Testinar Grade 6 math

Translating Words into Expressions

Students will build Grade 6 mastery of translating words into expressions using models, equations, and test-style reasoning.

CH03-02 Expressions and Equations

Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

Which expression represents "the sum of a number \(n\) and \(7\), divided by \(2\)"?
1. \(\frac{n}{2}+7\)
2. \(\frac{n+7}{2}\)
3. \(2(n+7)\)
4. \(n+\frac{7}{2}\)
Which expression means "a number \(x\) minus \(9\)"?
1. \(9 - x\)
2. \(x - 9\)
3. \(x + 9\)
4. \(\frac{x}{9}\)
Which expression represents "the quotient of \(20\) and a number \(p\)"?
1. \(20p\)
2. \(20 - p\)
3. \(20 + p\)
4. \(\frac{20}{p}\)
Which expression matches "the difference of a number \(t\) and \(3\)"?
1. \(3 - t\)
2. \(t - 3\)
3. \(t + 3\)
4. \(3t\)
Write an expression for "a number \(b\) more than \(12\)".
1. \(12 - b\)
2. \(b - 12\)
3. \(12b\)
4. \(12 + b\)
Write an expression for "the sum of three times a number \(d\) and \(5\)".
1. \(3d + 5\)
2. \(3(d + 5)\)
3. \(3d - 5\)
4. \(d + 3 + 5\)
Which expression matches "the product of \(2\) and the sum of \(x\) and \(4\)"?
1. \(2x + 4\)
2. \(2 + x + 4\)
3. \(2x \cdot 4\)
4. \(2(x + 4)\)
Which expression represents "the quotient of a number \(g\) and \(3\), increased by \(1\)"?
1. \(\frac{g}{3} + 1\)
2. \(3 + \frac{g}{1}\)
3. \(\frac{g + 1}{3}\)
4. \(g(3 + 1)\)

Teacher and parent reference

Answer key and explanations

B. \(\frac{n+7}{2}\)
"The sum of \(n\) and \(7\)" means \(n+7\). "Divided by \(2\)" places the entire sum over \(2\): \(\frac{n+7}{2}\).
B. \(x - 9\)
"A number \(x\) minus \(9\)" means we subtract \(9\) from \(x\), giving \(x - 9\). Order matters: \(9 - x\) would be wrong.
D. \(\frac{20}{p}\)
"Quotient" means division. The quotient of \(20\) and \(p\) is \(\frac{20}{p}\) or \(20 \div p\).
B. \(t - 3\)
"The difference of \(t\) and \(3\)" starts with \(t\), so we compute \(t - 3\). Order matters: \(3 - t\) gives a different result.
D. \(12 + b\)
"\(b\) more than \(12\)" means we add \(b\) to \(12\), giving \(12 + b\).
A. \(3d + 5\)
"Three times a number \(d\)" is \(3d\). "The sum of \(3d\) and \(5\)" means \(3d + 5\).
D. \(2(x + 4)\)
"The sum of \(x\) and \(4\)" is \((x + 4)\). "The product of \(2\) and" that sum requires parentheses: \(2(x + 4)\).
A. \(\frac{g}{3} + 1\)
"The quotient of \(g\) and \(3\)" is \(\frac{g}{3}\). "Increased by \(1\)" means add \(1\): \(\frac{g}{3} + 1\).