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 = 18 3/4
So, Daniel received 18 3/4 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 = 8 7/10
So, Charles paid $8 7/10.
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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