
− =
6 6
i)
=
11 5
−
=
16 16
=
=
9
1
−
=
10 10
=
=
19 7
−
=
24 24
o)
=
.........................................
www.mathsmate.net
=
.........................................
.........................................
=
=
.........................................
l)
9
3
−
=
20 20
=
.........................................
.........................................
n)
.........................................
20 2
− =
7 7
...........................................................
=
=
=
=
.........................................
f)
13 8
−
=
15 15
k)
1
2
=
.........................................
h)
4
8
=
=
=
.........................................
m)
=
8 1
− =
3 3
1
8
11 9
−
=
13 13
...........................................................
2
=
12 ÷ 2
.........................................
=
=
c)
=
÷2
9
5
−
=
14 14
j)
4
8
1
2
=
=
.........................................
e)
= 1
−
Simplify
=
11 − 2 9
Change to
=
mixed number
5
5
...........................................................
=9÷5
−
5
8
8 1
− =
9 9
b)
5
11
Subtract the numerators
(top numbers) only
=
=
.........................................
© Math’s Mate Blue/Green Skill Builder 9
continues on page 43
Skill 9.3
•
•
•
MMBlue 1 1 2 2 3 3 4 4
MMGreen 1 1 2 2 3 3 4 4
Adding mixed numbers with the same denominator (1).
Add the whole numbers first.
Add the fractions. (see skill 9.1, page 39)
Simplify the resulting fraction and/or change it to a mixed number if necessary.
(see skill 9.1, page 39)
•
Write the result as a mixed number.
Q. 1
3
5
+1 =
10
10
A. 1 + 1 +
5
3
+
10 10
8 ÷2
10 ÷ 2
4
= 2+
5
= 2+
Add the numerators
(top numbers) only
+
Simplify
5
1
10
+
3
1
10
+
=
4
=2
5
=
+
2
8
10
=
2
+
+
2
2
2 +1 =
5
5
a)
b) 1
4
=
5
.........................................
= 3+
d) 3
=
.........................................
1 3
+ =
8 8
1
=
2
.........................................
1
4
1
7
+2 =
12
12
=
page 42
...........................................................
=
=
.........................................
2
1
4
+ =
10 10
2
1
4
+3 =
15
15
=
...........................................................
=
=
.........................................
l)
=
.........................................
2
1
1 +2 =
9
9
i)
=
=
...........................................................
=
.........................................
...........................................................
k)
3 3
+ =
7 7
=
=
1
2
=
=
2
f)
3
3
+ =
10 10
=
.........................................
=
h) 2
1 4
+ =
9 9
=
.........................................
4÷4
Simplify
= 4+
8 ÷4
...........................................................
j)
=
2
5
1 +2 =
9
9
e)
= 4+
3
c)
.........................................
=
g) 4
1
5
+3 =
7
7
=
5 4
+ =
11 11
=
4
5
=
.........................................
www.mathsmate.net
...........................................................
=
=
.........................................
© Math’s Mate Blue/Green Skill Builder 9
continued from page 42
MMBlue 1 1 2 2 3 3 4 4
Skill 9.3
Adding mixed numbers with the same denominator (2).
MMGreen 1 1 2 2 3 3 4 4
5
6
4
2
2
2
m) 1 + 2 =
n) 1 + 4 =
o) 3 + 2 =
7
7
5
3
5
3
Change to
6
mixed number
5
...........................................................
= 3+
1
=
5
.........................................
= 3+1
p) 2
4
=
1
5
5 5
+ =
9 9
=
...........................................................
=
...........................................................
=
=
.........................................
q) 3
=
4 10
+
=
11 11
.........................................
=
3
r)
=
...........................................................
=
8 8
+ =
9 9
=
...........................................................
=
.........................................
=
...........................................................
=
=
.........................................
=
.........................................
+
s)
3
11
7
+2 =
15
15
18 ÷ 3 Simplify
15 ÷ 3
...........................................................
=
6
Change to
mixed number
5
...........................................................
