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Answer:
Step-by-step explanation:
Both expressions are examples of the <em>distributive property</em>, which basically says "if I have <em>this </em>many groups of some size and <em>that</em> many groups of the same size, I've got <em>this </em>+ <em>that</em> groups of that size altogether."
To give an example, if I've got <em>3 groups of 5 </em>and <em>2 groups of 5</em>, I've got 3 + 2 = <em>5 groups of 5 </em>in total. I've attached a visual from Math with Bad Drawings to illustrate this idea.
Mathematically, we'd capture that last example with the equation
. We can also read that in reverse: 3 + 2 groups of 5 is the same as adding together 3 groups of 5 and 2 groups of 5; both directions get us 8 groups of 5. We can use this fact to rewrite the first expression like this:
.
This idea extends to subtraction too: If we have 3 groups of 4 and we take away 1 group of 4, we'd expect to be left with 3 - 1 = 2 groups of 4, or in symbols: . When we start with two numbers like 15 and 10, our first question should be if we can split them up into groups of the same size. Obviously, you could make 15 groups of 1 and 10 groups of 1, but 15 is also the same as <em>3 groups of 5</em> and 10 is the same as <em>2 groups of 5</em>. Using the distributive property, we could write this as
, so we can say that
.
Answer:
Value of b = =1.25.
Step-by-step explanation:
Direct Variation states that a relationship between two variables in which one is a constant multiple of the other.
*if one variable changes the other changes in proportion to the first.
*If a is directly proportional to b i.e,
then it is of the form
a = kb ;where k is constant variation.
Given: a varies directly as b;
then, by definition of direct variation;
we have;
.....[1]
Substitute the value of a =28 and b =7 to solve for k;
Divide both sides by 7 we have;
Simplify:
k =4
now, find b using same method when a =5;
then;
after substituting the value of a = 5 and k=4 in [1] ;
Divide by 4 to both sides we get;
Therefore, the value of b = =1.25