Equivalent Fractions: Problems with Solutions

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

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.

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.

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

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 $3 \times 8 = 6 \times 4 = 24$.

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.

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.

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].

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.

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].

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]

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]

Solution:
$\frac{2}{5} = \frac{4}{10}$

$\frac{4}{10} = \frac{4}{x}$ => $x = 10$

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.

Solution:
5 is 4 times less than 20, so a is 4 times less than 28
a = 28 ÷ 4 = 7

Solution:
a × 6 = 3 × 4
a × 6 = 12
a = 12 ÷ 6 = 2

Solution:
6 × a = 2 × 15
6 × a = 30
a = 30 ÷ 6 = 5

Solution:
If the fractions are equivalent, then 9 × a = 36
a = 36 ÷ 9 = 4