Exercise 110 Page 481

Before we evaluate the expression, let's first rewrite the expression so that all of the numbers are fractions.

When we multiply fractions, we need to remember that the product of two fractions is equal to the product of the numerators divided by the product of the denominators. Let's find the given product!

When multiplying real numbers, the product will be positive if the signs are the same and it will be negative if the signs are different. cc Same Sign & Different Signs (+)(+)=(+) & (+)(-)=(-) (-)(-)=(+) & (-)(+)=(-)In our case both numbers are positive, so the product will be positive.

We can verify this using a calculator.

Recall that dividing fractions is the same as multiplying the first fraction by the reciprocal of the second fraction. 4/3÷5/8=4/3*8/5 When we multiply fractions, we need to remember that the product of two fractions is equal to the product of the numerators divided by the product of the denominators. Let's find the given product!

According to the order of operations, expressions inside parentheses are evaluated first, followed by exponents, then multiplication and division, and finally addition and subtraction are evaluated last. We can use the acronym PEMDAS to help us remember the correct order!

For the given expression, this means evaluating the expression inside the parenthesis completely before performing other operations. 2+4(- 5)+1/2(3+9) Notice also that even within this parenthetical expression, we must follow the order of operations. 3+9 Let's do it!

Operation	Before Simplification	After Simplification
Add terms	2+4(- 5)+1/2( 3+ 9)	2+4(- 5)+1/2( 12)
Multiply	2+ 4( - 5)+ 1/2( 12)	2+( - 20)+ 6
Add terms	2+( - 20)+ 6	- 12

The expression is equal to 28.

According to the order of operations, expressions inside parentheses are evaluated first, followed by exponents, then multiplication and division, and finally addition and subtraction are evaluated last. We can use the acronym PEMDAS to help us remember the correct order!

For the given expression, this means evaluating the expression inside the parenthesis before performing other operations.

2(3+4(10-2)) Notice also that even within this parenthetical expression, we must follow the order of operations. 3+4(10-2) Let's do it!

Operation	Before Simplification	After Simplification
Subtract term	2(3+4( 10- 2))	2(3+4( 8))
Multiply	2(3+ 4( 8))	2(3+ 32)
Add terms	2( 3+ 32)	2( 35)
Multiply	2( 35)	70

The expression is equal to 70.

Alternative Solution

Using a Calculator

We can also evaluate this expression using a calculator. To do so, we type it as shown below.

Whenever using a calculator for a complicated expression such as this, be very careful when placing the parentheses. A calculator will only do what it is told to do, not what you meant for it do.