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 $9000. 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 ⅕ 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 :

= ⅙ + 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

⅔ miles + ⅗ 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 + ⅗ = ⁽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 :

= (⅓ + ¼ + ⅕) 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 :

= ⅔ x 120

= 2 x 40

= 80

Number of cookies remaning :

= 120 - 80

= 40

Number of cookies given to the friend :

= ⅕ 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. 

(⅓)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 :

= ⅔ of the third angle

= (⅔)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 :

= (⅓)x

Amount of money spent for cookies :

= (¼)(⅔)x

= (⅙)x

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

x - (⅓)x - (⅙)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 - (⅓)x - (⅙)x] = 6(15)

6(x) - 6(⅓)x - 6(⅙)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 = (⅕)t = ᵗ⁄₅

a = (⅓)p

a = (⅓)(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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