MENU
❌
Home
Math Forum/Help
Problem Solver
Practice
Algebra
Geometry
Tests
College Math
History
Games
MAIN MENU
1 Grade
Adding and subtracting up to 10
Comparing numbers up to 10
Adding and subtracting up to 20
Addition and Subtraction within 20
2 Grade
Adding and Subtracting up to 100
Addition and Subtraction within 20
3 Grade
Addition and Subtraction within 1000
Multiplication up to 5
Multiplication Table
Rounding
Dividing
Perimeter
Addition, Multiplication, Division
4 Grade
Adding and Subtracting
Addition, Multiplication, Division
Equivalent Fractions
Divisibility by 2, 3, 4, 5, 9
Area of Squares and Rectangles
Fractions
Equivalent Fractions
Least Common Multiple
Adding and Subtracting
Fraction Multiplication and Division
Operations
Mixed Numbers
Decimals
Expressions
6 Grade
Percents
Signed Numbers
The Coordinate Plane
Equations
Expressions
Polynomials
Symplifying Expressions
Polynomial Vocabulary
Polynomial Expressions
Factoring
7 Grade
Angles
Inequalities
Linear Functions
8 Grade
Congurence of Triangles
Linear Functions
Systems of equations
Slope
Parametric Linear Equations
Word Problems
Exponents
Roots
Quadratic Equations
Quadratic Inequalities
Rational Inequalities
Vieta's Formulas
Progressions
Arithmetic Progressions
Geometric Progression
Progressions
Number Sequences
Reciprocal Equations
Logarithms
Logarithmic Expressions
Logarithmic Equations
Trigonometry
Trigonometry
Identities
Trigonometry
Trigonometric Inequalities
Extremal value problems
Numbers Classification
Geometry
Intercept Theorem
Slope
Law of Sines
Law of Cosines
Vectors
Probability
Limits of Functions
Properties of Triangles
Pythagorean Theorem
Matrices
Complex Numbers
Inverse Trigonometric Functions
Analytic Geometry
Analytic Geometry
Circle
Parabola
Ellipse
Conic sections
Polar coordinates
Integrals
Integrals
Integration by Parts
Trigonometric Substitutions
Differential Equations
Home
Practice
Equivalent Fractions
Equivalent Fractions: Problems with Solutions
By Catalin David
Problem 1
Are the fractions pictured in the two drawings equivalent?
Yes
No
Solution:
The fraction pictured in the first drawing is [tex] \frac{2}{4}[/tex] and the fraction pictured in the second drawing is [tex] \frac{1}{2} [/tex]. The two fractions are equivalent because the blue zones are equal.
The numerator and the denominator of the first fraction are two times greater than the numerator and the denominator of the second fraction. At the same time, 2 x 2 = 1 x 4
Problem 2
John cut his pizza into 6 equal slices and ate two of them. Tim cut his pizza(the same size) into 3 equal slices and ate one of them. Did they eat the same amount of pizza?
Yes
No
Solution:
These drawings show the slices eaten by the two of them. John ate [tex] \frac{2}{6}[/tex] of the pizza, while Tim ate [tex]\frac{1}{3}[/tex] of the pizza. The two fractions are equivalent so both of them eat the same amount.
Problem 3
Are the fractions pictured in the two drawings equivalent?
Yes
No
Solution:
The fraction pictured in the first drawing is [tex]\frac{2}{6}[/tex] and the fraction pictured in the second drawing is [tex]\frac{1}{3}[/tex]. The two fractions are equivalent because the numerator and the denominator of the first fraction are two times greater than the numerator and the denominator of the second fraction.
Problem 4
Are the fractions pictured in the two drawings equivalent?
Yes
No
Solution:
The fraction pictured in the first drawing is [tex]\frac{3}{4}[/tex] and the fraction pictured in the second drawing is [tex]\frac{1}{2}[/tex]. The two fractions are not equivalent because the red zones are not equal and 3 × 2 = 6 and 4 × 1 = 4
Problem 5
Are the fractions pictured in the two drawings equivalent?
Yes
No
Solution:
The fraction pictured in the first drawing is [tex] \frac {3}{6}[/tex] and the fraction pictured in the second drawing is [tex]\frac {4}{8}[/tex]. The two fractions are equivalent because $3 \times 8 = 6 \times 4 = 24$.
Problem 6
Are the fractions [tex] \frac{2}{3}[/tex] and [tex]\frac {6}{7} [/tex] equivalent?
Yes
No
Solution:
The numerator of the second fraction is 3 times greater than the numerator of the first fraction. The denominator of the second fraction is not 3 times greater than the denominator of the first fraction. In this case, they're not equivalent.
Problem 7
Are the fractions [tex]\frac{9}{6}[/tex] and [tex]\frac{6}{4}[/tex] equivalent?
