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Answer :
To find the equivalent forms of these fractions, we can either multiply or divide both the numerator and the denominator by the same number. This process does not change the value of the fraction.
Let's tackle each part step-by-step:
a. [tex]\frac{1}{2} = \frac{\square}{10}[/tex]
To find the value of the square, we need to make [tex]\frac{1}{2}[/tex] an equivalent fraction with a denominator of 10.
To do this, multiply both the numerator and the denominator of [tex]\frac{1}{2}[/tex] by 5:
[tex]\frac{1 \times 5}{2 \times 5} = \frac{5}{10}[/tex]
Therefore, [tex]\frac{1}{2} = \frac{5}{10}[/tex].
b. [tex]\frac{1}{4} = \frac{\square}{8}[/tex]
Here, we need an equivalent fraction with a denominator of 8.
Multiply the numerator and the denominator of [tex]\frac{1}{4}[/tex] by 2:
[tex]\frac{1 \times 2}{4 \times 2} = \frac{2}{8}[/tex]
Thus, [tex]\frac{1}{4} = \frac{2}{8}[/tex].
c. [tex]\frac{\square}{20} = \frac{3}{5}[/tex]
For this, we want [tex]\frac{3}{5}[/tex] as a fraction with a denominator of 20.
Multiply both the numerator and the denominator of [tex]\frac{3}{5}[/tex] by 4:
[tex]\frac{3 \times 4}{5 \times 4} = \frac{12}{20}[/tex]
Therefore, [tex]\frac{\square}{20} = \frac{12}{20}[/tex] and the square is 12.
d. [tex]\frac{\square}{4} = \frac{12}{16}[/tex]
Reduce [tex]\frac{12}{16}[/tex] by dividing both the numerator and the denominator by 4:
[tex]\frac{12 \div 4}{16 \div 4} = \frac{3}{4}[/tex]
Thus, [tex]\frac{\square}{4} = \frac{3}{4}[/tex] and the square is 3.
e. [tex]\frac{5}{6} = \frac{\square}{24}[/tex]
To find an equivalent fraction with a denominator of 24, multiply the numerator and denominator of [tex]\frac{5}{6}[/tex] by 4:
[tex]\frac{5 \times 4}{6 \times 4} = \frac{20}{24}[/tex]
Thus, [tex]\frac{5}{6} = \frac{20}{24}[/tex] and the square is 20.
f. [tex]\frac{3}{8} = \frac{9}{\square}[/tex]
Here, multiply both the numerator and denominator by 3:
[tex]\frac{3 \times 3}{8 \times 3} = \frac{9}{24}[/tex]
Therefore, [tex]\frac{3}{8} = \frac{9}{24}[/tex] and the square is 24.
g. [tex]\frac{4}{\square} = \frac{2}{3}[/tex]
[tex]\frac{2}{3}[/tex] as a fraction equivalent to [tex]\frac{4}{\square}[/tex] can be derived by multiplying by 2:
[tex]\frac{2 \times 2}{3 \times 2} = \frac{4}{6}[/tex]
So, [tex]\frac{4}{\square} = \frac{4}{6}[/tex] and the square is 6.
h. [tex]\frac{32}{40} = \frac{4}{\square}[/tex]
Simplify [tex]\frac{32}{40}[/tex] by dividing both the numerator and denominator by 8:
[tex]\frac{32 \div 8}{40 \div 8} = \frac{4}{5}[/tex]
Therefore, [tex]\frac{32}{40} = \frac{4}{5}[/tex] and the square is 5.
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