Word problem with fractions

Here are some examples and solutions of fraction word problems.
The first example is a one-step word problem.
The second example shows how blocks can be used to help illustrate the problem.
The third example is a two-step word problem.

More examples and solutions using the bar modeling method to solve fraction word problems are shown in
the videos. The bar modeling method, also called tape diagrams, are used in Singapore Math and the Common
Core.

Example:
Martha spent
of her allowance on food and shopping. What fraction of her allowance had she left?

Solution:

She had
of her allowance left.

Example:
of a group of children were girls. If there were 24 girls, how many children were there in the group?

Solution:

3 units = 24
1 unit = 24 ÷ 3 = 8
5 units = 5 × 8 = 40

There were 40 children in the group.

Example:
Sam had 120 teddy bears in his toy store. He sold

of them at $12 each. How much did he receive?

Solution:
Step 1: Find the number of teddy bears sold.

He sold 80 teddy bears.

Step 2: Find how much money he received.
80 × 12 = 960

He received $960.

Bar Modeling With Fractions

Examples:

1. Grace thought that a plane journey would take 7/10 hr but the actual journey took 1/5 hr longer.
   How long did the actual journey take?
2. Timothy took 2/3 hr to paint a portrait. This was 1/3 hr shorter than the time he took to paint
   scenery. How long did he take to paint scenery?

• Show Video Lesson

How To Solve Real World Problems Involving Multiplication Of Fractions By Using Visual Fraction Models Or Equations To Represent The Problem?

Examples:

1. At the animal shelter 4/6 of the animals are cats. Of the cats 1/2 are male. What fraction of the
   animals at the shelter are male cats?
2. A taco recipe called for 2/3 cup of cheese per taco. If Andrew wanted to make 3 tacos, how much
   cheese would he need?

• Show Video Lesson

How To Solve Word Problems Using Tape Diagrams And Fraction-By-Fraction Multiplication?

Examples:

1. Ethan is icing 30 cupcakes. He spreads mint icing on 1/5 of the cupcakes and chocolate on 1/2 of the
   remaining cupcakes. The rest will get vanilla frosting. How many cupcakes have vanilla frosting?
2. Maddox puts 1/4 of her lawn-mowing money in savings and uses 1/2 of the remaining money to pay back
   her sister. If she has $15 left, how much did she have at first?

• Show Video Lesson

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problem and check your answer with the step-by-step explanations.

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Fraction word problems are an important piece in teaching fractions. Fractions are a key component of the National Curriculum throughout primary, with children introduced to the concept in Year 1 and continuously building upon their knowledge and understanding, through to Year 6 and beyond.

The abstract nature of fractions makes them one of the more difficult areas of maths for children to understand. It is essential that they are taught through the use of concrete resources and visual images, but also through a link to the real world. Word problems are a great way to help children develop this understanding and should be used alongside any fluency work the children do.

To help you with this, we have put together a collection of 20 word problems which can be used with children from Year 2 to Year 6.

Fraction word problems in the national curriculum

Fractions in KS1

Pupils are first introduced to fractions in Year 1, where they begin to recognise a half and quarter of a shape or quantity. As they progress through Key Stage 1, they are introduced to a wider range of fractions.

In Year 2 pupils need to be able to recognise, find, name and write fractions frac{1}{3}, frac{1}{4}, frac{2}{4} and frac{3}{4} of lengths, shape, a set of objects or quantity.

Fractions in lower KS2

Once pupils move into Key Stage 2, there is an increased focus on fractions, with a significant period of time dedicated to developing students’ knowledge and building on previous learning from Year 3 through to Year 6.

In Year 3, pupils are taught to count in tenths; recognise, find and write fractions of a discrete set of objects; understand the term ‘unit’ and ‘non-unit’ fractions; recognise equivalent fractions, compare and order fractions and add/subtract fractions with the same denominator. At this stage, pupils also begin to solve simple problems involving fractions.

