WORD PROBLEMS ON FRACTIONS AND DECIMALS

Problem 1 : 

Each part of a multipart question on a test is worth the same number of points. The whole question is worth 37.5 points. Daniel got 1/2 of the parts of a question correct. How many points did Daniel receive ?

Solution :

To find the total points received by Daniel, we have to multiply 1/2 and 37.5 

We can solve this word problem using the two methods explained below. 

Method 1 : 

Step 1 :

Convert the decimal 3.75 as the fraction 75/2

(1/2) x 37.5  =  (1/2) x (75/2) 

Step 2 :

Multiply. Write the product in simplest form.

(1/2) x (75/2)  =  75/4  =  18¾

So, Daniel received 18¾ points. 

Method 2 : 

Step 1 :

Convert the fraction 1/2 as the decimal 0.5

(1/2) x 37.5  =  0.5 x 37.5

Step 2 :

Multiply. 

0.5 x 37.5  =  18.75

So, Daniel received 18.75 points. 

Problem 2 : 

The bill for a pizza was $14.50. Charles paid for 3/5 of the bill. How much did he pay ?

Solution :

To find the amount paid by Charles, we have to multiply 3/5 and 14.50 

We can solve this word problem using the two methods explained below. 

Method 1 : 

Step 1 :

Convert the decimal 14.50 as the fraction 29/2

(3/5) x 14.50  =  (3/5) x (29/2) 

Step 2 :

Multiply. Write the product in simplest form.

(3/5) x (29/2)  =  87/10  =  8⁷⁄₁₀

So, Charles paid $8⁷⁄₁₀. 

Method 2 : 

Step 1 :

Convert the fraction 3/5 as the decimal 0.6

(3/5) x 14.50  =  0.6 x 14.50

Step 2 :

Multiply. 

0.6 x 14.50  =  8.7

So, Charles paid $8.7

Problem 3 :

The inner radius of a pipe is 12.625 mm and the outer radius is 18.025 mm. Find the thickness of the pipe.

Solution :

Thickness of the pipe is 

=  Outer radius - Inner radius

=  18.025 - 12.625

=  5.40 mm

Problem 4 :

Jennifer bought 6.5 kg of sugar. she used 3750 grams. How many kilograms of sugar were left ?

Solution :

3750 grams  =  3750/1000 kg

3750 grams  =  3.75 grams

Amount of sugar left (in kilograms) is 

=  6.5 - 3.75

2.75 kg

Problem 5 :

Of the students in the band, 1/4 play the flute and another 1/10 play the clarinet. What fraction of the students in the band play either the flute or the clarinet ?

Solution :

Fraction of the students in the band play either the flute or the clarinet is 

=  1/4 + 1/10

LCM of (4, 10) is 20. 

So, make each denominator as 20 by multiplying the numerator and denominator of the first fraction by 5 and the second fraction by 2. 

Then we have, 

=  (1 ⋅ 5) / (4 ⋅ 5)  +  (1 ⋅ 2) / (10 ⋅ 2)

=  5/20 + 2/20

=  (5 + 2)/20

=  7/20

So, the fraction of the students who play either the flute or the clarinet is 7/20.

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