RATIO AND PROPORTION WORKSHEET

Ratio and Proportion Worksheet :

Worksheet given in this section will be much useful for the students who would like to practice problems on ratio and proportion. 

Before look at the worksheet, if you would like to know the stuff related to ratio and proportion,

Please click here

Ratio and Proportion Worksheet - Problems

Problem 1 :

Simplify the ratio : 

16 cm / 4 m

Problem 2 : 

Simplify the ratio : 

12 ft / 24 in.

Problem 3 : 

The perimeter of rectangle PQRS shown below is 60 centimeters. The ratio of PQ : QR is 3 : 2. Find the length and width of the rectangle. 

Problem 4 : 

The ratios of the side lengths of ΔABC to the corresponding side lengths of ΔPQR are 2 : 1. Find the unknown lengths. 

Problem 5 :

The measure of the angles in ABC are in the extended ratio of 1 : 2 : 3. Find the measures of the angles. 

Problem 6 :

Solve the proportion : 

6 / x  =  12 / 5

Problem 7 :

Solve the proportion : 

3 / (p + 2)  =  2 / p

Problem 8 :

The photo below shows a painting. The actual painting is 12 inches high. How wide is it ?

Ratio and Proportion Worksheet - Solutions

Problem 1 :

Simplify the ratio : 

16 cm / 4 m

Solution : 

To simplify ratios with unlike units, convert to like units so that the units divide out. Then simplify the fraction, if possible.

16 cm / 4 m  =  16 cm / 4 ⋅ 100 cm

16 cm / 4 m  =  16 cm / 400 cm

16 cm / 4 m  =  16 / 400

16 cm / 4 m  =  1 / 25 or 1 : 25

Problem 2 : 

Simplify the ratio : 

12 ft / 24 in.

Solution : 

The given two quantities are in different units.

That is, the first one is in feet and the second in inches.

As we did in the first example, we can convert them into like units and then simplify the fraction, if possible.

12 ft / 24 in.  =  12 ⋅ 12 in. / 24 in.

12 ft / 24 in.  =  144 in. / 24 in.

12 ft / 24 in.  =  144 / 24

12 ft / 24 in.  =  6 / 1 or 6 : 1

Problem 3 : 

The perimeter of rectangle PQRS shown below is 60 centimeters. The ratio of PQ : QR is 3 : 2. Find the length and width of the rectangle. 

Solution : 

Because the ratio of PQ : QR is 3 : 2, we can represent the length PQ as 3x and the width QR as 2x.

2l + 2w  =  p

Substitute l  =  3x and w  =  2x. 

2(3x) + 2(2x)  =  60

Simplify. 

6x + 4x  =  60

10x  =  60

Divide both sides by 10. 

x  =  6

So, we have 

length  =  3 ⋅ 6  =  18 cm

width  =  2 ⋅ 6  =  12 cm

Hence, rectangle PQRS has a length of 18 centimeters and a width of 12 centimeters.

Problem 4 : 

The ratios of the side lengths of ΔABC to the corresponding side lengths of ΔPQR are 2 : 1. Find the unknown lengths. 

Solution : 

From the given information and the diagram shown above, we can consider the following points. 

• AB is twice PQ and AB = 8, so PQ  =  1/2 ⋅ 8  =  4 in. 
• Using the Pythagorean Theorem, we can determine that QR  =  5.
• AC is twice PR and PR = 3, so AC  =  2 ⋅ 3  =  6 in. 
• BC is twice QR and QR = 5, so BC  =  2 ⋅ 5  =  10 in. 

Problem 5 :

The measure of the angles in ABC are in the extended ratio of 1 : 2 : 3. Find the measures of the angles. 

Solution : 

Begin by sketching a triangle. Then use the extended ratio of 1 : 2 : 3 to label the measures of the angles as x°, 2x°, and 3x°.

By Triangle Sum Theorem, 

x° + 2x° + 3x°  =  180°

x + 2x + 3x  =  180

Simplify.

6x  =  180

Divide both sides by 6. 

x  =  30

So, we have

x°  =  30°

2x°  =  2 ⋅ 30°  =  60°

3x°  =  3 ⋅ 30°  =  90°

Hence, the angle measures are 30°, 60° and 90°.

Problem 6 :

Solve the proportion : 

6 / x  =  12 / 5

Solution : 

Write the original proportion.

6 / x  =  12 / 5

By reciprocal property, we have

x / 6  =  5 / 12 

Multiply each side by 6.

6 ⋅ (x / 6)  =  (5 / 12) ⋅ 6

Simplify.

x  =  5 / 2

Problem 7 :

Solve the proportion : 

3 / (p + 2)  =  2 / p

Solution : 

Write the original proportion.

3 / (p + 2)  =  2 / p

By cross product property, we have

3p  =  2(p + 2)

3p  =  2p + 4

Subtract 2p from both sides. 

p  =  4

Problem 8 :

The photo below shows a painting. The actual painting is 12 inches high. How wide is it ?

Solution :

We can reason that in the photograph all measurements of the artist’s painting have been reduced by the same ratio.

That is, the ratio of the actual width to the reduced width is equal to the ratio of the actual height to the reduced height.

The photograph is 1¼ inches by 4⅜ inches.

Problem Solving Strategy :

Multiply each side by 4.375

4.375 ⋅ (x / 4.375)  =  (12 / 1.25) ⋅ 4.375

Simplify. 

x  =  (12 / 1.25) ⋅ 4.375

Using calculator, we have

x  =  42

So, the actual painting is 42 inches wide.

After having gone through the stuff given above, we hope that the students would have understood, how to solve problems on ratio and proportion. 

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

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

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