As pupils progress into Year 4, they are also introduced to the concept of decimals alongside the work on fractions. They build upon their understanding of equivalent fractions and adding/subtracting fractions (still with the same denominator.

They also learn to count up and down in hundredths, recognise and write decimals equivalent to frac{1}{4}, frac{1}{2} and frac{3}{4} and begin to solve problems with increasingly harder fractions.

Fractions in upper KS2

As pupils continue through the school, into upper Key Stage 2, they continue to build on their learning. They are introduced to mixed numbers and improper fractions. They are also introduced to the concept of percentages alongside fractions and decimals.

In Year 5, children build on the knowledge gained in Year 4, comparing and ordering fractions; recognising equivalent fractions; addition and subtraction of fractions (with different denominators, but multiples of the same number). Fractions appear in addition and subtraction word problems.

They are also introduced to the multiplication of fractions; converting between improper fractions and mixed numbers and the link between fractions, decimals and percentages. By Year 5 pupils will be completing more complex problems, including multi-step word problems and multiplication word problems.

In Year 6, pupils consolidate and build upon the knowledge of fractions they have gained so far. Pupils continue to add and subtract fractions (with different denominators and mixed numbers). They also develop their understanding of how to multiply fractions and begin to divide fractions by whole numbers, combining fraction and division word problems.

Pupils also continue to build upon their understanding of the equivalences between fractions, decimals and percentages and solve increasingly complex one-step, two-step and multi-step percentage word problems.

Why are word problems important for children’s understanding of fractions?

Word problems, alongside the use of concrete resources and visual images, help children to make sense of the abstract nature of fractions. 

For example, if children were presented with the question frac{6}{8} ÷ 3, some might find this difficult to access. If children are given it as a word problem, alongside a visual image, it becomes much more accessible.

The above calculation as a word problem:

 ‘3 children shared it{frac{6}{8}} of a pizza, how much did each child get?’

Children can see and understand the concept of 3 children sharing 6 slices of pizza, compared to just seeing the written calculation.

How to teach fraction word problem solving in primary school

As with all word problems, the first thing children need to do is read the question carefully and make sure they understand what is being asked. They then have to decide what calculation is needed and whether they can represent it pictorially.

Here is an example:

Ben has a bag of 48 sweets.

He gives frac{3}{8} of his bag to his brother

How many sweets does he have left?

How to solve:

What do you already know?

• There are 48 sweets altogether. 
• The denominator is 8, so we know we need to divide the 48 by 8. This will tell us how many sweets in frac{1}{8} .
• The numerator is 3, therefore we need to multiply the answer by 3, to tell us how many sweets are frac{3}{8} .
• The last step of the problem is to find out how many sweets Ben has left.
• We can either calculate frac{5}{8} , as we know Ben must have frac{5}{8} left, or we subtract the number of sweets in frac{3}{8} from the total of 48.

How can this be drawn/represented pictorially?

• We can draw a bar model, split into 8 sections. 
• The 48 sweets are then shared between the 8 sections (each worth frac{1}{8} ). 
• We can see that frac{3}{8} of the 48 sweets equals 18 sweets. 
• We can then either subtract 18 from 48, to work out how many sweets were left. 48 – 18 = 30
• Alternatively, we can calculate how many sweets are in frac{5}{8} , which is 30.

Word problems are tied in throughout Third Space Learning’s online one-to-one tuition programmes. Tutors work with students to break down word problems and identify the operations needed to solve problems.

Fraction word problems for primary 

The following section lays out the types of fraction word problems that you can expect to see by year group in primary school. 

At Third Space Learning we incorporate word problems into our one-to-one online tutoring. With each lesson designed to suit the needs of each individual student, our tutoring programme aims to deepen mathematical understanding and confidence in maths. 

Fraction word problems are a great way to strengthen students’ conceptual understanding of fractions and grow their problem solving skills. 

