SOLVING MULTI STEP PROBLEMS WITH FRACTIONS AND MIXED NUMBERS WORKSHEET

Solving Multi Step Problems with Fractions and Mixed Numbers Worksheet :

Worksheet given in this section will be much useful for the students who would like to practice solving multi step problems with fractions and mixed numbers. 

Solving Multi Step Problems with Fractions and Mixed Numbers Worksheet - Problems

Problem 1 :

A fruit merchant bought mangoes in bulk. He sold 5/8 of the mangoes. 1/16 of the mangoes were spoiled. 300 mangoes remained with him. How many mangoes did he buy ?

Solution :

Let x be the number of mangoes that the merchant bought.

Number of mangoes sold is 

=  (5/8) ⋅ x

=  5x / 8

Number of mangoes spoiled is

=  (1/16⋅ x

=  x / 16

Number of mangoes remaining is 300. 

Then, we have 

x - (5x/8 + x/16)  =  300

x - (10x/16 + x/16)  =  300

x - 11x/16  =  300

16x/16 - 11x/16  =  300

(16x - 11x) / 16  =  300

5x / 16  =  300

Multiply each side by 16.

5x  =  4800

Divide each side by 5

x  =  960

So, the number of mangoes bought by the merchant is 960.

Problem 2 :

A family requires 2 1/2 liters of milk per day.How much milk would family require in a month of 31 days ?  

Solution :

Milk required per day is 2 1/2 liters. 

Then, number of liters of milk required for 31 days is

=  31 ⋅ 2 1/2

=  31 ⋅ 5/2

=  155/2

=  77 1/2

So, the family would require 77 1/2 liters of milk for 31 days. 

Problem 3 :

A ream of paper weighs 12 1/2 kg What is the weight per quire, if 20 quire make one ream ? 

Solution : 

Weight of 1 ream of paper  =  12 1/2 kg

Because one ream is equal to 20 quire, we have 

Weight of 20 quire paper  =  12 1/2 kg

Weight of 1 quire paper  =  (12 1/2) ÷ 20 kg

Weight of 1 quire paper  =   (25/2) ÷ 20 kg

Weight of 1 quire paper  =   25/(2 ⋅ 20) kg

Weight of 1 quire paper  =   25/40 kg

Weight of 1 quire paper  =   5/8 kg

Problem 4 :

It was Richard's birthday. He distributed 6 kg of sweets among her friends. If he gave 1/8 kg of sweet to each. How many friends were there ?  

Solution :

Total quantity of sweet distributed is 6 kg. 

If each friend receives 1/8 kg, then the number of friends is 

=  6 ÷ (1/8)

=  6 ⋅ 8

=  48

So, 48 friends were there.

Problem 5 :

6 students went on a picnic. One student agreed to bear half of the expenses. The remaining 5 students shared the remaining expenses equally. What fraction of the total expenses does each of 5 students pay ?

Solution : 

Let x be the total expense 

Given : One student agreed to bear half of the expenses.

So, the remaining expenses is x/2. 

Given : The remaining expenses is shared by 5 students equally.

Then, the share of each student is 

=  (x/2) ÷ 5

=  x / 10

=  (1/10) ⋅ x

So, 1/10 of the total expenses is shared by each of 5 students. 

Problem 6 :

I have 2 1/2 times money that David has. If i have $100, how much money does David have ? 

Solution :

Let x be the money that David has. 

Then, we have

(2 1/2) ⋅ x  =  100

(5/2) ⋅ x  =  100

5x / 2  =  100

Multiply each side by 2. 

5x  =  200

Divide each side by 5.

x  =  40

So, David has $40. 

Problem 7 :

In a basket there are two kinds of sweet packets. There are 7 packets of the first kind each weighing 1 1/4 kg and 9 packets of the second kind each weighing 3/4 kg . What is the total weight of the sweets in the basket ?

Solution : 

First Kind :

Weight of each packet  is 1 1/4 kg.

Number of packets is 7.

Then, the total weight is

=  7 ⋅ (1 1/4) kg

=  7 ⋅ (5/4) kg

=  35/4 kg -----(1)

Second Kind :

Weight of each packet  is 3/4 kg.

Number of packets is 9.

Then, the total weight is

=  9 ⋅ (3/4) kg

=  27/4 kg -----(2)

Weight (1st kind) + Weight (2nd kind)  =  35/4 + 27/4 

Weight (1st kind) + Weight (2nd kind)  =  (35 + 27) / 4

Weight (1st kind) + Weight (2nd kind)  =  62 / 4

Weight (1st kind) + Weight (2nd kind)  =  15 1/2

So, the total weight of sweets in the basket is 15 1/2 kg.

Problem 8 :

How many half-liter bottles can be filled from a can containing 37 1/2 liters of milk ? 

Solution : 

Total quantity of milk is 37 1/2 liters. 

Number of half liter bottles can be filled is 

=  (37 1/2) ÷ (1/2)

=  (75/2) ÷ (1/2)

=  (75/2) ⋅ (2/1)

=  75

So, 75 half-liter bottles can be filled. 

Problem 9 :

A gentleman bought 200 liters of milk for a function. 4/5 of it was used for preparing candies. 3/4 of the remaining milk was used for preparing coffee. How much of the milk is remaining ?   

Solution : 

Total quantity of milk is 200 liters.   fraction word problems 9

Milk used for preparing candies is 

=  (4/5) ⋅ 200

=  160 liters

Remaining milk (after milk used for preparing sweets) is

=  200 - 160

=  40 liters

Given : 3/4 of the remaining milk was used for preparing coffee. 

