MULTIPLYING FRACTIONS

Problem 1 :

2/15 × 5/6

Solution :

= (2/15) × (5/6)

= 10/90

HCF of 10 and 90 is 10.

So, dividing the numerator and denominator by 10. We get,

= 1/9

Problem 2 :

6/7 × 1/3

Solution :

= (6/7) × (1/3)

= 6/21

HCF of 6 and 21 is 3.

So, dividing the numerator and denominator by 3. We get,

= 2/7

Problem 3 :

3 × 3/6

Solution :

= 3 × 3/6

= (3/1) × (3/6)

= 9/6

HCF of 9 and 6 is 3.

So, dividing the numerator and denominator by 3. We get,

= 3/2

= 1  1/2

Problem 4 :

2/3 × 7

Solution :

= (2/3) × (7/1)

= 14/3

HCF of 14 and 3 is 1.

So, dividing the numerator and denominator by 1. We get,

= 14/3

= 4 2/3

Problem 5 :

1  1/3 × 6/7

Solution :

= 1  1/3 × 6/7

Converting the mixed fraction into improper fraction, we get

= (4/3) × (6/7)

= 24/21

HCF of 24 and 21 is 3.

So, dividing the numerator and denominator by 3. We get,

= 8/7

= 1  1/7

Problem  6 :

1  1/8 × 4/9

Solution :

= 1  1/8 × 4/9

= (9/8) × (4/9)

= 36/72

HCF of 36 and 72 is 6.

So, dividing the numerator and denominator by 6. We get,

= 6/12

= 1/2

Problem 7 :

(2  1/2)²

Solution :

= (2  1/2)²

Converting the mixed fraction to improper fraction, we get

= (5/2)²

= (5/2) x (5/2)

= 25/4

Converting the improper fraction to mixed fraction, we get

= 6  1/4

Problem 8 :

(1  1/3)³

Solution :

= (1  1/3)³

Converting the mixed fraction to improper fraction, we get

= (4/3)³

= (4/3) x (4/3) x (4/3)

= 64/27

Converting the improper fraction to mixed fraction, we get

= 2  10/27

Problem 9 :

You have 2/3 of a bag of flour. You use 3/4 of the flour to make empanada dough. How much of the entire bag do you use to make the dough?

Solution :

Quantity of flour yoyu have = 2/3 of flour

Quantity of flour used to make empanada dough = 3/4 of flour

= 3/4 of 2/3 of flour

= 3/4 x 2/3

Quantity of flour used to make the dough = 1/2

Quantity of flour remaining = 1/2 of flour.

Problem 10 :

In an aquarium, 2/5 of the fish are surgeon fish. Of these, 3/4 are yellow tangs. What fraction of all fi sh in the aquarium are yellow tangs?

Solution :

Fraction of fishes which are yellow tangs = 3/4 of 2/5

= 3/4 x 2/5

After simplifying it, we get

= 3/10

Problem 11 :

You exercise for 3/4 of an hour. You jump rope for 1/3 of that time. What fraction of the hour do you spend jumping rope?

Solution :

Fraction of the hour you spend jumping rope = 1/3 of 3/4 of an hour

= 1/3 x 3/4

= 1/4 of an hour.

Problem 12 :

About 9/10 of the weight of a watermelon is water. How many pounds of water are in the watermelon?

Solution :

Weight of water melon = 20 lbs

Quantity of water in the water melon = 9/10 of weight

= 9/10 of 20

= 9/10 x 20

= 9 x 2

= 18 lbs

So, the quantity of water in the water melon is 18 lbs.

Problem 13 :

Evaluate the expression when a = 3/4, b = 1/6 , and c = 2/5.

a)  a ⋅ 5/12

b)  4/7 ⋅ b

c)  a ⋅ b

d)  c ⋅ a

e) (5/9) a + 1/9

f) 14/15 − (7/12) c

g)  bc + 2/3

h)  ab + c

Solution :

a)  a ⋅ 5/12

Applying a = 3/4, we get

= (3/4) ⋅ (5/12)

= 5/16

b)  4/7 ⋅ b

Applying b = 1/6, we get

= 4/7 ⋅ (1/6)

= 2/21

c)  a ⋅ b

Applying a = 3/4 and b = 1/6, we get

= (3/4) ⋅ (1/6)

= 1/8

d)  c ⋅ a

Applying a = 3/4 and c = 2/5 , we get

= (3/4) ⋅ (2/5)

= 3/10

e) (5/9) a + 1/9

Applying a = 3/4, we get

= (5/9) ⋅ (3/4) + 1/9

= 5/12 + 1/9

LCM of (9, 12) = 36

= (15 + 4)/36

= 19/36

f) 14/15 − (7/12) c

Applying c = 2/5, we get

= 14/15 − (7/12) (2/5)

= 14/15 + 7/30

LCM of 15 and 30 = 30

= (28 + 7)/15

= 35/15

7/3

g)  bc + 2/3

Here b = 1/6 , and c = 2/5

= (1/6) (2/5) + 2/3

= 1/15 + 2/3

= (1 + 10)/15

= 11/15

h)  ab + c

Here a = 3/4, b = 1/6 , and c = 2/5.

= (3/4) (1/6) + 2/5

= 1/8 + 2/5

= (5 + 16)/40

= 21/40