FREE ONLINE MATH WORKSHEET FOR 5TH GRADE

Question 1 :

Peterson had $57 at the end of the game. While playing the game he won $200, lost $150, won $25, lost $10, and lost $35. How much had Peterson had at the beginning in dollars?

(A) 87    (B) 38     (C) 14

Solution :

Money won by Peterson in the game  =  200, 25

Money loss by Peterson in the game  =  150, 10 and 35

Remaining amount he has  =  57

Initial amount  =  200 + 25 - 150 - 10 - 35 + 57

  =  282 - 195

  =  87

Question 2 :

The number of lines of symmetry for a square is

(A) 2     (B) 5      (C) 4

Solution :

Hence line of symmetry is 4.

Question 3 :

Lily is one year younger to her husband Jack. If 650 is the product of their ages. How old is Lily in years?

(A) 12     (B) 15      (C) 25

Solution :

Let x be the age of Jack.

Age of Lily  =  x - 1

Product of ages  =  650

x(x - 1)  =  650

x² - x  =  650

x² - x -  650  =  0

(x - 26) (x + 25)  =  0

x  =  26 and x  =  -25

x - 1  =  25

Hence age of Lily is 25.

Question 4 :

Cameroon is tossing a fair coin two times. What is the probability for getting two heads?

(A) 1/2     (B) 1/4      (C) 1/5

Solution :

Sample space  =  {HH, TT, HT, TH}

n(s)  =  4

Let A be the event of getting two heads.

A  =  {HH}

n(A)  =  1

p(A)  =  n(A)/n(S)

p(A)  =  1/4

Question 5 :

A shirt is sold for $20.00 by a cloth store. The store has decided to raise the price by 20%. After a few days, again they decided to raise the price another 20%. What is the price of the shirt now?

(A) 15.2      (B) 28.8    (C) 10.5

Solution :

Cost price of the shirt  =  20

Raised price  =  20 + 20% of 20

  =  20 + 4

  =  24

After few more days, the shop decided to increase its price by 20% again.

New price after the second increment  =  24 + 20% of 24

  =  24 + 4.8

  =  28.8

Hence the new price is 28.8.

Question 6 :

The list price of a calculator is $130. Amy got 20% discount on list price while buying it. How much did she pay for the calculator?

(A) 142        (B) 150       (C) 104

Solution :

List price of calculator  =  130

Discount  =  20%

New price of calculator after discount 

  =  130 - 20% of 130

  =  130 - 26

  =  104

Hence the price of calculator is 104.

Question 7 :

The ratio of boys to girls on the St.John’s Math Team was 2:3. Four boys joined the team and the ratio changed to 4:5. How many boys are now on the St.John’ Math Team?

(A) 57      (B) 15      (C) 24

Solution :

From the ratio 2 : 3, the number of boys  =  2x and number of girls  =  3x

After four boys admitted in the school, the ratio be changed as 4 : 5.

(2x + 4) :  3x  =  4 : 5

(2x + 4) / 3x  =  4 / 5 

5(2x + 4)  =  4(3x)

10x + 20  =  12x

12x - 10x  =  20

x  =  10

Number of boys initially  =  2x  ==>  2(10)

=  20

After 4 boys admitted  =  20 + 4

  =  24 boys

Question 8 :

The sum and product of the two numbers are 9 and 20 respectively. Which of the smallest of those two numbers ?

(A) 4         (B) 2       (C) 5

Solution :

Let x and y be two numbers.

x + y  =  9 ---(1)

xy  =  20 ----(2)

x  =  9 - y

By applying the value of x in (2), we get

y(9 - y)  =  20

9y - y²  =  20

y² - 9y + 20  =  0

(y - 5) (y - 4)  =  0

y  =  5 and 4

Smallest age is 4.

Question 9 :

The cost 6-inch diameter pizza is $8.00 while the cost of 12- inch diameter pizza is $16.00. Which is the better deal ?

(A) Both         (B) First      (C) Second

Solution :

To choose which is better, we should find the quantity of pizza.

Pizza will be the in the shape of circle.

Area of circle  =  πr²

Radius of pizza that costs $8.00  =  3

  =  π(3)²

  =  9π  -----(1)

Radius of pizza that costs $8.00  =  6

  =  π(6)²

  =  36π 

=  4(quantity of 1st pizza) -----(2)

In case 2, we are getting 4 times more pizza as case 1 for $16.

So, 2nd deal is better.

Question 10 :

In which quadrant does the point (-3,4) lie on ?

(A) 1st       (B) 2nd       (C) 3rd

Solution :

In the given coordinate, x is negative and  y is positive. So the given point lies in second quadrant.

Question 11 :

A farmer harvested 240 apples. He threw away 20 spoiled apples. Then packed remaining apples in packs of 5. Each pack sold for $10. Which of the following represents the correct way to find how much the farmer earned ?

