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The product of two POSITIVE fractions less than one is less than either factor. Try thinking of multiplication as ‘of’ when performing multiplication of fractions less than one. E.g. 1/4 x 1/4 = is asking what is one quarter of one quarter, which is one sixteenth 1/4 x 1/4 = 1/16 (multiply 1 x 1 to get the numerator and 4 x 4 to get the denominator (1/16)
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When is the product of two nonzero integers less than or equal to both of the two factors?
If the numbers have to be positive, at least one of the two factor must be 1. In that case the product will be greater than or equal to 1 and equal to the other factor.If the numbers can be negative, in addition to the first case, any product of a positive and a negative integer will be less than or equal to both of the two factors. The product is negative so it's automatically less than the positive factor. If the positive factor is 1, the product is equal to the negative factor; if the positive factor is > 1 the product is less than the negative factor. E.g.1 * -14 = -14 which is equal to -14 and less than 1-3 * 5 = -15, which is less than both 5 and -3
What are three rules you can use to compare fractions?
Rule #1 When two fractions have the same denominator, the bigger fraction is the one with the bigger numerator. Rule # 2 When comparing fractions that have the same numerator, the bigger fraction is the one with the smaller denominator. Rule # 3 You can convert the fractions and then just put the greater than, less than or equal to sign to see what the comparison is between the fractions.
What is the situation in which you would use fractions to express a number less than one?
When the numerator is less than the denominator. For example 1/2, 3/4, 18/27, ...
An integer less than zero?
-1. An integer is any number that can be represented without decimals or fractions - including negatives.
Is the difference of two integers less than either integer?
If both numbers are positive....yes If either or both numbers are negative ....no
When is the product of two fractions less than its factors?
If the fractions are both proper fractions ... equivalent to less than 1 ... thenthat's always true ... the product is always less than either factor.
What is the product of factors that are both positive proper fractions?
The product of two positive proper fractions is always a positive proper fraction. A proper fraction is defined as a fraction where the numerator is less than the denominator. Therefore, when multiplying two fractions, the result will have a numerator smaller than the denominator, maintaining its status as a proper fraction.
Why is the product of two fractions smaller than two fractions thet were multiplied?
That's only true if the fractions are "proper" fractions ... with numerator smaller than denominator. The reason is: If you take (a piece less than the whole thing) out of (a piece less than the whole thing), you wind up with a piece smaller than either of the original pieces.
When multiplying proper fractions why is the product less than the both factors?
A proper fraction is less than 1. Any positive number multiplied by a positive number less 1 will be less than itself. In multiplying two proper fractions, each one is being multiplied by a number less than 1.
When will the quotient of two fractions less than 1 be greater than either fraction?
Yes. Consider two negative fractions. Since they are negative, both are less than 1. But their product is positive and so greater than either.
Why is the product of two positive proper fractions always less than either fraction?
because when you multiply the denominators it creates a much smaller proportion. for example multiply 0.5 by 0.5, the result is 0.25 in fractions it is 1/2 x 1/2, the result 1/4
What are proper fractions?
Proper fractions are fractions having a numerator that is smaller than the denominator.A proper fraction is when its numerator is less than its denominator as for example 3/4
What fractions are greater than 0 and less than 1?
Proper fractions.
Are mixed numbers less than proper fractions?
No.
Are proper fractions less than one?
yes
Is it true that when you multiply two natural numbers the product is never less than either of the two numbers?
Yes. Natural numbers are counting numbers, equal to or greater than 0. The only ways a product can be less than its multiplicands is when multiplying fractions by fractions or multiplying a positive number by a negative number.
If you multiply two decimals less than 1 can you predict whether the product will be less than or greater than either of the factors Explain?
When you multiply two decimals that are both less than 1, the product will always be less than either of the factors. This is because each factor represents a fraction of a whole, and multiplying these fractions results in an even smaller fraction. For example, multiplying 0.5 and 0.3 yields 0.15, which is less than both 0.5 and 0.3. Thus, the product is guaranteed to be less than either factor.