Fraction word problems for Year 2

Word problems in Year 2 involve recognising and naming simple fractions and beginning to understand the concept of equivalence.

Fraction word problems for Year 3

Word problems for Year 3 include proper fractions, fractions of amounts, simple equivalent fractions and adding and subtracting fractions with the same denominator. 

Fraction word problems for Year 4

Word problems for year 4 include equivalent fractions, fractions of quantities (including non-unit fractions and adding/subtracting fractions with the same denominator. Money word problems often appear in Year 4.

Fraction word problems for Year 5

Word problems for Year 5 include more complex equivalent fractions, problems involving mixed numbers and improper fractions, adding and subtracting fractions (with different denominators) and multiplying fractions.

Fraction word problems for Year 6

Word problems for year 6 include adding and subtracting fractions with different denominators and mixed numbers, multiplying fractions, dividing fractions by whole numbers and finding equivalent fractions, decimals and percentages.

More word problems resources

Third Space Learning offers a wide range of practice word problems for all primary year groups and covering a large number of topics, including; time word problems, ratio word problems, addition word problems and subtraction word problems.

In word problems on fraction we will solve different types
of problems on multiplication of fractional numbers and division of fractional
numbers.

2. Rachel took (frac{1}{2}) hour to paint a table and (frac{1}{3}) hour to paint a chair. How much time did she take in all?

3. If 3(frac{1}{2}) m of wire is cut from a piece of 10 m
long wire, how much of wire is left?

Total length of the wire = 10 m

Fraction of the wire cut out = 3(frac{1}{2}) m = (frac{7}{2})
m

Length of the wire left = 10 m – 3(frac{1}{2}) m

            = [(frac{10}{1}) — (frac{7}{2})] m,    [L.C.M. of 1, 2 is 2]

            = [(frac{20}{2}) — (frac{7}{2})]
m,    [(frac{10}{1}) × (frac{2}{2})]

            = [(frac{20 — 7}{2})] m

            = (frac{13}{2}) m

            = 6(frac{1}{2}) m

4. One half of the students in a school are girls, 3/5 of
these girls are studying in lower classes. What fraction of girls are studying
in lower classes?

Solution:

Fraction of girls studying in school = 1/2

Fraction of girls studying in lower classes = 3/5 of 1/2

                                                            =
3/5 × 1/2

                                                            = (3 × 1)/(5 × 2)

                                                            =
3/10

Therefore, 3/10 of girls studying in lower classes.

Questions and Answers on Word problems on Fractions:

1. Shelly walked (frac{1}{3}) km. Kelly walked (frac{4}{15})
km. Who walked farther? How much farther did one walk than the other?

2. A frog took three jumps. The first jump was (frac{2}{3})
m long, the second was (frac{5}{6}) m long and the third was (frac{1}{3})
m long. How far did the frog jump in all?

3. A vessel contains 1(frac{1}{2}) l of milk. John drinks
(frac{1}{4}) l of milk; Joe drinks (frac{1}{2}) l of milk. How much of
milk is left in the vessel?

● Multiplication is Repeated Addition.

● Multiplication of Fractional Number by a Whole Number.

● Multiplication of a Fraction by Fraction.

● Properties of Multiplication of Fractional Numbers.

● Multiplicative Inverse.

● Worksheet on Multiplication on Fraction.

● Division of a Fraction by a Whole Number.

● Division of a Fractional Number.

● Division of a Whole Number by a Fraction.

● Properties of Fractional Division.

● Worksheet on Division of Fractions.

● Simplification of Fractions.

● Worksheet on Simplification of Fractions.

● Word Problems on Fraction.

● Worksheet on Word Problems on Fractions.

5th Grade Numbers 

5th Grade Math Problems 

From Word Problems on Fraction to HOME PAGE

A great variety of fraction word problems with solutions. These word problems will help you find out when you need to add, subtract, multiply or divide fractions.

