Year 7 Maths: Convert Between Decimals and Mixed Numbers

Introduction

Hello, Year 7! Today, we are going to learn how to convert between decimals and mixed numbers. This is an important skill that will help you in many areas of maths. Let’s break it down step by step!

What is a Mixed Number?

A mixed number is a whole number combined with a fraction. For example, in the mixed number (2 \frac{1}{4}), the whole number is 2 and the fraction is ( \frac{1}{4} ).

Example of a Mixed Number:

• (2 \frac{1}{4}) means you have 2 whole parts and 1 quarter of another part.

What is a Decimal?

A decimal is another way to represent fractions. For example, the decimal 0.25 is the same as the fraction ( \frac{1}{4} ).

Example of a Decimal:

• 0.75 is the decimal for ( \frac{3}{4} ) because it means three-quarters of a whole.

Converting Mixed Numbers to Decimals

To convert a mixed number to a decimal, you can follow these steps:

1. Convert the fraction to a decimal.
   • For example, ( \frac{1}{4} = 0.25).
2. Add the decimal to the whole number.
   • So, (2 \frac{1}{4}) becomes (2 + 0.25 = 2.25).

Example:

Convert (3 \frac{2}{5}) to a decimal.

1. ( \frac{2}{5} = 0.4).
2. (3 + 0.4 = 3.4).

Converting Decimals to Mixed Numbers

To convert a decimal to a mixed number, follow these steps:

1. Separate the whole number from the decimal.
   • For example, in 3.75, the whole number is 3.
2. Convert the decimal part back to a fraction.
   • Here, (0.75 = \frac{3}{4}).
3. Combine them to form a mixed number.
   • So, (3.75) becomes (3 \frac{3}{4}).

Example:

Convert 4.6 to a mixed number.

1. The whole number is 4.
2. The decimal 0.6 is ( \frac{3}{5}).
3. Combine them: 4.6 becomes (4 \frac{3}{5}).

Key Rules

• Remember that a mixed number has both a whole part and a fraction part.
• Decimals can be converted to fractions by recognising common decimal values (e.g., 0.5 is ( \frac{1}{2}), 0.25 is ( \frac{1}{4})).
• Always add the whole number and decimal or fraction correctly when converting.

Tips and Tricks

• Use a calculator if you are unsure about decimal to fraction conversions.
• Practice with common fractions and their decimal equivalents.
• Write down your steps clearly to avoid mistakes!

Questions

Easy Level (20 Questions)

1. Convert (1 \frac{1}{2}) to a decimal.
2. Convert (2 \frac{3}{4}) to a decimal.
3. Convert (3 \frac{1}{5}) to a decimal.
4. Convert (0.5) to a mixed number.
5. Convert (0.2) to a mixed number.
6. Convert (1.25) to a mixed number.
7. Convert (2.5) to a mixed number.
8. Convert (0.75) to a mixed number.
9. Convert (1 \frac{3}{4}) to a decimal.
10. Convert (0.6) to a mixed number.
11. Convert (3 \frac{2}{3}) to a decimal.
12. Convert (1.5) to a mixed number.
13. Convert (2 \frac{1}{10}) to a decimal.
14. Convert (0.8) to a mixed number.
15. Convert (4 \frac{1}{2}) to a decimal.
16. Convert (0.3) to a mixed number.
17. Convert (1.75) to a mixed number.
18. Convert (5 \frac{4}{5}) to a decimal.
19. Convert (0.1) to a mixed number.
20. Convert (3.2) to a mixed number.

Medium Level (20 Questions)

1. Convert (4 \frac{2}{5}) to a decimal.
2. Convert (3.8) to a mixed number.
3. Convert (2 \frac{7}{10}) to a decimal.
4. Convert (1.4) to a mixed number.
5. Convert (5 \frac{1}{8}) to a decimal.
6. Convert (0.125) to a mixed number.
7. Convert (2.6) to a mixed number.
8. Convert (3 \frac{4}{6}) to a decimal.
9. Convert (0.9) to a mixed number.
10. Convert (1.6) to a mixed number.
11. Convert (3 \frac{5}{12}) to a decimal.
12. Convert (2.75) to a mixed number.
13. Convert (4 \frac{3}{4}) to a decimal.
14. Convert (0.15) to a mixed number.
15. Convert (5.5) to a mixed number.
16. Convert (2 \frac{2}{3}) to a decimal.
17. Convert (1.2) to a mixed number.
18. Convert (0.4) to a mixed number.
19. Convert (6 \frac{5}{6}) to a decimal.
20. Convert (0.6) to a mixed number.