=
= 5+
= 5+
1
=
5
.........................................
= 5+1
v)
4
t)
6
1
5
1
1
1 +4 =
2
2
3 7
+ =
8 8
u) 2
3
3
+3 =
4
4
=
...........................................................
...........................................................
=
...........................................................
=
...........................................................
=
=
.........................................
w) 2
5 11
+
=
12 12
=
.........................................
x)
4
3 9
+ =
10 10
...........................................................
...........................................................
...........................................................
...........................................................
...........................................................
...........................................................
=
.........................................
page 43
=
.........................................
www.mathsmate.net
=
.........................................
© Math’s Mate Blue/Green Skill Builder 9
continues on page 45
Skill 9.4
•
•
•
MMBlue 1 1 2 2 3 3 4 4
MMGreen 1 1 2 2 3 3 4 4
Subtracting mixed numbers with the same denominator (1).
Change mixed numbers to improper fractions before subtracting. (see skill 9.1, page 39)
Subtract the fractions. (see skill 9.2, page 41)
Simplify the resulting fraction and/or change it to a mixed number if necessary.
(see skill 9.1, page 39)
Q. 3
2
5
−1 =
9
9
2
5
A. 3 − 1
9
9
Change to
improper fractions
29 14
Subtract the numerators
−
(top numbers) only
9
9
15
Change to
=
mixed number
9
6 ÷3
Simplify
=1
9 ÷3
=
=1
1
4
3 −1 =
5
5
a)
=
=
b) 3
Subtract the numerators
16 9
−
(top numbers) only
5 5
...........................................................
7
=
5
.........................................
d) 3
1
=
g) 2
3
7
−
=
10 10
1
c)
1
2
4 −1 =
3
3
=
=
=
page 44
2
f)
3
8
−1 =
11 11
...........................................................
=
h) 3
6
=
10 ÷ 2
.........................................
=1
÷2
=
.........................................
=
.........................................
=
2
3
=
=
16
Change to
mixed number
10
...........................................................
5
9
...........................................................
...........................................................
=
1
=
1
5
4 −1 =
9
9
23 7
−
10 10
...........................................................
−
6
15
=1
9
9
.........................................
.........................................
2
9
=
=
=
=
=
=
2
4
−1 =
7
7
=
...........................................................
=
3
...........................................................
e)
=
−
=
2
5
4
6
−1 =
7
7
2
3
2 3 × 9 + 2 29
3 =
=
9
9
9
5 1 × 9 + 5 14
1 =
=
9
9
9
1 5
− =
6 6
=
.........................................
4
i)
5
7
−1 =
12 12
=
...........................................................
...........................................................
=
...........................................................
=
.........................................
www.mathsmate.net
...........................................................
=
=
.........................................
© Math’s Mate Blue/Green Skill Builder 9
continued from page 44
Skill 9.4
•
•
•
MMBlue 1 1 2 2 3 3 4 4
MMGreen 1 1 2 2 3 3 4 4
Subtracting mixed numbers with the same denominator (2).
Subtract the whole numbers first.
Subtract the fractions. (see skill 9.2, page 41)
Simplify the resulting fraction if necessary. (see skill 9.1, page 39)
Hint: For subtractions you may need to convert 1 to an equivalent fraction.
5
3
Example:
numerator = denominator
1 whole circle
=
=
1
5
3
−
1
5
Q. 4 − 2 =
8
8
1 5
A. 4 − 2
8 8
1 5
= 2+ −
8 8
1 5
= 1+ 1 + −
8 8
8 1 5
= 1+ + −
8 8 8
9 5
= 1+ −
8 8
4 ÷4
= 1+
8 ÷4
1
1
= 1+ = 1
2
2
4 − 2 = 2 and
1 5
− =?
8 8
1
5
can not be subtracted from and
8
8
give a positive answer, so borrow a 1
from the 2.
8
(see hint)
8
8 1 8+1 9
+ =
=
8
8 8
8
9 5 9−5 4
− =
=
8
8 8
8
1=
Simplify.
