Multiplication, Division, and Rational Numbers - Practice Problems

Background

Let's work some practice problems!

Question

Evaluate:

1.  
2.  
3. 2.54 x 3.10986 x 175 

Answer

1. 
2.  
3. 2.54 x 3.10986 x 175 = 1382.33277

Analysis

Question 1

Let's see that we can rewrite the division part of the expression and turn it into a multiplication by using the inverted form of what we're dividing by:



And now we can combine the fractions:



And now we can see that we have exactly the same in the numerator and denominator, so the whole thing reduces to 1. Therefore:



It's in situations like this where we can "cancel" out terms in the numerators and denominators because they end up being a form of the number 1. Let's look at the statement again:



See the 3 in the numerator and that other 3 in the denominator? We can cancel them - we know that when we multiply the fractions together, we'll end up with 3 divided by 3, which is 1:



We cross out the 3s because with them dividing each other, they are now both 1.

And we can do the same thing with the 5s and 7s:



With all of the numerators and denominators being equal to 1, the whole thing is equal to 1.

Question 2

Let's once again notice that we have multiplication and division operations. We can convert the division operations to multiplication by taking the inverse of the fraction we are dividing by. We end up doing this:





Is there anything we can cancel? Yes - remember that 4 = 2 x 2 and that 6 = 2 x 3, so we can rewrite this way:



Now let's cancel 2s where we can:



That leaves:



Since 3, 5, and 7 are all prime, we can't do any more cancellations - we just do the multiplication and end up with the result of:



Therefore:



Question 3

I put this last question in less to work out the math (it'd be a long calculation but certainly do-able), and more to make the point that with calculators everywhere now, all we have to do is type the calculation into the machine and have it spit out the number:

2.54 x 3.10986 x 175 = 1382.33277

Vocabulary used:

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Where might you have come from?

Fact-orials Index

Operations with different kinds of numbers:

• Multiplication, Division, and Integers - Practice Problems
• Addition, Subtraction, and Rational Numbers
• Multiplication, Division, and Rational Numbers

Relations:

• Equality and Rational Numbers

Where might we go?

Operations with different kinds of numbers:

• Addition, Subtraction, and Rational Numbers - Practice Problems