I know its true but why?
When you multiply a whole number by a whole number the result is a larger number. When you multiply fractions the result is a smaller number.
Think of it as multiplying the fraction by a whole number. One third three times is 1. The order in which you look at multiplication does not matter, the results are the same. 3x(1/3)=1 and (1/3)x3=1
It is because MOST fractions are smaller than 1. So when you multiply fractions together, they get smaller. On the other hand, ALL integers (except 0) are greater than or equal to 1 (in absolute value), so the product tends to be bigger.
Examples that support what you observe:
2*2=4, 3*2=6,
(1/2)*4=2, (1/2)*(1/4)=1/8
Examples that contest what you observe:
2*0 = 0, 3*1=3 (not bigger)
(4/3)*6=8, (8/3)*(9/4)=6
Hope that answers your question.
If RS=8y+T,ST=4y+8, and RT=15y-9, find the value of y
To understand why multiplying whole numbers results in a larger number while multiplying fractions results in a smaller number, let's break it down step by step:
Multiplying Whole Numbers:
When you multiply two whole numbers, you are essentially combining equal groups of those numbers. For example, 2 multiplied by 3 is equal to 2 + 2 + 2, which results in 6. As you can see, by multiplying the whole numbers, you are increasing the quantity or size of the original number.
Multiplying Fractions:
When you multiply fractions, you are essentially finding a fraction of a fraction. To multiply fractions, you multiply the numerators (the top numbers) to get the new numerator, and multiply the denominators (the bottom numbers) to get the new denominator. For example, 1/2 multiplied by 1/3 is equal to (1 * 1) / (2 * 3), which simplifies to 1/6. As you can see, by multiplying fractions, you are dividing the original quantities into smaller parts, resulting in a smaller overall value.
In summary, multiplying whole numbers increases the quantity or size, while multiplying fractions divides the original quantities into smaller parts, resulting in a smaller value.