−
j)
4
7
2
−1 =
9
9
2
k)
Subtract the numerators
7
2
(top numbers) only
= 3+ −
9
9
...........................................................
5
=
9
.........................................
= 3+
7
5
−1 =
8
8
8
1
3 −2 =
9
9
l)
=
=
...........................................................
=
=
...........................................................
=
.........................................
=
.........................................
−
m) 4
1
3
−1 =
4
4
n) 3
1
3
−
4
4
...........................................................
=
1
3
−
4
4
...........................................................
=
3
4 1
+ −
4
4 4
...........................................................
=
= 3+
=2+1 +
= 2+
÷2
=
page 45
...........................................................
=
...........................................................
=
...........................................................
1
=
2
.........................................
2
7
−2 =
15 15
=
...........................................................
=
= 2+
o) 4
...........................................................
2
4 ÷2
...........................................................
= 2+
1
5
−1 =
12 12
...........................................................
=
...........................................................
=
.........................................
www.mathsmate.net
...........................................................
=
=
.........................................
© Math’s Mate Blue/Green Skill Builder 9
continues on page 47
MMBlue 1 1 2 2 3 3 4 4
Skill 9.5
•
Subtracting a fraction or a mixed number from a whole number (1). MMGreen 1 1 2 2 3 3 4 4
Write the whole number as an improper fraction with the same denominator as the mixed
number.
Change the mixed number to an improper fraction before subtracting. (see skill 9.1, page 39)
Subtract the fractions. (see skill 9.2, page 41)
Simplify the resulting fraction and/or change it to a mixed number if necessary.
•
•
•
(see skill 9.1, page 39)
Q. 3 − 1
1
=
4
A. 3 − 1
1
4
3 5
−
1 4
12 5
−
=
4 4
7
=
4
3 12
=
1 4
1 1× 4 + 1 5
and 1 =
=
4
4
4
Change to
improper fractions
3 can be written as:
=
=1
2−
a)
=
2
=
9
d) 5 − 2
5 18
1...........................................................
7
= −
35 18
= −
7
7
...........................................................
=
17
=
7
.........................................
g) 4 − 1
7
=
8
7
=
10
=
=
=
4−2
4
=
5
=
page 46
3−1
6
=
11
=
...........................................................
...........................................................
=
=
...........................................................
=
...........................................................
=
=
.........................................
1
=
8
=
.........................................
5−3
i)
5
=
12
=
...........................................................
...........................................................
=
...........................................................
=
=
.........................................
=
=
.........................................
=
f)
=
=
...........................................................
.........................................
...........................................................
1
=
6
...........................................................
...........................................................
...........................................................
=
3−
c)
=
h) 3 − 2
=
5
4
3
7
=1
4
4
=
e)
−
=
=
...........................................................
7
1
9
4
=
7
12
4
=
Subtract the numerators
18 2
= −
(top numbers) only
9 9
...........................................................
16
=
=
9
.........................................
−
Change to
mixed number
3
4
b) 4 −
2 can be written
2 2
2 18
−
as or
9
1
1...........................................................
9
Subtract the numerators
(top numbers) only
=
.........................................
www.mathsmate.net
...........................................................
=
=
.........................................
© Math’s Mate Blue/Green Skill Builder 9
continued from page 46
MMBlue 1 1 2 2 3 3 4 4
Skill 9.5
•
•
•
Subtracting a fraction or a mixed number from a whole number (2). MMGreen 1 1 2 2 3 3 4 4
Subtract the whole numbers first.
Borrow 1 from the whole number and write it as a fraction with the same denominator.
Subtract the fractions. (see skill 9.2, page 41)
−
5
Q. 4 − 1 =
7
5
7
5
= 3−
7
4 − 1 = 3 and 3 = 2 + 1
A. 4 − 1
7
7
7 5 7−5 2
− =
=
7 7
7
7
1=
5
7
7 5
= 2+ −
7 7
2
2
= 2+ = 2
7
7
= 2+1−
4−
j)
2
=
5
2
5
...........................................................
