Why multiplying a fraction by a fraction gives a result that is smaller than either of the original factors?

The identity property of multiplication tells us that a number x 1 has a product equal to the number (itself). For example, 4 x 1 = 4. So when we multiply by a fraction that is less than 1, our product has to be less than the number we are multiplying the fraction by. For example, 4 x 1/3 = 1 1/3.

Why does multiplying by a fraction greater than 1 result in a product greater than the original number?

When a number is multiplied by a fraction equivalent to 1, the product is equal to the number. When a positive whole number is multiplied by a fraction greater than 1, the product is greater than the whole number.

Why is the product smaller when multiplying fractions?

Multiplying by a “proper fraction” makes a number smaller because it is tantamount to division and division makes a larger number smaller. However, it makes a number smaller only if the numerator<the denominator; otherwise, it makes the number larger, which see below.

Will the product be greater or less than each factor?

Whenever you multiply a positive number by a factor greater than 1, the product will be larger than the original number. … Both factors are less than 1, and the product is less than both factors. Of course, whenever you multiply a number by 1, the product will be equal to the original number.

Is the product of a fraction less than 1?

The product of a number and a fraction smaller than 1 is a number that is less than the original number you started with.

When you multiply a given fraction by a factor greater than 1 the product will always be less than the given fraction?

1 Expert Answer

if the original fraction is negative, multiplying it by a factor > 1 will always produce a result less than the original fraction.

What happens when you multiply by a fraction less than 1?

The identity property of multiplication tells us that a number x 1 has a product equal to the number (itself). For example, 4 x 1 = 4. So when we multiply by a fraction that is less than 1, our product has to be less than the number we are multiplying the fraction by. For example, 4 x 1/3 = 1 1/3.

When you multiply two fractions that are less than 1 is the product always less than either fractions?

When two fractions are multiplied, if one of the fractions is greater than 1, it will increase the size of the second fraction as the product. If it is less than 1, it will decrease the size of the second fraction as the product.

Why does the product get smaller when you multiply by a decimal?

When multiplying a number by a decimal less than one, the product will be smaller than the number being multiplied. This is because we are finding a fractional amount of a quantity. For example, 0.1 x 0.8 = 0.08, because the question is asking us to find one tenth of eight tenths.

When we multiply two fractions together the product is less than the two factors when?

The reason is that you are taking a FRACTION of the number, not a whole of it, or more than a whole of it. So, if you take 1/2 or 1/3 or 1/10 of a number, you are taking a FRACTION (not a whole) of that number, so the result will be smaller (less).

What is the difference between a factor and a product?

Multiplying two whole numbers gives a product. The numbers that we multiply are the factors of the product.

What is the product of factor and quotient?

In multiplication, the numbers being multiplied are called factors; the result of the multiplication is called the product. In division, the number being divided is the dividend, the number that divides it is the divisor, and the result of the division is the quotient.

Why does it make sense that the result of multiplying two fractions each between 0 and 1 is less than either of the two fractions being multiplied?

Since the numerous stories less than denominator, its value will be between zero and one. So, since a proper fraction, multiplied by a number of fraction means only a portion of that number of fraction. When we multiply two proper fractions. We’ll get an answer that is less than both the fractions.

Is the product of two fractions greater than each of the factors?

To multiply a whole number with a proper or an improper fraction, we multiply the whole number with the numerator of the fraction, keeping the denominator same. … When two improper fractions are multiplied the product of two improper fractions is greater than each of the two fractions.

Can the product of two fractions ever be greater than the factors?

So as both factors are less than 1 the product is some fraction of one of the original factors. … This means the product will always be smaller than both factors as it can be expressed as the smaller factor divided by some number.

Does multiplication always make numbers bigger?

Multiplication doesn’t always make bigger numbers

But, it doesn’t, not always. Children initially learn that multiplication is repeated addition, so it would make sense that multiplying two values together makes a larger product than both of the multipliers.

What fraction is less than 1?

Fractions that are greater than 0 but less than 1 are called proper fractions. In proper fractions, the numerator is less than the denominator. When a fraction has a numerator that is greater than or equal to the denominator, the fraction is an improper fraction.

What is the effect of multiplying a whole number by a number less than 1 and greater than 0?

Multiplying by a number between 0 and 1

The multiplication sign can be replaced by the phrase ‘lots of’. When you multiply by a number greater than 1, the answer is greater than the original number. But when you multiply by a number between 0 and 1, the answer is smaller than the original number.

Which fraction is less than 1 whole?

Proper fraction

This fraction is less than one whole. The number of equal parts being counted, the numerator, is smaller than the number of parts in the whole, the denominator.

What type of fraction has a value that is less than 1?

Hint: A fraction whose value is less than $1$ is known as a proper fraction, while the fraction whose value is one or more than one is an improper fraction. A proper fraction is the fraction where the numerator is lower than the denominator.

Why does dividing fractions make them bigger?

Something positive less than one goes into a (positive) number more than that number of times. A fraction less than one goes into a (positive) number more than that number of times. Hence dividing by a fraction (less than one) increases the size of a number (whether that number is a fraction or not).

Why are proper fractions less than one?

In a proper fraction, the numerator is always smaller than the denominator, and its value is always less than 1. Because a proper fraction represents just part of a whole thing, the denominator is the number value of the “whole thing” while the numerator is the number value of the “part.”

When you multiply two decimals less than 1 How does the product compare to the factors?

Thus, when you multiply two decimal factors, where each is less than one, the product will be less than each individual factor.

Why does squaring a decimal make it smaller?

When you square a decimal number it becomes smaller because while squaring the numerator you are squaring the denominator as well, hence the value becomes smaller. Thus 4^2 = 4*4 = 16.

What happens when you multiply fractions?

When you multiply a number by a fraction, you are finding part of that number. For example, if you multiply 6 by 1/2, you are finding 1/2 of 6. … Anytime you’re multiplying a number by a fraction, you’re finding part of that number. If you’re multiplying 1/4 by 1/2, you’re finding 1/2 of 1/4.

How do multiply fractions?

1. Multiply the top numbers (the numerators).
2. Multiply the bottom numbers (the denominators).
3. Simplify the fraction if needed.

What is the product of 1 and any number?

THE PRODUCT OF 1 AND ANY NUMBER IS THE NUMBER ITSELF.

What is it called when you make a fraction smaller?

We reduce a fraction to lowest terms by finding an equivalent fraction in which the numerator and denominator are as small as possible. … To reduce a fraction to lowest terms, divide the numerator and denominator by their Greatest Common Factor (GCF). This is also called simplifying the fraction.

What does a product of two factors mean?

In mathematics, a product is the result of multiplication, or an expression that identifies factors to be multiplied. For example, 30 is the product of 6 and 5 (the result of multiplication), and is the product of and. (indicating that the two factors should be multiplied together).