(A) 5 x 10       (B) 240 ÷ 5 - 20 x 10

(C) 240 - 20 ÷ 5 x 10      (D) (240 - 20) ÷ 5 x 10

Solution :

Number of apples harvested = 240

Number of apples thrown away = 20

Number of apples packed = 240 - 20

Number of packets = (240 - 20)/5

Cost of each pack = $10

The required cost,

240 - 20 ÷ 5 x 10

Question 12 :

Mr. Koh bought 5/6 kg of rice. He cooked 3/5 of it. How many kilograms of rice had Mr. Koh left ?

(A)  1/3 kg       (B) 1/2 kg    (C) 7/30 kg      (D) 13/20 kg

Solution :

Quantity of rice purchased = 5/6 kg

Quantity of rice cooked = 3/5 of 5/6 kg

= 3/6 kg

= 1/2 kg

Quantity of rice remaining = 5/6 - 1/2

= (5 - 3)/6

= 2/6

= 1/3 kg

Question 13 :

John used a piece of rope to form a rectangle 5/12 m long and 1/3 m wide. What was the length of rope used 

Solution :

Length of rope = 2(length + width)

= 2(5/12 + 1/3)

= 2(5 + 4)/12

= 2(9/12)

= 1.5 m

So, the length of rope used is 1.5 m.

Question 14 :

The diagram below shows the number pattern represented by the letter A to F.

B + D + F = 27

What is the value of F ?

Solution :

Let x be the numeral in A,

x + 1 = B

x + 3 = D

x + 5 = F

B + D + F = 27

x + 1 + x + 3 + x + 5 = 27

3x + 9 = 27

3x = 27 - 9

3x = 18

x = 18/3

x = 6

F = 6 + 5

= 11

So, the numeral in the place of F is 11.

Question 15 :

Erasers are sold at 10 for $5 and pens are sold at 8 for $6. Julius bought an equal number of erasers and pens for $540. How many pens did he buy ?

Solution :

Let x be the number of package consists of 10 pens in each package.

Let y be the number of packages consist of 8 pens in each pack.

Number of pens purchased = number of erasers purchased 

Cost of 1 pen = 5/10 ==> 0.5

Cost of 1 eraser = 6/8 ==> 0.75

Cost of 1 part = 0.5 + 0.75

= 1.25

Total amount spent for purchase 540

Number of parts = 540/1.25

= 432

432 pens are purchased and 432 erasers has been purchased.

Question 16 :

A computer with a sticker price of 1800 euros is sold with 25% paid upfront and the remaining amount divided into 9 equal installments. How much is each installment that the customer has to pay?

A) 120    B) 135    C) 150    D) 165

Solution :

Amount paid initially = 25%

Rest of the amount to be paid = 75% of 1800

= 0.75(1800)

= 1350

Number of installments = 9

Amount paid on each installment = 1350/9

= 150

Question 17 :

The opposite sides are parallel.

• The sum of the interior angles is 360°.
• The lengths of the diagonals are not equal.
• The diagonals are perpendicular to each other.
• The diagonals bisect each other.

Which polygon do the above properties belong to?

A) Square    B) Rectangle    C) Rhombus    D) Parallelogram

Solution :

In all quadrilateral, the sum of the interior angle measures will be 360 degree. In rhombus, the diagonals will be perpendicular and bisecting as well. So, option (C) is correct.

Question 18 :

If the length of the longer side of the rectangle given above is decreased by 20%, and the length of the shorter side is increased by 10%, how does the perimeter change?

A) Increased by 6       B) Increased by 10

C) Decreased by 12      D) Constant

Solution :

Original length of the rectangle = 40 cm

Width of the rectangle = 20 cm

After decreasing 20% of length, we get

= 80% of 40

= 0.80(40)

= 32 cm

After increasing 10% of width, we get

= 110% of 20

= 1.10 (20)

= 22

Perimeter of the old rectangle = 2(40 + 20)

= 2(60)

= 120 cm

Perimeter of the small rectangle = 2(32 + 22)

= 2(54)

= 108 cm

= 120 - 108 ==> 12

Decrease by 12

Question 19 :

In a school, there are five classes before the lunch break and four classes after the lunch break. Each class is 40 minutes long. There are 10-minute breaks between each class. The lunch break is 45 minutes long. If a student starts the first class at 09:00, what time does the student leave the school? 

Solution :

A) 4 : 55 pm     B) 5 : 05 pm   C) 5 : 15 pm      D) 5 : 30 pm

Let us consider the periods as,

1, 2, 3, 4, 5, _____, 6, 7, 8, 9

In between 1 to 5, there are 4 equal intervals which has 50 minutes duration.

4 x 50 = 200

5th period will be of 40 minutes, lunch break 45 minutes and in between 6 to 9 periods, we get 3 equal intervals with 50 minutes duration.

3 x 50 = 150

Duration of 9th period = 40 minutes

= 200 + 40 + 45 + 150 + 40

= 475 minutes

Dividing 475 by 60, we get

= 420 minutes + 55 minutes

= 7 hours and 55 minutes

= 9 am + 7 hours and 55 minutes

= 16 : 55

Converting into 12 hours clock, we get 4 : 55.

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