Yes
No
Solution:
We verify if, in this case, the condition of equivalence of two fractions is true. If [tex]\frac{a}{b} = \frac{c}{d}[/tex] then a × d = b × c . In our case, 9 × 4 = 6 × 6 = 36 Then the fractions are equivalent.
Problem 8
The fraction [tex] \frac {3}{5}[/tex] is equivalent to
[tex]\frac{6}{8}[/tex]
[tex]\frac{6}{10}[/tex]
[tex]\frac{3}{10}[/tex]
[tex]\frac{9}{10}[/tex]
Solution:
[tex]\frac{6}{10}[/tex] because the numerator and the denominator of the second fraction are two times greater than the numerator and the denominator of [tex]\frac {3}{5}[/tex].
Problem 9
Which fraction is equivalent to [tex]\frac{21}{12}[/tex]?
[tex]\frac{7}{12}[/tex]
[tex]\frac{21}{4}[/tex]
[tex]\frac{7}{4}[/tex]
[tex]\frac{7}{2}[/tex]
Solution:
[tex]\frac{7}{4}[/tex] because the numerator and the denominator of the second fraction are three times smaller than the numerator and the denominator of the first fraction.
Problem 10
Which two fractions are equivalent to [tex]\frac{4}{6}[/tex]
[tex]\frac{3}{2}, \frac{12}{18}[/tex]
[tex]\frac{8}{10}, \frac{12}{18}[/tex]
[tex]\frac{2}{4}, \frac{1}{4}[/tex]
[tex]\frac{2}{3}, \frac{12}{18}[/tex]
Solution:
To find fractions equivalent to the given one, it's enough to multiply or divide the numerator and the denominator by the same number. 4÷2 = 2, 6÷2=3, so a fraction equivalent with [tex] \frac {4}{6}[/tex] is [tex] \frac {2}{3}[/tex]. 4 × 3 = 12, 6 × 3 = 18, so another fraction equivalent with [tex] \frac {4}{6}[/tex] is [tex] \frac {12}{18}[/tex].
Problem 11
Can 3, 5, 6, and 10 form 2 equivalent fractions?
Yes
No
Solution:
4 numbers form 2 equivalent fractions if the results of the multiplication of each numerator with the denominator of the other fraction are equal. We observe that $3 \times 10 = 5 \times 6$. The fractions are [tex] \frac {3}{5} = \frac {6}{10} [/tex]
Problem 12
Create 2 equivalent fractions with the numbers 4, 9, 2, and 18.
$\frac{2}{18} =\frac{4}{9}$
$\frac{2}{4} =\frac{18}{9}$
$\frac{9}{2} =\frac{4}{18}$
$\frac{2}{9} =\frac{4}{18}$
Solution:
We're searching for pairs of numbers which, when multiplied, have the same product. We observe that 4 x 9 = 18 x 2 = 36, so the fractions will be [tex] \frac {2}{9} and \frac {4}{18} [/tex]
Problem 13
Calculate the value of x,
if $\frac{2}{5} = \frac{4}{x}$
Solution:
$\frac{2}{5} = \frac{4}{10}$
$\frac{4}{10} = \frac{4}{x}$ => $x = 10$
Problem 14
If [tex]\frac{1}{4}=\frac {a}{12}[/tex], then
a
=
Solution:
If [tex]\frac{a}{b} = \frac{c}{d} [/tex] then a × d = b × c. In our case, 1 × 12 = 4 × a
12 = 4 × a
a = 12 ÷ 4 = 3
Another solution:
We notice that the denominator of the second fraction is three times greater than the denominator of the first fraction. Thus, the numerator of the second fraction is three times greater than the numerator of the first fraction. Consequently, a = 3.
Problem 15
If [tex]\frac{5}{a} = \frac{20}{28}[/tex] then
a
is
Solution:
5 is 4 times less than 20, so
a
is 4 times less than 28
a = 28 ÷ 4 = 7
Problem 16
If [tex] \frac {a}{3} = \frac {4}{6} [/tex], then
a
=
Solution:
a × 6 = 3 × 4
a × 6 = 12
a = 12 ÷ 6 = 2
Problem 17
If [tex] \frac {6}{2} = \frac {15}{a} [/tex], then
a
is
Solution:
6 × a = 2 × 15
6 × a = 30
a = 30 ÷ 6 = 5
Problem 18
If the fraction [tex]\frac{9}{6}[/tex] is equivalent to [tex]\frac{6}{a}[/tex], then a is
2
4
3
1
Solution:
If the fractions are equivalent, then 9 × a = 36
a = 36 ÷ 9 = 4
Submit a problem on this page.
Problem text:
Solution:
Answer:
Your name(if you would like to be published):
E-mail(you will be notified when the problem is published)
Notes
: use [tex][/tex] (as in the forum if you would like to use latex).
Correct:
Wrong:
Unsolved problems:
Contact email:
Follow us on
Twitter
Facebook
Copyright © 2005 - 2021.