=3+1 −
5 2
= 3+ −
5 5
...........................................................
3
=
5
.........................................
= 3+
−
m) 4 − 2
2
=
3
2
3
...........................................................
2
=1+1 −
3
...........................................................
= 1+ 3 − 2
3 3
...........................................................
1
3
=
3
=
7
...........................................................
=
...........................................................
=
5
=
8
o) 5 − 2
=
page 47
...........................................................
=
=
...........................................................
...........................................................
=
=
...........................................................
=
...........................................................
=
=
.........................................
9
=
10
5 −1
11
=
12
=
...........................................................
...........................................................
=
...........................................................
...........................................................
=
...........................................................
=
=
.........................................
r)
=
.........................................
3
=
10
=
...........................................................
...........................................................
=
.........................................
=
...........................................................
=
=
.........................................
=
=
...........................................................
=
=
=
...........................................................
=
...........................................................
3
=
11
=
q) 3 − 2
=
2−
l)
=
.........................................
p) 4 − 1
5
=
9
n) 2 − 1
= 2−
= 1+
3−
k)
=
.........................................
www.mathsmate.net
...........................................................
=
=
.........................................
© Math’s Mate Blue/Green Skill Builder 9
continues on page 49
Skill 9.6
Adding fractions with different denominators one denominator divides evenly into the other denominator (1).
MMBlue 1 1 2 2 3 3 4 4
MMGreen 1 1 2 2 3 3 4 4
Least Common Multiple (LCM) of two numbers
•
•
Write in ascending order some multiples of the smaller number first.
Write in ascending order some multiples of the bigger number and stop when you find a
multiple that appears in the first list ⇒ Least Common Multiple (LCM).
Hint: The least common multiple is the smallest number that the two numbers divide into.
Examples:
One number divides evenly into the other
number
5
15
5
10
15
20
15 stop
30
45
60
Greatest Common Factor (GCF) of the
numbers is 1
LCM of 5 and 15
Hint: LCM is the largest number.
2
3
2
4
6
8
LCM of 2 and 3
3
stop
6
9
12
Hint: LCM is the product of the numbers.
Equivalent Fractions
same
area
shaded
1
2
2
4
=
3
6
=
4
8
=
different numerators
and denominators
same value
(equivalent fractions)
×2
1
2
=
2× 2 4
×3
1
3
=
2× 3 6
×4
1
4
=
2× 4 8
Equivalent fractions have the same value.
Equivalent fractions are formed by multiplying the numerator and denominator by the same number.
•
•
•
•
Find the least common denominator of the fractions, which is the Least Common Multiple
(LCM) of the denominators. In this case the LCM is the largest denominator.
Change the fractions to equivalent fractions with the least common denominator.
Add the fractions with the same denominators. (see skill 9.1, page 39)
Simplify the resulting fraction and/or change it to a mixed number if necessary.
(see skill 9.1, page 39)
Hint: If unsure which is the LCM of the denominators, use their product as the common denominator.
Examples:
5 1 5 3 8÷2 4
1
+ = + =
= =1
6 2 6 6 6÷2 3
3
OR
page 48
(LCM of 6 and 2 is 6, because 2 divides evenly into 6)
1
5 1 10 6 16 ÷ 4 4
+ =
+
=
= =1
3
6 2 12 12 12 ÷ 4 3
(common denominator of 6 and 2 is 6 × 2 = 12)
www.mathsmate.net
© Math’s Mate Blue/Green Skill Builder 9
continued from page 48
Skill 9.6
Q.
Adding fractions with different denominators one denominator divides evenly into the other denominator (2).
3 3
+ =
10 2
A.
3 3
+
10 2
LCM of 10 and 2
is 10
3 3 ×5
+
10 2 × 5
3 15
+
=
10 10
18 ÷ 2
=
10 ÷ 2
4
9
=
=1
5
5
=
2 1
+ =
9 3
a)
LCM of 9 and 3
is 9
2 1 ×3
9 3 ×3
...........................................................
