Question

name: allan
date: 2/4/26
write an algebraic expression for each phrase.

1. a number b divided by thirty - six
2. sixty - six subtracted from a number p
3. the quotient of twenty - nine and a number h
4. a number n plus forty - nine
5. three divided by a number g
6. the total of twenty - four and a number x
7. the difference between eighteen and a number m
8. a number k added to twenty - eight
9. ninety - eight more than a number d
10. a number j multiplied by fifty - six
11. a number y increased by eighty - six
12. twenty - nine to the w^th power
13. a number q decreased by eighty - five
14. the difference between a number f and two
15. the quotient of a number t and thirty - seven
16. a number s minus eighty - two
17. the product of a number z and eighty - four
18. a number v to the power of sixty - five
19. the sum of forty - five and a number r
20. the product of fifty - two and a number c

Explanation:

Problem 4: a number \( n \) plus forty - nine

Step 1: Identify the operation

The phrase "plus" indicates addition. We are adding forty - nine to the number \( n \).

Step 2: Write the algebraic expression

Using the addition operation, the expression is \( n + 49 \).

Problem 5: three divided by a number \( g \)

Step 1: Identify the operation

The word "divided by" indicates division. We are dividing 3 by the number \( g \).

Step 2: Write the algebraic expression

In algebraic form, division can be represented as a fraction. So the expression is \( \frac{3}{g} \) (or \( 3\div g \)).

Problem 6: the total of twenty - four and a number \( x \)

Step 1: Identify the operation

The word "total" in this context indicates addition. We are adding 24 and the number \( x \).

Step 2: Write the algebraic expression

The algebraic expression for the sum of 24 and \( x \) is \( 24 + x \) (or \( x + 24 \)).

Problem 7: the difference between eighteen and a number \( m \)

Answer:

s:

1. \( n + 49 \)
2. \( \frac{3}{g} \) (or \( 3\div g \))
3. \( 24 + x \) (or \( x + 24 \))
4. \( 18 - m \)
5. \( 28 + k \) (or \( k + 28 \))
6. \( d + 98 \)
7. \( 56j \) (or \( j\times56 \))
8. \( y + 86 \)
9. \( 29^{w} \)
10. \( q - 85 \)
11. \( f - 2 \)
12. \( \frac{t}{37} \) (or \( t\div37 \))
13. \( s - 82 \)
14. \( 84z \) (or \( z\times84 \))
15. \( v^{65} \)
16. \( 45 + r \) (or \( r + 45 \))
17. \( 52c \) (or \( c\times52 \))