INTERPRETING FRACTIONS INVOLVING ALL OPERATIONS WORD PROBLEMS

Problem 1 :

Tina’s mother baked a cake. When she was finished, she cut the cake in half. Then she cut each of these pieces in half. Finally, she cut each of these last pieces in half.

Part A :

How many equal pieces of cake did she have when she was finished ?

Part B :

What unit fraction represents each piece of cake ?

Solution :

Part A :

Part B :

Each piece represents 1/8.

Problem 2 :

Prasad and Victoria are in the same class and have the same homework. Prasad has done 1/4 of his homework. Victoria has done 2/8 of her homework. Has Victoria done a greater part of the homework ?

Solution :

Work done by Prasad = 1/4

Work done by Victoria = 2/8

= 1/4

Both did same amount of work.

Problem 3 :

Jamal's father ordered a pizza. The pizza has 8 slices. The order called 4 slices with sausage, 2 slices with mushrooms, and 2 slices with peppers.

a) what fraction of pizza has sausage ?

b) What fraction of the pizza has mushrooms ?

c) What fraction of the pizza does not have peppers ?

Solution :

Number of slices = 8

Number of slices with sausage = 4

Number of slices with mushrooms = 2

Number of slices with peppers = 2

a) fraction of pizza with sausage = 4/8 ==> 1/2

b) Fraction of pizza with mushrooms = 2/8 ==> 1/4

c) Fraction of pizza with peppers = 2/8 ==> 1/4

Problem 4 :

Sean made fresh fruit salad for his sister's birthday party. He cut up 2 bananas, 2 oranges, 3 apples and 1 small pine apple. What fraction of these fruit were oranges ?

Solution :

Total number of fruits = 2 + 2 + 3 + 1

= 8

Fraction part of fruit that are oranges = 2/8

= 1/4

Problem 5 :

Jessica checked her piggy bank. She found that she had 2 quarters, 1 dime, 2 nickels and 3 pennies. What fraction of the coins in Jessica's piggy bank were either nickels or pennies ?

Solution :

Total number of coins = 2 + 1 + 2 + 3

= 8

Number of coins that are nickels or pennies = 2 + 3

= 5

Fraction of coins that are nickels or pennies = 5/8

Problem 6 :

A vase has 6 flowers in it. There are 3 roses, 1/3 are peonies, and the rest are lilies. What fraction of the flowers are lilies ?

Solution :

Number of roses = 3

Number of peonies = 1/3 of 6

= (1/3) x 6

= 2

Number of flowers which are lilies = 6 - (3 + 2)

= 6 - 5

= 1

Fraction of flowers which are lilies = 1/6

Problem 7 :

Jane has 8 pairs of socks. She has 2 pairs of white socks, 4 pairs of black socks, 1 pair of pink socks and 1 pair of purple socks. Which equivalent fraction represent the pairs of black socks that Jane has ?

a)  2/8        b)  4/8     c)  1/4     d) 1/2

Solution :

Total number of pair of socks Jane has = 8

Fraction part of white socks = 2/8  ==> 1/4

Fraction part of black socks that Jane has = 4/8

So, option b is correct.

Problem 8 :

Choose the number for the numerator that makes the fraction ?/8 equivalent to the fraction 3/4

a)   3     b)  4     c)  5      d)  6

Solution :

3/4 = ?/8

? = 6

3/4 = 6/8

So, option d is correct.

Problem 9 :

Tamara drew the star at the right and shaded it as shown. Write the fraction that represents the shaded parts of the star.

Solution :

Total number of equal parts = 6

Number of shaded part = 3

Fraction part of shaded = 3/6

= 1/2

Problem 10 :

A small cake is divided into 6 equal pieces. Which fraction shows how much cake is left in 4 pieces have been eaten ?

a)  1/6      b)  2/6    c)  3/6       d)  4/6

Solution :

Number of equal pieces = 6

4 pieces have been eaten. Fraction part of pieces have been eaten

= 4/6

= 2/3

Problem 11 :

Eric has 4 marbles. He had 3 green marbles and 1 purple marble. Write the fraction that represents the part of marble that are not purple.

Solution :

Total number of marbles = 4 + 3 + 1

= 8

Fraction of marble that are not purple = (4 + 3) / 8

= 7/8

Problem 12 :

Erica made 4 of the 8 shots she attempted in one basketball game. Tyler attempted 6 shot and made same fraction of his shots that Erica made. How many shots did Tyler make ?

Solution :

Erica made = 4/8

Tyler made = ?/6

Simplifying the first fraction, we get 1/2. To make ?/6 equivalent to 4/8, we have to replace 3 as ?. So, the number of shorts made by Tyler = 3.