WORKSHEET ON FRACTIONS WORD PROBLEMS

Problem 1 :

One-sixth of the students in a band play flute and another one-fourth of the students play piano. What fraction of the students in the band play either the flute or piano?

Problem 2 :

Adam walks regular in the morning. He walks two-third of a mile in the first 35 minutes and three fifth of a mile in the next 25 minutes. How many miles does he walk in 1 hour?

Problem 3 :

Jessica is a sales representative in a store. In January, she had a sales target of $20000. She completed one-fourth of the target in the first two weeks, one-third in the third week and one-fifth in the last week of January. Find the amount of sales done by Jessica in January.

Problem 4 :

Noah has 120 cookies. He ate two-third of them and gave one-fifth of the remianing cookies to his friend. How many cookies did Noah give his friend?

Problem 5 :

One-third of John's present age is equal to his age 10 years ago. Find the present age of John.

Problem 6 :

In a triangle, measure of the first angle is one half of measure the second angle and measure of the second hangle is two-third of measure the third third angle. Find the measures of three angles of the triangle.

Problem 7 :

James had some money. He spent one-third of the money for buying candies and one-fourth of the remaning amoney for buying cookies. After having bought candies and cookies, he has left $15. Find the amount money James had in the begining.

Problem 8 :

Three students Andrew, Peter and Thomas participated in a quiz competition. Andrew scored ⅓ of the points scored by Peter and Peter scored  of the points sored by Thomas. If they all together had scored 760 points, how many points did Andrew, Peter and Thomas score separately?

Answers

1. Answer :

Fraction of the students in the band play either the flute or piano :

=  + ¼

Least common multiple of the denominators (6, 4) is 12.

Make each denominator as 12 by multiplying the numerator and denominator of the first fraction by 2 and the second fraction by 3.

= ⁽¹ ˣ ²⁾⁄₍₆ ₓ ₂₎  +  ⁽¹ ˣ ³⁾⁄₍₄ ₓ ₃₎

= ²⁄₁₂ + ³⁄₁₂

= ⁽² ⁺ ³⁾⁄₁₂

= ⁵⁄₁₂

2. Answer :

35 minute + 25 minutes = 60 minutes

35 minutes + 25 minutes = 1 hour

 miles + miles + = ?

Least common multiple of the denominators 3 and 5 is 15.

Make each denominator as 15 by multiplying the numerator and denominator of the first fraction by 5 and the second fraction by 3.

⅔ + = ⁽² ˣ ⁵⁾⁄₍₃ ₓ ₅₎ ⁽³ ˣ ³⁾⁄₍₅ ₓ ₃₎

= ¹⁰⁄₁₅ ⁹⁄₁₅

= ⁽¹⁰ ⁺ ⁹⁾⁄₁₅

¹⁹⁄₁₅

= 1⁴⁄₁₅

Adam walks 1⁴⁄₁₅ miles in 1 hour.

3. Answer :

Amount of sales Jessica completed in January :

= ( + ¼ ) x 9000

Least common multiple of the denominatoirs (3, 4, 5) is 60.

Make each denominator as 60 by multiplying the numerator and denominator of each fraction by an appropriate number. 

= (²⁰⁄₆₀ + ¹⁵⁄₆₀ + ¹²⁄₆₀) x 9000

= ⁽²⁰ ⁺ ¹⁵ ⁺ ¹²⁾⁄₆₀ x 9000

= ⁴⁷⁄₆₀ x 9000

= 47 x 150

= $7050

4. Answer :

Numberb of cookies eaten by Noah :

= 120

= 2 x 40

= 80

Number of cookies remaning :

= 120 - 80

= 40

Number of cookies given to the friend :

 x 40

= 8

5. Answer :

Let x be the present age of John.

Jhon's age ten years ago = x - 10

Given : One-third of John's present age is equal to his age 10 years ago. 

()x = x - 10

Multiply both sides by 3.

x = 3(x - 10)

x = 3x - 30

Subtract 3x from both sides.

-2x = -30

Divide both sides by -2.

x = 15

The present age of John is 15 years.

6. Answer :

Let x be the measure of the third amngle.

Measure of the second angle :

=  of the third angle

= ()x

²ˣ⁄₃

Measure of the first angle :

= ½ of the second angle

= (½)(²ˣ⁄₃)

ˣ⁄₃

In a triangle, three angles add up to 180°.

first angle + second angle + third angle = 180°

ˣ⁄₃ + ²ˣ⁄₃ + x = 180°

Multiply both sides by 3 to get rid of the denominators.

3(ˣ⁄₃ + ²ˣ⁄₃ + x) = 3(180°)

3(ˣ⁄₃) + 3(²ˣ⁄₃) + 3(x) = 3(180°)

x + 2x + 3x = 540°

6x = 540°

x = 90°

ˣ⁄₃ = ⁹⁰⁄₃ = 30°

²ˣ⁄₃ = ⁽² ˣ ⁹⁰⁾⁄₃ = 60°

The three angles of the triangle are 30°, 60° and 90°.

7. Answer :

Let x be the amount of money that James had in the begining.

Amount of money spoent for candies :

= ()x

Amount of money spent for cookies :

= (¼)()x

= ()x

Given : After having bought candies and cookies, James has left $15.

x - ()()= 15

Least common multiple of the denominators (3, 6) is 6. Multiply both sides of the equation by 6 to get rid of the denominators 3 and 6.

6[x - ()()x] = 6(15)

6(x) - 6()- 6()x = 90

6x - 2x - x = 90

3x = 90

Divide both sides by 3.

x = 30

James had $30 in the begning.

8. Answer :

Let a, p and t be the points scored by Andrew, Peter and Thomas score separately.

p = ()ᵗ⁄₅

a = ()p

a = ()(ᵗ⁄₅)

a = ᵗ⁄1₅

Given : Andrew, Peter and Thomas together scored 760 points.

a + p + t = 760

ᵗ⁄1₅ + ᵗ⁄₅ + t = 760

Least common multiple of the denominators 15 and 5 is 15.

Multiply both sides of the euation by 15 to get rid of the denominatos 15 and 5.

15(ᵗ⁄1₅ + ᵗ⁄₅ + t) = 15(760)

15(ᵗ⁄1₅) + 15(ᵗ⁄₅) + 15(t) = 11400

t + 3t + 15t = 11400

19t = 11400

t = 600

a = ᵗ⁄1₅ ⁶⁰⁰⁄₁₅ = 40

p = ᵗ⁄₅ ⁶⁰⁰⁄₅ = 120

Therefore, Andrew scored 40 points, Peeter scored 120 points and Thomas scored 600 points.

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