write the number of terms in each expression.
1. $5 + 6 \cdot 4$ ______ 2. $7(9 + 3)$ ______ 3. $12 + 9 \div 3 - 2$ ______
evaluate each expression.
4. $36 + 42 \div 7$ ______ 5. $2^3 - 3 \cdot 2$ ______
6. $9 + 18 \div 2 \cdot 3 - 4$ ______ 7. $8 + (6 - 2)^3 \div 2$ ______
8. for the season kassidi has made 24 field goals worth 2 points each, 7 field goals worth 3 points each, and 15 free throws worth 1 point each. write and evaluate a numerical expression to find the number of points that kassidi has scored this season.

Question

write the number of terms in each expression.
1. $5 + 6 \cdot 4$ ______  2. $7(9 + 3)$ ______  3. $12 + 9 \div 3 - 2$ ______
evaluate each expression.
4. $36 + 42 \div 7$ ______  5. $2^3 - 3 \cdot 2$ ______
6. $9 + 18 \div 2 \cdot 3 - 4$ ______  7. $8 + (6 - 2)^3 \div 2$ ______
8. for the season kassidi has made 24 field goals worth 2 points each, 7 field goals worth 3 points each, and 15 free throws worth 1 point each. write and evaluate a numerical expression to find the number of points that kassidi has scored this season.

Accepted Answer

### Problem 1: Number of terms in $ 5 + 6 \cdot 4 $
# Explanation:
## Step 1: Recall term definition
Terms are separated by addition or subtraction. Here, $ 5 $ and $ 6 \cdot 4 $ are separated by $ + $.
## Step 2: Count terms
So there are 2 terms.
# Answer: 2

### Problem 2: Number of terms in $ 7(9 + 3) $
# Explanation:
## Step 1: Simplify or analyze
First, simplify the parentheses: $ 9 + 3 = 12 $, so the expression is $ 7 \cdot 12 $, but originally, inside the parentheses, $ 9 $ and $ 3 $ are terms? Wait, no—wait, the expression is $ 7(9 + 3) $. Wait, actually, when considering the original expression, the terms are the parts separated by +/-. But here, the expression is a product of 7 and (9 + 3). Wait, no—wait, the expression $ 7(9 + 3) $ is a single term? Wait, no, maybe I made a mistake. Wait, terms are separated by addition or subtraction. So in $ 7(9 + 3) $, the expression is $ 7 \times (9 + 3) $, but the $ 9 + 3 $ is inside parentheses. Wait, actually, the original expression: let's see, the expression is $ 7(9 + 3) $. So when we expand it, it's $ 7 \times 9 + 7 \times 3 $, but as written, the expression is $ 7(9 + 3) $. Wait, maybe the problem is considering the expression as given. Wait, the expression $ 7(9 + 3) $: the terms are the parts before multiplication? No, terms are separated by + or -. So in $ 7(9 + 3) $, there are no + or - outside the parentheses, so is it one term? Wait, no, maybe the question is about the number of terms in the expression as written. Wait, the expression is $ 7(9 + 3) $. Let's parse it: the expression has a coefficient 7 and a parenthetical part $ (9 + 3) $. But terms are separated by +/-. So in the expression $ 7(9 + 3) $, there are no + or - outside the parentheses, so is it one term? Wait, maybe I'm overcomplicating. Wait, the expression $ 7(9 + 3) $: when we look at the expression, the terms are the parts separated by addition or subtraction. So here, the expression is $ 7 \times (9 + 3) $, but the $ 9 + 3 $ is inside the parentheses. Wait, maybe the problem is considering the expression as $ 7(9 + 3) $, so the terms are 7 and (9 + 3)? No, that's not right. Wait, no—terms are separated by + or -. So in $ 7(9 + 3) $, there are no + or - outside the parentheses, so the entire expression is one term? Wait, but that seems wrong. Wait, maybe the problem is that when you have a product, like $ a(b + c) $, the terms are $ ab $ and $ ac $ when expanded, but as written, the expression $ a(b + c) $ is a single term? Wait, no, maybe the question is about the number of terms in the expression as given. Let's check the original problem: "Write the number of terms in each expression." So for $ 7(9 + 3) $, the expression is $ 7(9 + 3) $. Let's see: the expression has a coefficient 7 and a parenthetical expression $ (9 + 3) $. But terms are separated by + or -. So in $ 7(9 + 3) $, there are no + or - outside the parentheses, so is it one term? Wait, maybe I made a mistake. Wait, let's take a step back. Terms are parts of an expression separated by addition or subtraction. So in $ 5 + 6 \cdot 4 $, terms are 5 and $ 6 \cdot 4 $ (2 terms). In $ 7(9 + 3) $, the expression is $ 7 \times (9 + 3) $. There are no + or - outside the parentheses, so the entire expression is one term? Wait, but that seems odd. Wait, maybe the problem is considering the expression after expanding? No, the problem says "in each expression" as written. Wait, maybe I'm wrong. Wait, let's check with another example: $ 2(3 + 4) $ has how many terms? If we expand it, it's $ 6 + 8 $, which has 2 terms, but as written, is it 1 term? Wait, maybe the question is considering the expression as written, so $ 7(9 + 3) $ is a single term? Wait, no, that can't be. Wait, maybe the problem is that the expression $ 7(9 + 3) $ is a product, so the terms are the factors? No, terms are not factors. Terms are separated by +/-. So I think I made a mistake earlier. Wait, the expression $ 7(9 + 3) $: the terms are the parts separated by + or -. So in this case, there are no + or - outside the parentheses, so the expression is a single term? Wait, but that seems incorrect. Wait, maybe the problem is that the expression is $ 7(9 + 3) $, which is equivalent to $ 7 \times 9 + 7 \times 3 $, but as written, the expression is $ 7(9 + 3) $, so maybe the number of terms is 1? Wait, I'm confused. Wait, let's check the first problem: $ 5 + 6 \cdot 4 $ has two terms: 5 and $ 6 \cdot 4 $. So in $ 7(9 + 3) $, the expression is $ 7(9 + 3) $, which is a single term because there are no + or - outside the parentheses. So the number of terms is 1? Wait, maybe. Let's go with that.
# Explanation:
## Step 1: Identify term separators
Terms are separated by $ + $ or $ - $. In $ 7(9 + 3) $, there are no $ + $ or $ - $ outside the parentheses.
## Step 2: Count terms
Thus, the expression has 1 term.
# Answer: 1

