Here are the algebraic expressions for each phrase:
1)
The quotient of 4 times v and 7 times w
→ “Quotient” means division.
→ “4 times v” = 4v
→ “7 times w” = 7w
→ So, divide 4v by 7w →
4v / 7w
2)
5 times s added to the sum of t and u
→ “Sum of t and u” = t + u
→ “5 times s” = 5s
→ Add them:
5s + (t + u) or just
5s + t + u
3)
Subtract b from the sum of c and d
→ “Sum of c and d” = c + d
→ Subtract b from that →
(c + d) - b or
c + d - b
4)
Two-fifths of h subtracted from 10 times j
→ “Two-fifths of h” = (2/5)h
→ “10 times j” = 10j
→ Subtracted *from* means: start with 10j, then subtract (2/5)h →
10j - (2/5)h
5)
9 times f increased by 3 times g
→ “9 times f” = 9f
→ “Increased by” means add
→ “3 times g” = 3g
→ So:
9f + 3g
6)
Product of x and the difference between y and z
→ “Difference between y and z” = y - z
→ “Product of x and...” means multiply x by that difference →
x(y - z)
7)
a increased by the product of b and c
→ “Product of b and c” = bc
→ “Increased by” means add to a →
a + bc
8)
36 decreased by the quotient of p and q
→ “Quotient of p and q” = p/q
→ “Decreased by” means subtract from 36 →
36 - p/q
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Final Answer:
1) 4v / 7w
2) 5s + t + u
3) c + d - b
4) 10j - (2/5)h
5) 9f + 3g
6) x(y - z)
7) a + bc
8) 36 - p/q
Parent Tip: Review the logic above to help your child master the concept of translating phrases into algebraic expressions worksheet.