So, the quantity of milk was used for preparing coffee is 

=  (3/4) ⋅ 40

=  30 liters

Milk used for preparing candies and coffee  is

=  160 + 30

=  190 liters

Remaining quantity of milk (after milk used for preparing sweets and coffee) is

=  200 - 190

=  10 liters

Problem 10 :

Two third of a tank can be filled in 18 minutes. How many minutes will it require to fill the whole tank ?  

Solution : 

Let x be the capacity of the whole tank. 

Given : Two third of a tank can be filled in 18 minutes

Then, we have

(2/3) ⋅ x -----> 18 minutes

x -----> 18 ⋅ (3/2) minutes

x -----> 27 minutes 

So, it will take 27 minutes to fill the whole tank. 

After having gone through the stuff given above, we hope that the students would have understood, how to solve multi step problems with fractions and mixed numbers. 

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

Widget is loading comments...

You can also visit our following web pages on different stuff in math. 

ALGEBRA

Variables and constants

Writing and evaluating expressions

Solving linear equations using elimination method

Solving linear equations using substitution method

Solving linear equations using cross multiplication method

Solving one step equations

Solving quadratic equations by factoring

Solving quadratic equations by quadratic formula

Solving quadratic equations by completing square

Nature of the roots of a quadratic equations

Sum and product of the roots of a quadratic equations 

Algebraic identities

Solving absolute value equations 

Solving Absolute value inequalities

Graphing absolute value equations  

Combining like terms

Square root of polynomials 

HCF and LCM 

Remainder theorem

Synthetic division

Logarithmic problems

Simplifying radical expression

Comparing surds

Simplifying logarithmic expressions

Negative exponents rules

Scientific notations

Exponents and power

COMPETITIVE EXAMS

Quantitative aptitude

Multiplication tricks

APTITUDE TESTS ONLINE

Aptitude test online

ACT MATH ONLINE TEST

Test - I

Test - II

TRANSFORMATIONS OF FUNCTIONS

Horizontal translation

Vertical translation

Reflection through x -axis

Reflection through y -axis

Horizontal expansion and compression

Vertical  expansion and compression

Rotation transformation

Geometry transformation

Translation transformation

Dilation transformation matrix

Transformations using matrices

ORDER OF OPERATIONS

BODMAS Rule

PEMDAS Rule

WORKSHEETS

Converting customary units worksheet

Converting metric units worksheet

Decimal representation worksheets

Double facts worksheets

Missing addend worksheets

Mensuration worksheets

Geometry worksheets

Comparing  rates worksheet

Customary units worksheet

Metric units worksheet

Complementary and supplementary worksheet

Complementary and supplementary word problems worksheet

Area and perimeter worksheets

Sum of the angles in a triangle is 180 degree worksheet

Types of angles worksheet

Properties of parallelogram worksheet

Proving triangle congruence worksheet

Special line segments in triangles worksheet

Proving trigonometric identities worksheet

Properties of triangle worksheet

Estimating percent worksheets

Quadratic equations word problems worksheet

Integers and absolute value worksheets

Decimal place value worksheets

Distributive property of multiplication worksheet - I

Distributive property of multiplication worksheet - II

Writing and evaluating expressions worksheet

Nature of the roots of a quadratic equation worksheets

Determine if the relationship is proportional worksheet

TRIGONOMETRY

SOHCAHTOA

Trigonometric ratio table

Problems on trigonometric ratios

Trigonometric ratios of some specific angles

ASTC formula

All silver tea cups

All students take calculus 

All sin tan cos rule

Trigonometric ratios of some negative angles

Trigonometric ratios of 90 degree minus theta

Trigonometric ratios of 90 degree plus theta

Trigonometric ratios of 180 degree plus theta

Trigonometric ratios of 180 degree minus theta

Trigonometric ratios of 180 degree plus theta

Trigonometric ratios of 270 degree minus theta

Trigonometric ratios of 270 degree plus theta

Trigonometric ratios of angles greater than or equal to 360 degree

Trigonometric ratios of complementary angles

Trigonometric ratios of supplementary angles 

Trigonometric identities 

Problems on trigonometric identities 

Trigonometry heights and distances

Domain and range of trigonometric functions 

Domain and range of inverse  trigonometric functions

Solving word problems in trigonometry

Pythagorean theorem

MENSURATION

Mensuration formulas

Area and perimeter

Volume

GEOMETRY

Types of angles 

Types of triangles

Properties of triangle

Sum of the angle in a triangle is 180 degree

Properties of parallelogram

Construction of triangles - I 

Construction of triangles - II

Construction of triangles - III

Construction of angles - I 

Construction of angles - II

Construction angle bisector

Construction of perpendicular

Construction of perpendicular bisector

Geometry dictionary

Geometry questions 

Angle bisector theorem

Basic proportionality theorem

ANALYTICAL GEOMETRY

Analytical geometry formulas

Distance between two points

Different forms equations of straight lines

Point of intersection

Slope of the line 

Perpendicular distance

Midpoint

Area of triangle

Area of quadrilateral

Parabola

CALCULATORS

Matrix Calculators

Analytical geometry calculators

Statistics calculators

Mensuration calculators

Algebra calculators

Chemistry periodic calculator

MATH FOR KIDS

Missing addend 

Double facts 

Doubles word problems

LIFE MATHEMATICS

Direct proportion and inverse proportion

Constant of proportionality 

Unitary method direct variation

Unitary method inverse variation

Unitary method time and work

SYMMETRY

Order of rotational symmetry

Order of rotational symmetry of a circle

Order of rotational symmetry of a square

Lines of symmetry

CONVERSIONS

Converting metric units

Converting customary units

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations 

Word problems on linear equations 

Word problems on quadratic equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation 

Word problems on unit price

Word problems on unit rate 

Word problems on comparing rates

Converting customary units word problems 

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles 

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems 

Profit and loss word problems 

Markup and markdown word problems 

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed 

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS 

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6