Hard Level (20 Questions)

1. Convert (7 \frac{3}{8}) to a decimal.
2. Convert (5.25) to a mixed number.
3. Convert (9 \frac{2}{3}) to a decimal.
4. Convert (4.125) to a mixed number.
5. Convert (8 \frac{5}{12}) to a decimal.
6. Convert (0.375) to a mixed number.
7. Convert (6 \frac{1}{4}) to a decimal.
8. Convert (0.875) to a mixed number.
9. Convert (12 \frac{7}{10}) to a decimal.
10. Convert (0.05) to a mixed number.
11. Convert (3.6) to a mixed number.
12. Convert (10 \frac{3}{5}) to a decimal.
13. Convert (0.2) to a mixed number.
14. Convert (11 \frac{1}{8}) to a decimal.
15. Convert (0.45) to a mixed number.
16. Convert (3 \frac{9}{10}) to a decimal.
17. Convert (0.55) to a mixed number.
18. Convert (15 \frac{2}{3}) to a decimal.
19. Convert (0.9) to a mixed number.
20. Convert (14.5) to a mixed number.

Answers

Easy Level Answers

1. (1 \frac{1}{2} = 1.5) (Convert ( \frac{1}{2}) to 0.5 and add to 1).
2. (2 \frac{3}{4} = 2.75) (Convert ( \frac{3}{4}) to 0.75 and add to 2).
3. (3 \frac{1}{5} = 3.2) (Convert ( \frac{1}{5}) to 0.2 and add to 3).
4. (0.5 = 0 \frac{1}{2}) (0 is the whole number and 0.5 is ( \frac{1}{2})).
5. (0.2 = 0 \frac{1}{5}) (0 is the whole number and 0.2 is ( \frac{1}{5})).
6. (1.25 = 1 \frac{1}{4}) (Whole number is 1, and 0.25 is ( \frac{1}{4})).
7. (2.5 = 2 \frac{1}{2}) (Whole number is 2, and 0.5 is ( \frac{1}{2})).
8. (0.75 = 0 \frac{3}{4}) (0 is the whole number and 0.75 is ( \frac{3}{4})).
9. (1 \frac{3}{4} = 1.75) (Convert ( \frac{3}{4}) to 0.75 and add to 1).
10. (0.6 = 0 \frac{3}{5}) (0 is the whole number and 0.6 is ( \frac{3}{5})).
11. (3 \frac{2}{3} = 3.67) (Convert ( \frac{2}{3}) to approximately 0.67 and add to 3).
12. (1.5 = 1 \frac{1}{2}) (Whole number is 1, and 0.5 is ( \frac{1}{2})).
13. (2 \frac{1}{10} = 2.1) (Convert ( \frac{1}{10}) to 0.1 and add to 2).
14. (0.8 = 0 \frac{4}{5}) (0 is the whole number and 0.8 is ( \frac{4}{5})).
15. (4 \frac{1}{2} = 4.5) (Convert ( \frac{1}{2}) to 0.5 and add to 4).
16. (0.3 = 0 \frac{3}{10}) (0 is the whole number and 0.3 is ( \frac{3}{10})).
17. (1.75 = 1 \frac{3}{4}) (Whole number is 1, and 0.75 is ( \frac{3}{4})).
18. (5 \frac{4}{5} = 5.8) (Convert ( \frac{4}{5}) to 0.8 and add to 5).
19. (0.1 = 0 \frac{1}{10}) (0 is the whole number and 0.1 is ( \frac{1}{10})).
20. (3.2 = 3 \frac{2}{10}) (Whole number is 3, and 0.2 is ( \frac{2}{10})).