= +
2 3
=
9 9
.........................................
= +
=
5
9
1 3
+ =
2 8
d)
3 5
+
=
8 16
b)
Change to a mixed number.
LCM of 8 and 16
is 16
=
...........................................................
=
=
=
3×3 1
+
4 × 3 12
...........................................................
9
1
= +
12 12
...........................................................
=
1 3
+
=
5 10
=
=
=
5 1
+ =
6 2
1 7
+
=
2 12
l)
=
...........................................................
=
...........................................................
=
=
.........................................
...........................................................
...........................................................
page 49
=
.........................................
=
=
...........................................................
=
=
.........................................
...........................................................
...........................................................
...........................................................
=
1 5
+
=
6 18
i)
=
k)
=
.........................................
...........................................................
10
=
12
÷2
.........................................
=
=
=
÷2
=
...........................................................
.........................................
=
7 3
+ =
15 5
7
3
+
=
10 20
f)
=
=
h)
=
.........................................
...........................................................
.........................................
3 1
+
=
4 12
1 2
+ =
6 3
c)
=
=
j)
Simplify.
1 1
+ =
4 8
e)
...........................................................
=
Add the fractions.
.........................................
=
g)
To give the second fraction
a denominator of 10,
multiply both the
numerator and
denominator by 5.
3 ×2 5
+
8
× 2 16
...........................................................
=
MMBlue 1 1 2 2 3 3 4 4
MMGreen 1 1 2 2 3 3 4 4
=
.........................................
www.mathsmate.net
...........................................................
=
=
.........................................
© Math’s Mate Blue/Green Skill Builder 9
Skill 9.7
•
MMBlue 1 1 2 2 3 3 4 4
MMGreen 1 1 2 2 3 3 4 4
Adding fractions with different denominators the GCF of the denominators is 1 (e.g. 2 and 3, 5 and 6).
Find the least common denominator of the fractions, which is the Least Common Multiple
(LCM) of the denominators. In this case the LCM is the product of the denominators.
(see skill 9.6, page 48)
•
•
•
Change the fractions to equivalent fractions with the least common denominator.
Add the fractions with the same denominators. (see skill 9.1, page 39)
Simplify the resulting fraction and/or change it to a mixed number if necessary.
(see skill 9.1, page 39)
Q.
1 5
+ =
3 8
A.
1 5
+
3 8
LCM of 3 and 8
is 24
1×8 5×3
+
3×8 8×3
8 15
+
=
24 24
=
=
1 2
+ =
7 3
a)
LCM of 7 and 3
is 21
1×3 2×7
+
=
7×3 3×7
...........................................................
=
3 14
=
+
21
21
.........................................
Add the fractions.
=
=
...........................................................
=
=
.........................................
1 2
+ =
4 3
e)
=
1 4
+ =
2 5
...........................................................
=
.........................................
page 50
2 4
+ =
3 5
=
...........................................................
=
...........................................................
=
=
.........................................
...........................................................
=
=
=
i)
=
...........................................................
=
...........................................................
.........................................
h)
=
=
=
.........................................
3 3
+ =
4 5
2 1
+ =
3 5
f)
...........................................................
=
=
.........................................
=
...........................................................
=
2 3
+ =
7 5
c)
...........................................................
=
g)
23
24
=
17
21
3 2
+ =
5 9
d)
Multiply the numerator and
denominator of the second
fraction by 3.
2 1
+ =
5 6
b)
Multiply the numerator and
denominator of the first
fraction by 8.
=
.........................................
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...........................................................
=
=
.........................................
© Math’s Mate Blue/Green Skill Builder 9
Skill 9.8
•
Subtracting fractions with different denominators one denominator divides evenly into the other denominator.
MMBlue 1 1 2 2 3 3 4 4
MMGreen 1 1 2 2 3 3 4 4
Find the least common denominator of the fractions, which is the Least Common Multiple
(LCM) of the denominators. In this case the LCM is the largest denominator.