1. Sarah knows 8 of the 25 students in her class. Write a fraction showing the number of students Sarah knows.

2. Peter correctly solved 18 out of the 20 math problems the teacher gave him. Write a fraction showing the number of math problems Peter solved correctly.

Solution

18/20

3. Darlene ate 3/5 of her pizza. How much pizza can Darlene share with her sister?

Solution

1 represents the entire pizza. To find how much pizza is left, just do 1 — 3/5

1 — 3/5 = 1/1 — 3/5 = 5/5 — 3/5 = 2/5

Darlene can share 2/5 of the pizza.

4. Last week, Steve spent 3 1/2 hours playing soccer and 4 1/2 hours playing table tennis. How much time did Steve spend playing both sports?

5. John jogged 1 3/4 miles yesterday and 2 1/2 miles today. How many miles did John spend jogging for the past two days?

1 + 2 = 3

3/4 + 1/2 = 3/4 + 2/4 = 5/4

John jogged 3 5/4 miles for the past two days.

6. Maria bought a pizza and ate half of it. Then, she gave the leftover to his brother and his brother ate half of it. How much of the pizza did his brother eat? 

Solution

The brother ate half of half the pizza.

Half of half = 1/2 of 1/2 = 1/2 × 1/2 = 1/4

7. Anthony caught some fish that weighted 6 1/2 pounds. If he gave 4 1/4 pounds of fish to some friends, how much fish does he have for himself?

Solution

Subtract 4 1/4 from 6 1/2.

6 — 4 = 2

1/2 — 1/4 = 2/4 — 1/4 = 1/4

Anthony has 2 1/4 pounds of fish for himself.

8. 1/4 of a tablespoon of baking soda is needed to make a loaf of bread. How many loaves of bread can be made with 5 tablespoons of baking soda?

Solution

Divide 5 by 1/4

5  ÷ 1/4 = 5/1 ÷ 1/4 = 5/1  × 4/1 = 20/1 = 20

20 loaves of bread can be made.

9. A recipe calls for 2 1/8 cups of butter for a casserole. How much butter is needed to make 6 1/2 casseroles?

2  1/8  × 6 1/2 = (2 × 8 + 1)/8 × (6 × 2 + 1)/2

2  1/8  × 6 1/2 = 17/8 × 13/2 = (17 × 13)/(8 × 2)  

2  1/8  × 6 1/2 = 221/16 = 13.8125

To make 6 1/2 casseroles, the recipe will need 13.8125 cups of butter. 

10. Kevin cooked 8 1/4 pounds of meat for a dinner. If each serving is 3/4 pound, how many servings did he prepare?

Solution

Just divide 8 1/4 by 3/4

8 1/4 ÷ 3/4 = (8 × 4 + 1)/4 ÷ 3/4 = 33/4 ÷ 3/4 = 33/4 × 4/3 = 132/12 = 11

Kevin prepared 11 servings.

Featured here is a vast collection of fraction word problems, which require learners to simplify fractions, add like and unlike fractions; subtract like and unlike fractions; multiply and divide fractions. The fraction word problems include proper fraction, improper fraction, and mixed numbers. Solve each word problem and scroll down each printable worksheet to verify your solutions using the answer key provided. Thumb through some of these word problem worksheets for free!

Problem 1 :

A cookie factory uses ¼ of a barrel of oatmeal in each batch of cookies. The factory used ½ of a barrel of oatmeal yesterday. How many batches of cookies did the factory make ?

Solution :

Amount of oatmeal used in each batch of cookies is

= ¼ of a barrel

No. of cookies made yesterday is

= Oatmeal used yesterday/Oatmeal used in each batch

= ½ ÷ ¼

= ½ ⋅ ⁴⁄₁

= 2

The factory made 2 batches of cookies yesterday.

Problem 2 :

Of the students in the band, ¼ play the flute and another ⅒play 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 :

= ¼ + ⅒

Least common  multiple of the denominators (4, 10) is 20.