### Problem 3: Number of terms in $ 12 + 9 \div 3 - 2 $
# Explanation:
## Step 1: Identify term separators
Terms are separated by $ + $ or $ - $. Here, $ 12 $, $ 9 \div 3 $, and $ 2 $ (with a $ - $ before it) are separated by $ + $ and $ - $.
## Step 2: Count terms
So terms are $ 12 $, $ 9 \div 3 $, and $ -2 $? Wait, no—wait, $ 12 + (9 \div 3) - 2 $. So the terms are $ 12 $, $ 9 \div 3 $, and $ 2 $ (but with a subtraction). Wait, terms are $ 12 $, $ 9 \div 3 $, and $ -2 $? Wait, no, the expression is $ 12 + 9 \div 3 - 2 $. So separated by $ + $ and $ - $, the terms are $ 12 $, $ 9 \div 3 $, and $ -2 $? Wait, no, actually, the terms are $ 12 $, $ 9 \div 3 $, and $ 2 $ with a subtraction. Wait, no—terms are the parts before/after $ + $ or $ - $. So $ 12 $ (before $ + $), $ 9 \div 3 $ (between $ + $ and $ - $), and $ -2 $ (after $ - $)? Wait, no, the $ -2 $ is a term? Wait, actually, the terms are $ 12 $, $ 9 \div 3 $, and $ -2 $? Wait, no, the expression is $ 12 + (9 \div 3) - 2 $. So the terms are $ 12 $, $ 9 \div 3 $, and $ -2 $? Wait, no, the $ -2 $ is a term? Wait, yes. So there are three terms: $ 12 $, $ 9 \div 3 $, and $ -2 $? Wait, no, $ 9 \div 3 $ is one term, $ 12 $ is another, and $ -2 $ is the third. Wait, let's list them: $ 12 $ (term 1), $ + 9 \div 3 $ (term 2), $ - 2 $ (term 3). So three terms.
# Explanation:
## Step 1: Identify term separators
Terms are separated by $ + $ or $ - $. The expression is $ 12 + (9 \div 3) - 2 $, so separators are $ + $ and $ - $.
## Step 2: Count terms
Terms: $ 12 $, $ 9 \div 3 $, $ -2 $ (or $ 2 $ with a subtraction, but as a term, it's $ -2 $ or $ 2 $ depending on sign). So 3 terms.
# Answer: 3

### Problem 4: Evaluate $ 36 + 42 \div 7 $
# Explanation:
## Step 1: Perform division first (PEMDAS)
$ 42 \div 7 = 6 $
## Step 2: Perform addition
$ 36 + 6 = 42 $
# Answer: 42

### Problem 5: Evaluate $ 2^3 - 3 \cdot 2 $
# Explanation:
## Step 1: Calculate exponents and multiplication
$ 2^3 = 8 $, $ 3 \cdot 2 = 6 $
## Step 2: Perform subtraction
$ 8 - 6 = 2 $
# Answer: 2

### Problem 6: Evaluate $ 9 + 18 \div 2 \cdot 3 - 4 $
# Explanation:
## Step 1: Perform division and multiplication (left to right)
$ 18 \div 2 = 9 $, then $ 9 \cdot 3 = 27 $
## Step 2: Perform addition and subtraction (left to right)
$ 9 + 27 = 36 $, then $ 36 - 4 = 32 $
# Answer: 32

### Problem 7: Evaluate $ 8 + (6 - 2)^3 \div 2 $
# Explanation:
## Step 1: Simplify parentheses
$ 6 - 2 = 4 $
## Step 2: Calculate exponent
$ 4^3 = 64 $
## Step 3: Perform division
$ 64 \div 2 = 32 $
## Step 4: Perform addition
$ 8 + 32 = 40 $
# Answer: 40

### Problem 8: Write and evaluate the numerical expression for Kassidi's points
# Explanation:
## Step 1: Define the expression
Points from 2-point field goals: $ 24 \times 2 $
Points from 3-point field goals: $ 7 \times 3 $
Points from free throws: $ 15 \times 1 $
Total points: $ (24 \times 2) + (7 \times 3) + (15 \times 1) $
## Step 2: Evaluate each part
$ 24 \times 2 = 48 $
$ 7 \times 3 = 21 $
$ 15 \times 1 = 15 $
## Step 3: Sum the parts
$ 48 + 21 + 15 = 84 $
# Answer: Numerical expression: $ 24 \times 2 + 7 \times 3 + 15 \times 1 $; Evaluation: 84

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 1: Number of terms in \( 5 + 6 \cdot 4 \)

Step 1: Recall term definition

Step 2: Count terms

Step 1: Simplify or analyze

Step 1: Identify term separators

Step 2: Count terms

Answer:

Problem 2: Number of terms in \( 7(9 + 3) \)