Without multiplying the numbers in each box, explain which box has the
greater value
Box A
Box B
​

Answer: A

Step-by-step explanation:

Box A has a greater value than Box B. Expression of box A on being solved will result in a bigger value than that of box B.

Expression, in mathematics, is a combination of numbers, variables, functions, etc in a meaningful way.

Without multiplying, it is needed to compare both expressions.

As in the operation 'multiplication', numbers can interchange their position around the symbol '×', so, changing places of 4 and 8 in the numerator of the expression of box A,

Box A: [tex]\dfrac{8}{5} \times \dfrac{4}{9}[/tex].

The first fractions in both expressions are the same now in both boxes, so the expression having a bigger second expression will have the greater value.

To compare the second terms of both expressions, make the denominator equal:

Box A: [tex]\dfrac{8}{9} = \dfrac{8}{9} \times\dfrac{2}{2} = \dfrac{16}{18}[/tex]

Box B: [tex]\dfrac{1}{2} =\dfrac{1}{2} \times \dfrac{9}{9} = \dfrac{9}{18}[/tex]

Since, [tex]\dfrac{16}{18}\geq \dfrac{9}{18}[/tex] as [tex]16 \geq 9[/tex],

Therefore, the expression in Box A is greater than that of Box B.

Learn more about Expressions here:

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The complete question is as follows:

Without multiplying the numbers in each box, explain which box has the greater value

Box A: [tex]\dfrac{4}{5} \times \dfrac{8}{9}[/tex]

Box B: [tex]\dfrac{8}{5} \times \dfrac{1}{2}[/tex].

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