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

= ⁽¹ ˣ ⁵⁾⁄₍₄ ₓ ₅₎ + ⁽¹ ˣ ²⁾⁄₍₁₀ ₓ ₂₎

= ⁵⁄₂₀ + ²⁄₂₀

= ⁽⁵ ⁺ ²⁾⁄₂₀

= ⁷⁄₂₀

Fraction of the students who play either the flute or the clarinet is ⁷⁄₂₀.

Problem 3 :

Lily rode her bicycle ⁵⁄₄ miles from her house to the park. Then she rode ³⁄₂ miles from the park to the library. How many miles did Lily ride in all ?

Solution :

Total number of miles that Lily rode in all is

= ⁵⁄₄ + ³⁄₂

Least common  multiple of the denominators (4, 2) is 4.

Make each denominator as 4 by multiplying the numerator and denominator of the first fraction by 1 and the second fraction by 2.

= ⁽⁵ ˣ ¹⁾⁄₍₄ ₓ ₁₎ + ⁽³ ˣ ²⁾⁄₍₂ ₓ ₂₎

= ⁵⁄₄ + ⁶⁄₄

= ⁽⁵ ⁺ ⁶⁾⁄₄

= ¹¹⁄₄

= 2¾

Lily rode 2¾ miles in all.

Problem 4 :

At the dealership where Mary works, she fulfilled ⅙ of her quarterly sales goal in January and another ³⁄₁₀ of her sales goal in February. If her quarterly sales goal is $12,000, what amount of sales did she make in January and February ?

Solution :

Fraction of her sales done in January and February is

= ⅙ + ³⁄₁₀

Least common multiple of the denominators (6, 10) is 30.

make each denominator as 30 by multiplying the numerator and denominator of the first fraction by 5 and the second fraction by 3.

Then we have,

= ⁽¹ ˣ ⁵⁾⁄₍₆ ₓ ₅₎ + ⁽³ ˣ ³⁾⁄₍₁₀ ₓ ₃₎

= ⁵⁄₃₀ + ⁹⁄₃₀

= ⁽⁵ ⁺ ⁹⁾⁄₃₀

= ¹⁴⁄₃₀

= ⁷⁄₁₅

Amount of sales she made in January and February is

= ⁷⁄₁₅ of quarterly sales goal 

= ⁷⁄₁₅ ⋅ 12000

= 5600

Amount of sales Mary made in January and February is $5,600.

Problem 5 :

Lucy made strawberry jam and raspberry jam. She made enough strawberry jam to fill ⅚ of a jar. If she made 2 times as much raspberry jam as strawberry jam, how many jars would the raspberry jam fill ?

Solution :

Amount of strawberry jam made by Lucy is

= ⅚ of a jar

2 times as much raspberry jam as strawberry jam is

= 2 ⋅ ⅚ of a jar

= ⁵⁄₃ of a jar

= 1⅔ of a jar

Lucy would make enough raspberry jam to fill 1⅔ jars.

Problem 6 :

David’s salary is $1800. David spent 2/3 of the total money for food. He spent 1/2 of the remaining for his kids education and saved the rest. How much did he save ?

Solution :

Money spent on food  is

= ⅔ ⋅ 1800

= 1200

Remaining = 1800 — 1200

= 600 —-(1)

Money spent on kids education is

= 1/2 of remaining

= 1/2 ⋅ 600

= 300 —-(2)

Then, his savings is

= (1) — (2)

= 600 — 300

= 300

David saved $300.

Problem 7 :

A, B and C are friends. A has one-third of the money that B has. C has one-half of the money that A has. If they all together have  $450. How much money do A, B and C have separately? 

Solution :

Let us assume that B has the money y.

Then,

A = (⅓)y = ʸ⁄₃

C = ½ of A

C = ½ ⋅ ʸ⁄₃

C = ʸ⁄₆

Given : A, B and C together have $450.

