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| 10 Theory slides |
| 10 Exercises - Grade E - A |
| Each lesson is meant to take 1-2 classroom sessions |
Here are a few recommended readings before getting started with this lesson.
But Kriz thinks that the multiplication should be done first. This is how Kriz evaluated the operations.
A numeric expression, or numerical expression, is a sequence of mathematical operations that only involves numbers. Consider the following examples.
Example | Is It a Numeric Expression? |
---|---|
5+3−2⋅8 | ✓ |
(9+12)3−4⋅7 | ✓ |
73+[(5−1)⋅(7+4)]5−71 | ✓ |
9w2+4s+7 | × |
1125 | × |
Select whether each given expression is a numerical expression or not.
Expression | Simplified | Operation |
---|---|---|
(1+2)⋅32−25+5 | 3⋅32−210 | Evaluating Parentheses and Grouping Symbols |
3⋅32−210 | 3⋅9−210 | Exponents |
3⋅9−210 | 27−5 | Multiplication and Division |
27−5 | 22 | Subtraction |
There are a few things to note about this evaluation.
To remember the order of operations, it is useful to memorize the acronym PEMDAS. Each letter of PEMDAS indicates a set of operations. A fun sentence to remember this acronym is Please Excuse My Dear Aunt Sally.
While waiting for baseball practice to start, Zain passed the time by counting how many people arrived to the field to practice and how many people left the field.
When Zain arrived and started counting, there were 9 people on the field practicing. Before Zain's practice started, two groups of three people left and four groups of six people arrived to the field. Then Zain's practice started.
Zain's baseball team needs new equipment before the season starts. Since Zain lives close to a good baseball equipment store, they were in charge of checking the prices. They noted these prices in a table.
Item | Price |
---|---|
Bat | $200 |
Glove | $95 |
Uniform | $130 |
Zain's team need 2 new bats, 8 new gloves, and 4 new uniforms. Luckily, there is a sale going on where bats and gloves are half their regular prices. Zain also has a $100 discount coupon that they will give the coach for equipment.
Zain is having a great time at bat in today's baseball game. He is hitting every single ball!
Multiply 0.87 by 147
Multiply 127.89 by 2.75
Round to nearest integer
Write the value of each given numerical expression. Remember the order of operations!
Tadeo solved the following numerical expression.
We want to determine whether the answer that Tadeo ended up with is correct.
We can do this by solving the numerical expression ourselves by using the order of operations.
Remember that the symbols * and * are used to indicate multiplication. We will start by evaluating the number with the exponent, according to the order of operations.
The next step is to multiply 2 by 25. If we look at Tadeo's procedure, we can see that he added 11 and 2 before multiplying. This mistake is described in option A.
We can find the correct value by evaluating the expression by following the order of operations. Let's finish what we started in Part A by multiplying and then adding the remaining numbers.
The correct value is 61.
Tearrik sells packs of cookies in two different sizes. The table shows the number of cookies in each pack.
Bag | Number of Cookies |
---|---|
Large | 20 |
Small | 6 |
We are asked to write a numerical expression for the total number of cookies. Let's consider the given information. Let's start by making a table to visualize how many cookies there are in each size of packs.
Bag | Number of Cookies |
---|---|
Large | 20 |
Small | 6 |
We are told that there are 8 large packs and 13 small packs of cookies. To find the total number of cookies in the large packs, we need to multiply the number of large packs by the number of cookies in each large pack. Cookies in Large Packs: 8*20 We can find the number of cookies in the small packs in a similar fashion. This time we multiply the number of small packs by the number of cookies in each small pack. Cookies in Small Packs: 13* 6 Now we have expressions for the total number of cookies in both the large and small packs. Things are going great. Now we we add the expressions for the number of cookies in each pack size so we can find the numerical expression to find the total number of cookies. 8*20 + 13* 6 Good job!
Now we want to find the total number of cookies in the packs. We can evaluate the expression from Part A to do this. In order to evaluate the expression correctly, we need to follow the steps of the order of operations.
Now let's carefully consider the numerical expression that we wrote in Part A.
8*20 + 13* 6
We can see that the expression does not have any parentheses or exponents, but there are two multiplications and an addition. Following the order of operations, we should do the multiplications from left to right and then we add the resulting numbers. Let's do it!
The value of the expression is 238, which means that there are 238 cookies in the packs. We did it!
Vincenzo bought some strawberries for an event. He bought 3 and 21 bags of strawberries.
Each bag of strawberries has a weight of 456 grams and each strawberry has a weight of 12 grams.
We want to write an expression for the total number of strawberries that Vincenzo bought. We know that he bought 3 and 12 bags of strawberries. Let's write this as an expression. Number of Bags:( 3 + 1/2) The total number of strawberries purchased is the product of the number of bags by the number of strawberries per bag. ( 3 + 1/2)* Strawberries per Bag Now we need to find the number of strawberries per bag. Each bag weighs 456 grams and each strawberry weighs 12 grams. The number of strawberries per bag can be found by dividing 456 by 12. Strawberries per Bag:456/12 We now have an expression for the number of strawberries per bag. Things are going great! To finish writing the expression total expression for how many strawberries Vincenzo bought, we will multiply the number of bags by the number of strawberries per bag. ( 3 + 1/2)*456/12 We did it!
Consider the numerical expression we wrote in Part A.
( 3 + 1/2)*456/12
Before we solve it, let's review the order of operations to be sure we solve it correctly.
Our expression has a set of parentheses, so we will start by solving the addition between them. Remember that any integer can be rewritten as a fraction with a denominator of one.
This fraction can be substituted for the expression between parentheses. 7/2*456/12 The result is the multiplication of two fractions. To multiply two fractions, we multiply their respective numerators and denominators. Let's do it!
We found that Vincenzo bought 133 strawberries.