Final answer:
The statement is true; by multiplying both fractions by the LCD, you can compare the numerators directly to determine which fraction is larger. This step-by-step process does not change the actual values of the fractions but makes comparison easier.
Step-by-step explanation:
The statement is true. Multiplying both fractions by their least common denominator (LCD) effectively removes the denominators and allows you to compare the numerators directly, which makes it easier to see which fraction is larger. Indeed, if you are given two fractions and you want to know which is larger without converting them to decimals, you can multiply the numerator of each fraction by the denominator of the other. This technique ensures that the fractions are compared on the basis of the same denominator without changing their actual values.
Here's a step-by-step explanation using an example:
Suppose you have two fractions, 7/8 and 5/6, and you want to compare them.
First, find the LCD, which in this case is 24.
Multiply the numerator and denominator of the first fraction (7/8) by the denominator of the second fraction (6), which gives you 42/48.
Do the same for the second fraction, multiplying the numerator and denominator of 5/6 by the first fraction's denominator (8), giving you 40/48.
Now that both fractions have the same denominator, you can easily compare the numerators: 42 is larger than 40, so 7/8 is larger than 5/6.
In conclusion, this method shows that 7/8 is indeed greater than 5/6 without completely removing the concept of fractions or converting to decimal form, and it remains a valid comparison.