A + B + C = 450

ʸ⁄₃ + y + ʸ⁄₆ = 450

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(ʸ⁄₃ + y + ʸ⁄₆) = 6(450)

6(ʸ⁄₃) + 6(y) + 6(ʸ⁄₆) = 2700

2y + 6y + y = 2700

9y = 2700

y = 300

ʸ⁄₃ = ³⁰⁰⁄₃ = 100

ʸ⁄₆ = ³⁰⁰⁄₆ = 50 

A has $100, B has $300 and C has $50.

Problem 8 :

John’s present age is one-third of David’s age 5 years back. If David is 20 years old now, find the present age of John.

Solution :

Present age of David = 20 years.

David’s age 5 years back = 20 — 5 = 15 years

Given : John’s present age is 1/3 of David’s age 5 years back.

John’s present age :

= ⅓ of 15 years

= (⅓) ⋅ 15

= 5 years

Problem 9 :

In a triangle, the first angle is one-half of the third angle and the second angle is three-fourth of the third angle. Find the three angles of the triangle.

Solution :

In the triangle, since both the first and second angles are linked to the third angle, introduce a variable for the third angle and  write the first and second angles in terms of that variable and solve for it.

Let x be the measure of the third angle.

First angle = (½)x = ˣ⁄₂

Second angle = (¾)x = ³ˣ⁄₄

In a triangle, sum of the three angles is equal to 180°.

first angle + second angle + third angle = 180°

ˣ⁄₂ + ³ˣ⁄₄ + x = 180°

Least commpon  multiple of the denominator (2, 4) is 4.

Multiply both sides of the equation by 4 to get rid of the denominators 2 and 4.

4(ˣ⁄₂ + ³ˣ⁄₄ + x) = 4(180°)

4(ˣ⁄₂) + 4(³ˣ⁄₄) + 4(x) = 720°

2x + 3x + 4x = 720°

9x = 720°

x = 80°

ˣ⁄₂ = ⁸⁰⁄₂ = 40°

³ˣ⁄₄ = ⁽³ ˣ ⁸⁰⁾⁄₄ = 60°

The three angles of the triangle are 40°, 60° and 80°.

Problem 10 :

The denominator of a fraction is 1 more than thrice the numerarotor. If 2 be added to both numerator and denominator, the fraction would become ⅓. Find the fraction.

Solution :

Let x be the numerator.

Then, the denominator is (4x + 1).

Fraction = ˣ⁄₍₄ₓ ₊ ₁₎

Given : Adding 2 to both numerator and denominator of the fraction results ⅓.

⁽ˣ ⁺ ²⁾⁄₍₄ₓ ₊ ₁ ₊ ₂₎ = ⅓

⁽ˣ ⁺ ²⁾⁄₍₄ₓ ₊ ₃₎ = ⅓

3(x + 2) = 1(4x + 3)

3x + 6 = 4x + 3

6 = x + 3

3 = x

4x + 1 = 4(3) + 1

= 12 + 1

= 13

Sustitute x = 3 and 4x + 1 = 13 in (1).

Fraction = ³⁄₁₃

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Example 1: Rachel rode her bike for one-fifth of a mile on Monday and two-fifths of a mile on Tuesday. How many miles did she ride altogether?

Analysis: To solve this problem, we will add two fractions with like denominators.

Solution: 

Answer: Rachel rode her bike for three-fifths of a mile altogether.

---

Example 2: Stefanie swam four-fifths of a lap in the morning and seven-fifteenths of a lap in the evening. How much farther did Stefanie swim in the morning than in the evening?

Analysis: To solve this problem, we will subtract two fractions with unlike denominators.

Solution: 

Answer: Stefanie swam one-third of a lap farther in the morning.

---

Example 3: It took Nick five-thirds of an hour to complete his math homework on Monday, three-fourths of an hour on Tuesday, and five-sixths of an hour on Wednesday. How many hours did he take to complete his homework altogether?

