The image shows a worksheet focused on writing basic algebraic expressions. Below, I will solve the problems step by step and explain the solution for each.
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Problem 1:
Task: Write an algebraic expression to match the phrase/situation:
"The sum of \(a\) and \(b\) divided by 3."
Solution:
1. Identify the key components:
- "The sum of \(a\) and \(b\)" translates to \(a + b\).
- "Divided by 3" means we divide the sum by 3.
2. Combine these into an expression:
\[
\frac{a + b}{3}
\]
Answer:
\[
\boxed{\frac{a + b}{3}}
\]
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Problem 2:
Task: Write an algebraic expression to match the phrase/situation:
"The difference of \(y\) and 7."
Solution:
1. Identify the key components:
- "The difference of \(y\) and 7" means subtract 7 from \(y\).
2. Write the expression:
\[
y - 7
\]
Answer:
\[
\boxed{y - 7}
\]
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Problem 3:
Task: Write an algebraic expression to match the phrase/situation:
"4 times a number plus 5."
Solution:
1. Identify the key components:
- "A number" can be represented by a variable, say \(x\).
- "4 times a number" translates to \(4x\).
- "Plus 5" means add 5 to \(4x\).
2. Combine these into an expression:
\[
4x + 5
\]
Answer:
\[
\boxed{4x + 5}
\]
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Problem 4:
Task: Rewrite each question as an algebraic expression:
1. What is the sum of \(a\) and 8?
2. What is the product of \(y\) and 10?
3. What do you get when you subtract 9 from \(b\)?
4. What is \(c\) divided by \(p\)?
5. What is 12 decreased by \(p\)?
Solution:
1.
What is the sum of \(a\) and 8?
- Sum means addition: \(a + 8\).
\[
a + 8
\]
2.
What is the product of \(y\) and 10?
- Product means multiplication: \(y \times 10\) or \(10y\).
\[
10y
\]
3.
What do you get when you subtract 9 from \(b\)?
- Subtract 9 from \(b\): \(b - 9\).
\[
b - 9
\]
4.
What is \(c\) divided by \(p\)?
- Division means \(c \div p\) or \(\frac{c}{p}\).
\[
\frac{c}{p}
\]
5.
What is 12 decreased by \(p\)?
- Decreased by means subtraction: \(12 - p\).
\[
12 - p
\]
Answers:
1. \(\boxed{a + 8}\)
2. \(\boxed{10y}\)
3. \(\boxed{b - 9}\)
4. \(\boxed{\frac{c}{p}}\)
5. \(\boxed{12 - p}\)
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Final Summary:
-
Problem 1: \(\boxed{\frac{a + b}{3}}\)
-
Problem 2: \(\boxed{y - 7}\)
-
Problem 3: \(\boxed{4x + 5}\)
-
Problem 4:
1. \(\boxed{a + 8}\)
2. \(\boxed{10y}\)
3. \(\boxed{b - 9}\)
4. \(\boxed{\frac{c}{p}}\)
5. \(\boxed{12 - p}\)
Parent Tip: Review the logic above to help your child master the concept of writing math expressions worksheet.
