Fraction multiplication as scaling

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Scaling or resizing means comparing the size of the product to the size of one factor on the basis of the size of the other factor, without performing the multiplication. Scaling a number by a fraction less than 1 will be lesser then the original number. Scaling a number by a fraction greater than 1 will be greater than the original number. Multiplication is denoted by a cross sign ‘×’. Fractions are numbers that can be expressed in the p/q form. Here p the numerator and q is the denominator of the fraction.

Example 1: Smith’s family ate three fourths of all the cookies in 4 cookie boxes. Write the equation of the quantity they ate and is it lesser than or greater than 4?
Solution: Number of cookie boxes = 4.
The fraction of cookies eaten from all the boxes = 3/4.
The amount to cookies eaten = 4 x 3/4. (This is the equation)
Now checking for the multiplication as scaling.
We have 4 x 3/4 < 4 (Because the fraction 3/4 < 1)  
Hence the amount eaten by the Smith’s family is less than 4 boxes.
Question: Multiple choice question (Pick the correct option.)
Without multiplying the numbers which one will have the product greater than 2?
a)    2 x 5/4                        b) 2 x 1/4                   c) 2 x 4/4        d) None of these.
Correct answer: option a.
Explanation: The fraction 5/4 >1. Multiplying a number to a fraction greater than 1 will be greater than the given number.
Hence 2 x 5/4 > 2.

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