One-Step Equations: Grade 6 Math Worksheet Answer Key – PDF Download

Problem 1: Is It a Solution

1. \(7 + 8 = 15\), which is true. Yes, it is a solution.
2. \(3\times 5 = 15\), and \(15 \ne 18\). No, it is not a solution.
3. \(3.5 + 2.5 = 6\), which is true. Yes.
4. \(4\times 2.5 = 10\), which is true. Yes.

Problem 2: Addition Equations

1. Subtract \(9\): \(x = 21 – 9 = \) \(12\)
2. \(x = 30 – 14 = \) \(16\)
3. \(x = 17 – 5 = \) \(12\)
4. \(x = 50 – 26 = \) \(24\)

Problem 3: Multiplication Equations

1. Divide by \(6\): \(x = 42: 6 = \) \(7\)
2. \(x = 72: 9 = \) \(8\)
3. \(x = 54: 6 = \) \(9\)
4. \(x = 60: 12 = \) \(5\)

Problem 4: Addition with Decimals

1. \(x = 9.1 – 3.4 = \) \(5.7\)
2. \(x = 2.5 – 0.75 = \) \(1.75\)
3. \(x = 12.6 – 4.9 = \) \(7.7\)
4. \(x = 0.5 – 0.08 = \) \(0.42\)

Problem 5: Multiplication with Decimals

1. \(x = 12.5: 5 = \) \(2.5\)
2. \(x = 3.2: 0.4 = \) \(8\)
3. \(x = 9: 1.5 = \) \(6\)
4. \(x = 6: 0.25 = \) \(24\)

Problem 6: Equations with Fractions

1. \(x = \frac{7}{8} – \frac{1}{4} = \frac{7}{8} – \frac{2}{8} = \) \(\frac{5}{8}\)
2. \(x = 1 – \frac{2}{5} = \frac{5}{5} – \frac{2}{5} = \) \(\frac{3}{5}\)
3. \(x = \frac{3}{4}: 3 = \frac{3}{4}\times \frac{1}{3} = \) \(\frac{1}{4}\)
4. \(x = \frac{3}{8}: \frac{1}{2} = \frac{3}{8}\times 2 = \frac{6}{8} = \) \(\frac{3}{4}\)

Problem 7: Writing Equations

1. \(n + 7 = 25\), so \(n = 25 – 7 = \) \(18\)
2. \(6n = 4.2\), so \(n = 4.2: 6 = \) \(0.7\)
3. \(n + \frac{3}{4} = 2\), so \(n = 2 – \frac{3}{4} = \frac{8}{4} – \frac{3}{4} = \) \(\frac{5}{4}\), or \(1\frac{1}{4}\)
4. \(8n = 100\), so \(n = 100: 8 = \) \(12.5\)

Problem 8: School Store Savings

Let \(m\) be the dollars she had at first: \(m + 8.50 = 20.00\).

Subtract \(8.50\): \(m = 20.00 – 8.50 = 11.50\). Check: \(11.50 + 8.50 = 20.00\).

Answer: \(\$11.50\)

Problem 9: Farmers Market Apples

The cost of \(2.5\) pounds at \(p\) dollars per pound is \(2.5p = 8.75\).

Divide by \(2.5\): \(p = 8.75: 2.5 = 3.5\). Check: \(2.5\times 3.5 = 8.75\).

Answer: \(\$3.50\) per pound

Problem 10: Road Trip

1. \(187.5 + m = 340\), so \(m = 340 – 187.5 = \) \(152.5\) miles
2. Distance equals speed times time: \(2.5s = 152.5\), so \(s = 152.5: 2.5 = \) \(61\) miles per hour
3. \(2.5\times 61 = 152.5\), which matches the distance left. The solution is correct.

See every chapter on the Grade 6 math page.