(see skill 9.6, page 48)
•
•
•
Change the fractions to equivalent fractions with the least common denominator.
Subtract the fractions with the same denominators. (see skill 9.2, page 41)
Simplify the resulting fraction and/or change it to a mixed number if necessary.
(see skill 9.1, page 39)
Hint: If unsure which is the LCM of the denominators, use their product as the common denominator.
Q.
3 3
−
=
4 20
A.
3 3
−
4 20
LCM of 4 and 20
is 20
3×5 3
−
4 × 5 20
15 3
−
=
20 20
12 ÷ 4
=
20 ÷ 4
=
=
5 2
− =
6 3
a)
LCM of 6 and 3
is 6
5 2 ×2
6 3 ×2
...........................................................
= −
5 4
= −
=
6 6
.........................................
3 5
− =
4 8
d)
=
1
6
4 ×4 3
−
5
× 4 20
...........................................................
=
...........................................................
=
=
2 2
−
=
7 21
e)
=
3 5
−
=
4 12
3×3 5
−
=
4 × 3 12
...........................................................
9
5
= −
12 12
...........................................................
÷4
4
=
12 ÷ 4
.........................................
page 51
3
3
−
=
10 20
f)
=
...........................................................
=
.........................................
...........................................................
=
=
.........................................
5 7
−
=
6 12
h)
=
.........................................
3
3
−
=
10 50
i)
=
=
...........................................................
=
...........................................................
=
...........................................................
=
=
.........................................
=
=
7 1
− =
8 2
c)
.........................................
...........................................................
=
Simplify.
3
5
=
=
g)
Subtract the fractions.
4 3
−
=
5 20
b)
To give the first fraction a
denominator of 20, multiply
both the numerator and
denominator by 5.
=
.........................................
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...........................................................
=
=
.........................................
© Math’s Mate Blue/Green Skill Builder 9
Skill 9.9
MMBlue 1 1 2 2 3 3 4 4
MMGreen 1 1 2 2 3 3 4 4
Subtracting fractions with different denominators the GCF of the denominators is 1 (e.g. 2 and 3, 5 and 6).
•
Find the least common denominator of the fractions, which is the Least Common Multiple
(LCM) of the denominators. In this case the LCM is the product of the denominators.
•
•
•
Change the fractions to equivalent fractions with the least common denominator.
Subtract the fractions with the same denominators. (see skill 9.2, page 41)
Simplify the resulting fraction and/or change it to a mixed number if necessary.
(see skill 9.6, page 48)
(see skill 9.1, page 39)
Q.
4 2
− =
5 3
A.
4 2
−
5 3
LCM of 5 and 3
is 15
4×3 2×5
−
=
=
5×3 3×5
12 10
−
=
15 15
=
3 5
− =
2 9
a)
=
=
LCM of 2 and 9
is 18
3×9 5×2
−
2×9 9×2
...........................................................
27 10
=
−
18
18
.........................................
...........................................................
=
=
.........................................
2 1
−
=
5 12
e)
=
=
.........................................
7 3
− =
9 4
...........................................................
=
=
.........................................
1 3
− =
2 7
h)
=
=
5 2
− =
6 7
...........................................................
=
.........................................
page 52
=
7 2
− =
9 5
=
...........................................................
=
=
.........................................
l)
=
=
...........................................................
.........................................
k)
=
=
=
.........................................
2 3
− =
5 8
2 3
−
=
3 10
i)
...........................................................
=
=
.........................................
=
...........................................................
=
3 3
−
=
5 11
f)
...........................................................
=
=
.........................................
=
=
4 1
− =
5 2
c)
=
=
...........................................................
j)
Subtract the fractions.
...........................................................
=
g)
2
15
=
17
18
5 2
− =
7 3
d)
Multiply the numerator
and denominator of the
second fraction by 5.
5 1
− =
7 4
b)
Multiply the numerator
and denominator of the
first fraction by 3.
=
.........................................
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...........................................................
=
=
.........................................
© Math’s Mate Blue/Green Skill Builder 9