DIVIDING FRACTION BY ANOTHER FRACTION

Problem 2 :

3/8 ÷ 6/11

Solution :

= 3/8 ÷ 6/11

Since we change the division sign to multiplication sign. We have to write the reciprocal of 6/11.

= 3/8 ⋅ 11/6

= 33/48

HCF of 33 and 48 is 3. Dividing both numerator and denominator by 3.we get,

= 11/16

Problem 3 :

4/15 ÷ 2/5

Solution :

= 4/15 ÷ 2/5

Since we change the division sign to multiplication sign. We have to write the reciprocal of 2/5.

= 4/15 ⋅ 5/2

= 20/30

HCF of 20 and 30 is 10. Dividing both numerator and denominator by 10.we get,

= 2/3

Problem 4 :

2/5 ÷ 4

Solution :

= 2/5 ÷ 4

Since we change the division sign to multiplication sign. We have to write the reciprocal of 4.

=  2/5 ⋅ 1/4

= 2/20

HCF of 2 and 20 is 2. Dividing both numerator and denominator by 2.we get,

= 1/10

Problem 5 :

1 ÷ 3/5

Solution :

= 1 ÷ 3/5

Since we change the division sign to multiplication sign. We have to write the reciprocal of 3/5.

= 1 ⋅ 5/3

= 5/3

Converting the improper fraction to mixed fraction, we get

= 1  2/3

Problem 6 :

1  1/3 ÷ 3/8

Solution :

=  1  1/3 ÷ 3/8

Converting the mixed fraction to improper fraction, we get

= 4/3 ÷ 3/8

Since we change the division sign to multiplication sign. We have to write the reciprocal of 3/8.

= 4/3 ⋅ 8/3

= 32/9

Converting the improper fraction to mixed fraction, we get

= 3  5/9

Problem 7 :

2/3 ÷ 1  1/2

Solution :

= 2/3 ÷ 1  1/2

Converting the mixed fraction to improper fraction, we get

= 2/3 ÷ 3/2

Since we change the division sign to multiplication sign. We have to write the reciprocal of 3/2.

= 2/3 ⋅ 2/3

= 4/9

Problem 8 :

2  1/4 ÷ 1   2/3

Solution :

= 2  1/4 ÷ 1   2/3

Converting the mixed fraction to improper fraction, we get

= 9/4 ÷ 5/3

Since we change the division sign to multiplication sign. We have to write the reciprocal of 5/3.

= 9/4 ⋅ 3/5

= 27 /20

Converting the improper fraction to mixed fraction, we get

= 1  7/20

Problem 9 :

Without finding the quotient, copy and complete the statement using <, >, or =. Explain your reasoning.

a) 4 ÷ (6/7) ____   4

b)  1 ÷(2/3) _____ 1

c)  4/5 ÷ (9/10) _____ (4/5)

Solution :

a) 4 ÷ (6/7) ____   4

Simplifying the left side :

= 4 ⋅ (7/6)

= 14/3

Comparing :

14/3 > 4

b)  1 ÷ (2/3) _____ 1

Simplifying the left side :

= 1 ÷ (2/3)

= 1 ⋅ (3/2)

= 3/2

Comparing :

3/2 > 1

c)  4/5 ÷ (9/10) _____ (4/5)

Simplifying the left side :

= 4/5 ÷ (9/10)

= (4/5) ⋅ (10/9)

= 8/9

non terminating decimal.

4/5 is terminating decimal.

Comparing :

8/9 > 4/5

Problem 10 :

Evaluate the expression. Write the answer in simplest form.

a) 1/5 ÷ 5 ÷ 3

b)  8 ÷ (4/5) + (7/9) 

c)  11/24 ⋅ [(5/16) ÷ (5/12)]

Solution :

a) 1/5 ÷ 5 ÷ 3

1/5 ÷ (5/1) ÷ (3/1)

= 1/5 ⋅ (1/5) ⋅ (1/3)

= 1/5 ⋅ 1/15

= 1/75

b)  8 ÷ (4/5) + (7/9) 

= 8 ⋅ (5/4) + 7/9

= 2 ⋅ 5 + 7/9

= 10 + 7/9

= (90 + 7)/9

= 97/9

c) 11/24 ⋅ [(5/16) ÷ (5/12)]

= 11/24 ⋅ [(5/16) ⋅ (12/5)]

= 11/24 ⋅ (3/4)

= 11/32

Problem 11 :

How many times larger is a 10-pound dog than a hamster weighing 5/8 pound?

Solution :

Weight of dog = 10 pounds

Weight of hamster = 5/8 pounds

Number of times larger of dog than hamster = 10 / (5/8)

= 10 ⋅ (8/5)

= 2 ⋅ 8

= 16 times

Problem 12 :

A digital camera memory card is 1/4 full. The card is 2/3 full when 375 more pictures have been taken.

a. How many pictures can the memory card hold?

b. How many pictures were originally on the memory card?

Solution :

Let x be the capacity of memory card.

Capcity of memery card = 1/4 of x

1/4 of x + 375 = 2/3 of x

x/4 + 375 = 2x/3

x/4 - 2x/3 = -375

(3x - 8x)/12 = -375

-5x/12 = -375

x = 375(12/5)

= 75(12)

= 900

a. 1/4 of 900

= 1/4 (900)

= 900/4

= 225 pictures

b. The number of pictures the memory card hold = 900

Problem 13 :

There are 3 pieces of pizza left. How many 1/4 pieces of pizza can be sliced from the 3 pieces of pizza?

Solution :

Total number of pieces = 3

Number of 1/4 pieces of pizza can be sliced = 3/(1/4)

= 12 pieces

Total number of 1/4 of pieces of pizzas are 12 pieces.

Problem 14 :

Amber says that 8 ÷ 1  3/4 is the same as 8 x 1  4/3

Is she correct? How do you know?

Solution :

Both area not same.