Percents: practice solutions, Grade 6

Sommaire

1 Reading a hundred grid ★★★

(a) 42 of the 100 squares are colored, so $ 42\% $ of the grid is colored.

(b) $ 42\% = \dfrac{42}{100} = 0.42 $.

(c) $ 100 - 42 = 58 $ squares are not colored, so $ 58\% $ is not colored.

2 Percent to fraction and decimal ★★★

(a) $ 9\% = \dfrac{9}{100} = 0.09 $.

(b) $ 50\% = \dfrac{50}{100} = 0.5 $.

(c) $ 75\% = \dfrac{75}{100} = 0.75 $.

(d) $ 120\% = \dfrac{120}{100} = 1.2 $. It is more than one whole.

3 Easy fractions ★★★

(a) $ \dfrac{1}{2} = \dfrac{50}{100} = 50\% $.

(b) $ \dfrac{1}{4} = \dfrac{25}{100} = 25\% $.

(c) $ \dfrac{3}{10} = \dfrac{30}{100} = 30\% $.

(d) $ \dfrac{4}{5} = \dfrac{80}{100} = 80\% $.

4 Free throws ★★★

(a) $ \dfrac{18}{20} = \dfrac{90}{100} = 90\% $. She made 90% of her free throws.

(b) $ \dfrac{12}{25} = \dfrac{48}{100} = 48\% $. The second player made 48%.

5 Ten percent shortcut ★★★

Dividing by 10 gives 10%.

(a) $ 70 \div 10 = 7 $. (b) $ 120 \div 10 = 12 $. (c) $ 45 \div 10 = 4.5 $. (d) $ 8 \div 10 = 0.8 $.

$ 20\% $ is twice $ 10\% $, so $ 20\% $ of 70 is $ 2 \times 7 = 14 $.

6 True or false? ★★★

(a) False. $ 0.3 = 0.30 = 30\% $, not $ 3\% $.

(b) True. $ \dfrac{1}{4} = \dfrac{25}{100} $.

(c) True. $ 150\% = 1.5 $, which is greater than 1.

(d) False. $ 5\% = \dfrac{5}{100} = 0.05 $.

7 Order the numbers ★★★

Convert all to decimals: $ 0.4 $; $ 35\% = 0.35 $; $ \dfrac{3}{5} = 0.6 $; $ \dfrac{1}{2} = 0.5 $.

Order: $ 0.35 \lt 0.4 \lt 0.5 \lt 0.6 $. So the order is $ 35\% $, $ 0.4 $, $ \dfrac{1}{2} $, $ \dfrac{3}{5} $.

8 Percent of a number ★★★

(a) $ 0.25 \times 84 = 21 $ (a quarter of 84).

(b) $ 0.6 \times 55 = 33 $.

(c) $ 10\% $ of 120 is 12, so $ 5\% $ is 6.

(d) $ 0.35 \times 200 = 70 $.

9 A day on the trail ★★★

$ 75\% = \dfrac{3}{4} $. A quarter of 12 is 3, so three quarters is $ 3 \times 3 = 9 $.

Tomás has hiked 9 miles (about 14.5 km). Left: $ 12 - 9 = 3 $ miles.

10 Trail mix ★★★

Raisins: $ 0.30 \times 250 = 75 $ g.

Everything else: $ 250 - 75 = 175 $ g, which is $ 70\% $ of the bag.

The raisins weigh 75 g and the rest weighs 175 g.

11 Harder fractions ★★★

(a) $ \dfrac{9}{25} = \dfrac{36}{100} = 36\% $.

(b) $ 3 \div 8 = 0.375 = 37.5\% $.

(c) $ 7 \div 40 = 0.175 = 17.5\% $.

12 Minutes on a tape diagram ★★★

(a) 4 of 10 equal parts is $ \dfrac{4}{10} = 40\% $.

(b) $ 0.4 \times 90 = 36 $ minutes.

(c) $ 90 \div 10 = 9 $ minutes per part, and $ 4 \times 9 = 36 $ agrees with (b).

13 Sales tax ★★★

Tax: $ 0.08 \times 50 = 4 $ dollars.

Total: $ 50 + 4 = 54 $ dollars.

The headphones cost $54 in all.

14 Jacket on sale ★★★

Discount: $ 0.20 \times 70 = 14 $ dollars.

Sale price: $ 70 - 14 = 56 $ dollars. Check: you pay $ 80\% $, and $ 0.8 \times 70 = 56 $.

15 Who is right? ★★★

$ 45\% \text{ of } 60 = 0.45 \times 60 = 27 $.

$ 60\% \text{ of } 45 = 0.6 \times 45 = 27 $.

Both are 27, so Mia is wrong: they are equal. (Multiplication can be done in either order.)

16 Finding the whole ★★★

(a) 25% is a quarter, so the whole is $ 9 \times 4 = 36 $.

(b) $ 60\% $ is 6 parts of 10. One part is $ 21 \div 6 = 3.5 $, so the whole is $ 10 \times 3.5 = 35 $. Check: $ 0.6 \times 35 = 21 $.

(c) $ 20\% $ is 2 parts of 10. One part is $ 15 \div 2 = 7.5 $, so the whole is 75. Check: $ 0.2 \times 75 = 15 $.

17 The school band ★★★

$ 30\% $ is 3 parts out of 10 equal parts. Three parts hold 72 students, so one part is $ 72 \div 3 = 24 $.

The whole school is $ 10 \times 24 = 240 $ students. Check: $ 0.3 \times 240 = 72 $.

18 Saving for a stand ★★★

(a) $ 100\% \div 5 = 20\% $ per part. (Three parts: $ 3 \times 20\% = 60\% $, as given.)

(b) $ 45 \div 3 = 15 $ dollars per part.

(c) $ 5 \times 15 = 75 $ dollars. The stand costs $75.

19 The original price ★★★

The sale price is $ 100\% - 25\% = 75\% $ of the original price.

$ 75\% = 3 $ parts of 4, so one part (25%) is $ 27 \div 3 = 9 $ dollars, and the original price is $ 4 \times 9 = 36 $ dollars.

Check: $ 0.75 \times 36 = 27 $. The discount was $9.

20 Over 100 percent ★★★

(a) $ 1.5 \times 8 = 12 $, so it is 12 cm tall.

(b) $ 1.2 \times 250 = 300 $, so the new price is $300.

(c) $ 1.25 \times 40 = 50 $. (Or: $ 100\% = 40 $ and $ 25\% = 10 $, total 50.)

21 Who did better? ★★★

Jordan: $ \dfrac{34}{40} = 0.85 = 85\% $.

Sam: $ \dfrac{21}{25} = \dfrac{84}{100} = 84\% $.

$ 85\% \gt 84\% $, so Jordan did slightly better.

22 Fruit survey ★★★

(a) $ 25\% $ of 120: $ 0.25 \times 120 = 30 $ students.

(b) $ 40\% $ of 120: $ 0.4 \times 120 = 48 $ students.

(c) Grape: $ 0.2 \times 120 = 24 $. Orange: $ 0.15 \times 120 = 18 $. So orange was chosen by 18 students.

23 Find the mistake ★★★

(a) Dev divided by 20. But $ 20\% $ means $ \dfrac{20}{100} = 0.2 $, so he should multiply 50 by 0.2 (or divide by 5).

(b) $ 0.2 \times 50 = 10 $. Also $ 10\% $ of 50 is 5, and $ 20\% $ is double: 10. Both give 10.

Percents: practice solutions, Grade 6 – download the PDF