two-thirds and eight-twelfths
To determine which fractions are equivalent, we can simplify them. The fraction ( \frac{15}{24} ) simplifies to ( \frac{5}{8} ) when both the numerator and denominator are divided by 3. The fraction ( \frac{3}{12} ) also simplifies to ( \frac{1}{4} ), which is not equivalent to ( \frac{5}{8} ). Therefore, the two equivalent fractions are ( \frac{15}{24} ) and ( \frac{5}{8} ).
To find two fractions equivalent to 2128, we can express it as a fraction over 1, like ( \frac{2128}{1} ). Another equivalent fraction can be created by multiplying both the numerator and denominator by the same number, such as ( \frac{2128 \times 2}{1 \times 2} = \frac{4256}{2} ). Thus, two equivalent fractions are ( \frac{2128}{1} ) and ( \frac{4256}{2} ).
Two fractions equivalent to ( \frac{5}{7} ) are ( \frac{10}{14} ) and ( \frac{15}{21} ). These fractions are obtained by multiplying both the numerator and denominator of ( \frac{5}{7} ) by 2 and 3, respectively. This property of fractions allows us to find many equivalent forms.
Two equivalent fractions for ( \frac{5}{8} ) are ( \frac{10}{16} ) and ( \frac{15}{24} ). These fractions are obtained by multiplying both the numerator and denominator of ( \frac{5}{8} ) by the same whole number. For example, multiplying by 2 gives ( \frac{5 \times 2}{8 \times 2} = \frac{10}{16} ), and multiplying by 3 gives ( \frac{5 \times 3}{8 \times 3} = \frac{15}{24} ).
To determine if ( \frac{1}{3} ) is equivalent to ( \frac{6}{24} ), we can simplify ( \frac{6}{24} ). Dividing both the numerator and denominator by 6 gives ( \frac{1}{4} ). Since ( \frac{1}{3} ) is not equal to ( \frac{1}{4} ), the two fractions are not equivalent.
To find what to add to four and two sevenths to make six, you first convert six into a fraction: six is equivalent to six over one, or twelve over two. Next, convert four and two sevenths into an improper fraction: four and two sevenths equals thirty and two sevenths, or thirty-two over seven. Now, you can set up the equation: ( x + \frac{32}{7} = \frac{6}{1} ) or ( x + \frac{32}{7} = \frac{42}{7} ). Solving for ( x ) gives you ( x = \frac{42}{7} - \frac{32}{7} = \frac{10}{7} ), which can also be expressed as one and three sevenths.
The fraction \frac{1}{2} can have many equivalent fractions. Equivalent fractions are fractions that represent the same value but have different numerators and denominators. Some examples of equivalent fractions for \frac{1}{2} are: • \frac{2}{4} • \frac{3}{6} • \frac{4}{8} • \frac{5}{10} • \frac{50}{100} These fractions are all equal to \frac{1}{2} because the ratio between the numerator and the denominator is the same.
Two equivalent fractions for ( \frac{36}{52} ) can be found by simplifying the fraction. First, we can divide both the numerator and denominator by their greatest common divisor, which is 4, resulting in ( \frac{9}{13} ). Additionally, multiplying both the numerator and denominator by 2 gives another equivalent fraction: ( \frac{72}{104} ). Thus, ( \frac{9}{13} ) and ( \frac{72}{104} ) are equivalent to ( \frac{36}{52} ).
To find equivalent fractions for the mixed number (2 \frac{7}{10}), first convert it to an improper fraction: (2 \frac{7}{10} = \frac{27}{10}). Two equivalent fractions can be found by multiplying the numerator and denominator by the same non-zero integer. For example, multiplying by 2 gives (\frac{54}{20}), and multiplying by 3 gives (\frac{81}{30}).
The expression ( \frac{7}{14} ) simplifies to ( \frac{1}{2} ). The quotient ( \frac{1}{2} ) is between the consecutive whole numbers 0 and 1.
Two sixteenths is equivalent to one eighth. This is because when you simplify the fraction ( \frac{2}{16} ) by dividing both the numerator and the denominator by 2, you get ( \frac{1}{8} ). Thus, two sixteenths simplifies directly to one eighth.
To find ( \frac{2}{3} ) of ( \frac{3}{7} ), you multiply the two fractions: [ \frac{2}{3} \times \frac{3}{7} = \frac{2 \times 3}{3 \times 7} = \frac{6}{21}. ] Simplifying ( \frac{6}{21} ) gives ( \frac{2}{7} ). Thus, ( \frac{2}{3} ) of ( \frac{3}{7} ) is ( \frac{2}{7} ).