Medium Level Answers

1. (4 \frac{2}{5} = 4.4) (Convert ( \frac{2}{5}) to 0.4 and add to 4).
2. (3.8 = 3 \frac{4}{5}) (Whole number is 3, and 0.8 is ( \frac{4}{5})).
3. (2 \frac{7}{10} = 2.7) (Convert ( \frac{7}{10}) to 0.7 and add to 2).
4. (1.4 = 1 \frac{2}{5}) (Whole number is 1, and 0.4 is ( \frac{2}{5})).
5. (5 \frac{1}{8} = 5.125) (Convert ( \frac{1}{8}) to 0.125 and add to 5).
6. (0.125 = 0 \frac{1}{8}) (0 is the whole number and 0.125 is ( \frac{1}{8})).
7. (2.6 = 2 \frac{3}{5}) (Whole number is 2, and 0.6 is ( \frac{3}{5})).
8. (3 \frac{4}{6} = 3.67) (Convert ( \frac{4}{6}) to approximately 0.67 and add to 3).
9. (0.9 = 0 \frac{9}{10}) (0 is the whole number and 0.9 is ( \frac{9}{10})).
10. (1.6 = 1 \frac{3}{5}) (Whole number is 1, and 0.6 is ( \frac{3}{5})).
11. (3 \frac{5}{12} = 3.42) (Convert ( \frac{5}{12}) to approximately 0.42 and add to 3).
12. (2.75 = 2 \frac{3}{4}) (Whole number is 2, and 0.75 is ( \frac{3}{4})).
13. (4 \frac{3}{4} = 4.75) (Convert ( \frac{3}{4}) to 0.75 and add to 4).
14. (0.15 = 0 \frac{3}{20}) (0 is the whole number and 0.15 is ( \frac{3}{20})).
15. (5.5 = 5 \frac{1}{2}) (Whole number is 5, and 0.5 is ( \frac{1}{2})).
16. (2 \frac{2}{3} = 2.67) (Convert ( \frac{2}{3}) to approximately 0.67 and add to 2).
17. (1.2 = 1 \frac{1}{5}) (Whole number is 1, and 0.2 is ( \frac{1}{5})).
18. (0.4 = 0 \frac{2}{5}) (0 is the whole number and 0.4 is ( \frac{2}{5})).
19. (6 \frac{5}{6} = 6.83) (Convert ( \frac{5}{6}) to approximately 0.83 and add to 6).
20. (0.6 = 0 \frac{3}{5}) (0 is the whole number and 0.6 is ( \frac{3}{5})).

Hard Level Answers

1. (7 \frac{3}{8} = 7.375) (Convert ( \frac{3}{8}) to 0.375 and add to 7).
2. (5.25 = 5 \frac{1}{4}) (Whole number is 5, and 0.25 is ( \frac{1}{4})).
3. (9 \frac{2}{3} = 9.67) (Convert ( \frac{2}{3}) to approximately 0.67 and add to 9).
4. (4.125 = 4 \frac{1}{8}) (Whole number is 4, and 0.125 is ( \frac{1}{8})).
5. (8 \frac{5}{12} = 8.42) (Convert ( \frac{5}{12}) to approximately 0.42 and add to 8).
6. (0.375 = 0 \frac{3}{8}) (0 is the whole number and 0.375 is ( \frac{3}{8})).
7. (6 \frac{1}{4} = 6.25) (Convert ( \frac{1}{4}) to 0.25 and add to 6).
8. (0.875 = 0 \frac{7}{8}) (0 is the whole number and 0.875 is ( \frac{7}{8})).
9. (12 \frac{7}{10} = 12.7) (Convert ( \frac{7}{10}) to 0.7 and add to 12).
10. (0.05 = 0 \frac{1}{20}) (0 is the whole number and 0.05 is ( \frac{1}{20})).
11. (3.6 = 3 \frac{3}{5}) (Whole number is 3, and 0.6 is ( \frac{3}{5})).
12. (10 \frac{3}{5} = 10.6) (Convert ( \frac{3}{5}) to 0.6 and add to 10).
13. (0.2 = 0 \frac{1}{5}) (0 is the whole number and 0.2 is ( \frac{1}{5})).
14. (11 \frac{1}{8} = 11.125) (Convert ( \frac{1}{8}) to 0.125 and add to 11).
15. (0.45 = 0 \frac{9}{20}) (0 is the whole number and 0.45 is ( \frac{9}{20})).
16. (3 \frac{9}{10} = 3.9) (Convert ( \frac{9}{10}) to 0.9 and add to 3).
17. (0.55 = 0 \frac{11}{20}) (0 is the whole number and 0.55 is ( \frac{11}{20})).
18. (15 \frac{2}{3} = 15.67) (Convert ( \frac{2}{3}) to approximately 0.67 and add to 15).
19. (0.9 = 0 \frac{9}{10}) (0 is the whole number and 0.9 is ( \frac{9}{10})).
20. (14.5 = 14 \frac{1}{2}) (Whole number is 14, and 0.5 is ( \frac{1}{2})).

I hope this explanation has helped you