Analysis: To solve this problem, we will add three fractions with unlike denominators. Note that the first is an improper fraction.

Solution:

Answer: It took Nick three and one-fourth hours to complete his homework altogether.

---

Example 4: Dina added five-sixths of a bag of soil to her garden. Her neighbor Natasha added eleven-eighths bags of soil to her garden. How much more soil did Natasha add than Dina?

Analysis: To solve this problem, we will subtract two fractions with unlike denominators.

Solution: 

Answer:

---

Example 5: At a pizza party, Diego and his friends ate three and one-fourth cheese pizzas and two and three-fourths pepperoni pizzas. How much pizza did they eat in all?

Analysis: To solve this problem, we will add two mixed numbers, with the fractional parts having like denominators.

Solution:

Answer: Diego and his friends ate six pizzas in all.

---

Example 6: The Cocozzelli family drove their car for five and five-sixths days to reach their vacation home, and then drove for six and one-sixth days to return home. How much longer did it take them to drive home?

Analysis: To solve this problem, we will subtract two mixed numbers, with the fractional parts having like denominators.

Solution: 

Answer: The Cocozzelli family took one-half more days to drive home.

---

Example 7: A warehouse has 12 and nine-tenths meters of tape in one area of the building, and eight and three-fifths meters of tape in another part. How much tape does the warehouse have in all?

Analysis: To solve this problem, we will add two mixed numbers, with the fractional parts having unlike denominators.

Solution: 

Answer: The warehouse has 21 and one-half meters of tape in all.

---

Example 8: An electrician has three and seven-sixteenths cm of wire. He needs only two and five-eighths cm of wire for a job. How much wire does he need to cut?

Analysis: To solve this problem, we will subtract two mixed numbers, with the fractional parts having unlike denominators.

Solution: 

Answer: The electrician needs to cut 13 sixteenths cm of wire.

---

Example 9: A carpenter had a piece of wood that was 15 feet in length. If he needs only 10 and five-twelfths feet of wood, then how much wood should he cut?

Analysis: To solve this problem, we will subtract a mixed number from a whole number.

Solution:

Answer: The carpenter needs to cut four and seven-twelfths feet of wood.

---

Summary: In this lesson we learned how to solve word problems involving addition and subtraction of fractions and mixed numbers. We used the following skills to solve these problems: 

1. Add fractions with like denominators.
2. Subtract fractions with like denominators.
3. Find the LCD.
4. Add fractions with unlike denominators.
5. Subtract fractions with unlike denominators.
6. Add mixed numbers with like denominators.
7. Subtract mixed numbers with like denominators.
8. Add mixed numbers with unlike denominators.
9. Subtract mixed numbers with unlike denominators.

---

Exercises

Directions: Subtract the mixed numbers in each exercise below. Be sure to simplify your result, if necessary. Click once in an ANSWER BOX and type in your answer; then click ENTER. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR.

Note: To write the fraction three-fourths, enter 3/4 into the form. To write the mixed number four and two-thirds, enter 4, a space, and then 2/3 into the form.

1.	A recipe needs 3/4 teaspoon black pepper and 1/4 red pepper. How much more black pepper is needed than red pepper for this recipe?

2.	One evening, a restaurant served a total of 1/2 of a loaf of wheat bread and 7/8 of a loaf of white bread. How many loaves were served in all?

3.	Robin and Kelly own neighboring cornfields. Robin harvested 4 and 3/10 acres of corn on Monday and Kelly harvested 2 and 1/10 acres. How many more acres did Robin harvest than Kelly?

4.	Juanita needed 3 and 2/3 hours to take a standardized test, and Jordan needed 5 and 1/4 hours. How much more time did Jordan need than Juanita to take the test?

5.	An airline agent checked in 10 and 1/3 kg of baggage for one passenger and another 8 and 5/6 kg of baggage for his travel companion. How many kilograms of luggage did the agent check in all?