Which expression has a product of 1(1)/(3) ? (A) 1(2)/(5)×(3)/(4) (B) 2(2)/(3)×(1)/(2) (C) 2(1)/(3)×(2)/(3) (D) 3(1)/(4)×(1)/(4)

Convert to Improper Fractions: To find the product that equals 1(1)/(3), we need to convert the mixed numbers to improper fractions and then multiply the numerators and denominators to see if the product matches 1(1)/(3), which is the same as 4/3 when converted to an improper fraction.Check Option A: Let's start with option A: 1(2)/(5)×(3)/(4). Convert the mixed number to an improper fraction: 1(2)/(5) = (5/5 + 2/5) = (7/5). Now multiply (7/5)×(3)/(4) = (7*3)/(5*4) = 21/20. This does not equal 4/3.Check Option B: Now, let's check option B: 2(2)/(3)×(1)/(2). Convert the mixed number to an improper fraction: 2(2)/(3) = (6/3 + 2/3) = (8/3). Now multiply (8/3)×(1)/(2) = (8*1)/(3*2) = 8/6 = 4/3. This equals 4/3, so option B is the correct answer.Check Option C: Even though we have found the correct answer, let's check the remaining options for completeness. Option C: 2(1)/(3)×(2)/(3). Convert the mixed number to an improper fraction: 2(1)/(3) = (6/3 + 1/3) = (7/3). Now multiply (7/3)×(2)/(3) = (7*2)/(3*3) = 14/9. This does not equal 4/3.Check Option D: Finally, let's check option D: 3(1)/(4)×(1)/(4). Convert the mixed number to an improper fraction: 3(1)/(4) = (12/4 + 1/4) = (13/4). Now multiply (13/4)×(1)/(4) = (13*1)/(4*4) = 13/16. This does not equal 4/3.

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Which expression has a product of 1(1)/(3) ?
(A) 1(2)/(5)×(3)/(4)
(B) 2(2)/(3)×(1)/(2)
(C) 2(1)/(3)×(2)/(3)
(D) 3(1)/(4)×(1)/(4)

Which expression has a product of $1 \frac{1}{3}$ ? $\newline$ (A) $1 \frac{2}{5} \times \frac{3}{4}$ $\newline$ (B) $2 \frac{2}{3} \times \frac{1}{2}$ $\newline$ (C) $2 \frac{1}{3} \times \frac{2}{3}$ $\newline$ (D) $3 \frac{1}{4} \times \frac{1}{4}$

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Math Problems

Algebra 2

Sum of finite series starts from 1

Full solution

Q. Which expression has a product of

1 \frac{1}{3}

\newline

(A)

1 \frac{2}{5} \times \frac{3}{4}

\newline

(B)

2 \frac{2}{3} \times \frac{1}{2}

\newline

(C)

2 \frac{1}{3} \times \frac{2}{3}

\newline

(D)

3 \frac{1}{4} \times \frac{1}{4}

Convert to Improper Fractions: To find the product that equals $1\frac{1}{3}$ , we need to convert the mixed numbers to improper fractions and then multiply the numerators and denominators to see if the product matches $1\frac{1}{3}$ , which is the same as $\frac{4}{3}$ when converted to an improper fraction.
Check Option A: Let's start with option A: $1\left(\frac{2}{5}\right)\times\left(\frac{3}{4}\right)$ . Convert the mixed number to an improper fraction: $1\left(\frac{2}{5}\right) = \left(\frac{5}{5} + \frac{2}{5}\right) = \left(\frac{7}{5}\right)$ . Now multiply $\left(\frac{7}{5}\right)\times\left(\frac{3}{4}\right) = \left(\frac{7\times3}{5\times4}\right) = \frac{21}{20}$ . This does not equal $\frac{4}{3}$ .
Check Option B: Now, let's check option B: $2\left(\frac{2}{3}\right)\times\left(\frac{1}{2}\right)$ . Convert the mixed number to an improper fraction: $2\left(\frac{2}{3}\right) = \left(\frac{6}{3} + \frac{2}{3}\right) = \left(\frac{8}{3}\right)$ . Now multiply $\left(\frac{8}{3}\right)\times\left(\frac{1}{2}\right) = \left(\frac{8\times1}{3\times2}\right) = \frac{8}{6} = \frac{4}{3}$ . This equals $\frac{4}{3}$ , so option B is the correct answer.
Check Option C: Even though we have found the correct answer, let's check the remaining options for completeness. $\newline$ Option C: $2\left(\frac{1}{3}\right)\times\left(\frac{2}{3}\right)$ . Convert the mixed number to an improper fraction: $2\left(\frac{1}{3}\right) = \left(\frac{6}{3} + \frac{1}{3}\right) = \left(\frac{7}{3}\right)$ . Now multiply $\left(\frac{7}{3}\right)\times\left(\frac{2}{3}\right) = \left(\frac{7\times2}{3\times3}\right) = \frac{14}{9}$ . This does not equal $\frac{4}{3}$ .
Check Option D: Finally, let's check option D: $3\left(\frac{1}{4}\right)\times\left(\frac{1}{4}\right)$ . Convert the mixed number to an improper fraction: $3\left(\frac{1}{4}\right) = \left(\frac{12}{4} + \frac{1}{4}\right) = \left(\frac{13}{4}\right)$ . Now multiply $\left(\frac{13}{4}\right)\times\left(\frac{1}{4}\right) = \left(\frac{13\times1}{4\times4}\right) = \frac{13}{16}$ . This does not equal $\frac{4}{3}$ .