This answer key shows a full worked solution for each of the 10 percents problems, with every step and a check. Compare your method and the bold final answers, especially where the problem asks for a part, a whole, or a percent.
Problem 1: Percent to fraction and decimal
Fraction: \(35\% = \frac{35}{100}\). The greatest common factor of 35 and 100 is 5, so \(\frac{35 : 5}{100 : 5} = \frac{7}{20}\).
Decimal: \(35 : 100 = 0.35\).
\(\frac{7}{20}\) and \(0.35\).
Problem 2: Fraction and decimal to percent
(a) \(\frac{3}{4} = \frac{75}{100} = 75\%\).
(b) \(0.08 \times 100 = 8\), so \(0.08 = 8\%\).
(a) \(75\%\). (b) \(8\%\).
Problem 3: Percent of a number
Write \(25\%\) as \(0.25\): \(0.25 \times 80 = 20\).
Check: \(25\%\) is one fourth, and \(80 : 4 = 20\).
20.
Problem 4: Percent of a quantity
\(40\% = 0.40\). Multiply: \(0.40 \times 65 = 26\).
26 miles.
Problem 5: Bake sale percent
\(15\% = 0.15\). Multiply: \(0.15 \times 60 = 9\).
9 oatmeal cookies.
Problem 6: Free throws
Divide the part by the whole: \(18 : 24 = 0.75\).
\(0.75 = 75\%\).
\(75\%\).
Problem 7: Finding the whole
Divide the part by the percent as a decimal: \(21 : 0.30 = 70\).
Check: \(0.30 \times 70 = 21\).
70.
Problem 8: Sale price
(a) \(20\% = 0.20\). Discount: \(0.20 \times 60 = 12\).
(b) Sale price: \(60 – 12 = 48\).
(a) \(\$12\). (b) \(\$48\).
Problem 9: Cupcake sales
45 cupcakes is \(75\%\) of the whole. Divide: \(45 : 0.75 = 60\).
Check: \(0.75 \times 60 = 45\).
60 cupcakes.
Problem 10: Class survey
Soccer: \(0.35 \times 40 = 14\) students. Basketball: \(0.25 \times 40 = 10\) students.
Baseball is the rest: \(100\% – 35\% – 25\% = 40\%\), and \(0.40 \times 40 = 16\).
Check: \(14 + 10 + 16 = 40\).
14 chose soccer, 10 chose basketball, 16 chose baseball.
See every chapter on the Grade 6 math page.