Introduction

Hello, Year 7! Today, we will learn how to convert decimals into mixed numbers. A mixed number consists of a whole number and a fraction. Understanding this concept is important because it helps us to express decimal values in a different way.

What is a Mixed Number?

A mixed number has two parts:

  1. Whole Number: This is the number before the fraction.
  2. Fraction: This represents the part of a whole.

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

Steps to Convert Decimals to Mixed Numbers

Step 1: Identify the Whole Number

Look at the decimal number. The part before the decimal point is the whole number. For example, in (3.75), (3) is the whole number.

Step 2: Convert the Decimal Part to a Fraction

Take the decimal part (the part after the decimal point) and convert it into a fraction.

  • If you have (0.75), think of it as (75) hundredths. This can be written as (\frac{75}{100}).
  • Now, simplify the fraction if possible. (\frac{75}{100} = \frac{3}{4}).

Step 3: Combine the Whole Number and the Fraction

Finally, put the whole number and the fraction together to form a mixed number.

  • So, (3.75) becomes (3\frac{3}{4}).

Example

Let’s convert (2.5) into a mixed number.

  1. The whole number is (2).
  2. The decimal part is (0.5). This is the same as (\frac{5}{10}), which simplifies to (\frac{1}{2}).
  3. Combine them: (2.5 = 2\frac{1}{2}).

Key Rules

  • Always identify the whole number first.
  • Convert the decimal to a fraction. Remember to simplify!
  • Combine both parts to complete the mixed number.

Tips and Tricks

  • If the decimal is (0.1), (0.2), etc., remember that (0.1 = \frac{1}{10}), (0.2 = \frac{2}{10} = \frac{1}{5}), and so on.
  • Practice with different decimals to become more comfortable with the process.

Questions

Easy Level Questions

  1. Convert (1.25) to a mixed number.
  2. Convert (2.5) to a mixed number.
  3. Convert (3.1) to a mixed number.
  4. Convert (4.75) to a mixed number.
  5. Convert (0.6) to a mixed number.
  6. Convert (5.0) to a mixed number.
  7. Convert (6.2) to a mixed number.
  8. Convert (7.5) to a mixed number.
  9. Convert (8.8) to a mixed number.
  10. Convert (9.3) to a mixed number.

Medium Level Questions

  1. Convert (1.6) to a mixed number.
  2. Convert (2.33) to a mixed number.
  3. Convert (3.75) to a mixed number.
  4. Convert (4.1) to a mixed number.
  5. Convert (5.5) to a mixed number.
  6. Convert (6.4) to a mixed number.
  7. Convert (7.25) to a mixed number.
  8. Convert (8.9) to a mixed number.
  9. Convert (9.75) to a mixed number.
  10. Convert (0.9) to a mixed number.

Hard Level Questions

  1. Convert (1.875) to a mixed number.
  2. Convert (2.666) to a mixed number.
  3. Convert (3.125) to a mixed number.
  4. Convert (4.875) to a mixed number.
  5. Convert (5.5) to a mixed number.
  6. Convert (6.333) to a mixed number.
  7. Convert (7.05) to a mixed number.
  8. Convert (8.2) to a mixed number.
  9. Convert (9.125) to a mixed number.
  10. Convert (0.875) to a mixed number.

Answers

Easy Level Answers

  1. (1.25 = 1\frac{1}{4}) (Whole number: 1, Decimal: 0.25 = (\frac{1}{4})).
  2. (2.5 = 2\frac{1}{2}) (Whole number: 2, Decimal: 0.5 = (\frac{1}{2})).
  3. (3.1 = 3\frac{1}{10}) (Whole number: 3, Decimal: 0.1 = (\frac{1}{10})).
  4. (4.75 = 4\frac{3}{4}) (Whole number: 4, Decimal: 0.75 = (\frac{3}{4})).
  5. (0.6 = 0\frac{3}{5}) (Whole number: 0, Decimal: 0.6 = (\frac{3}{5})).
  6. (5.0 = 5\frac{0}{1}) (Whole number: 5, Decimal: 0 = (\frac{0}{1})).
  7. (6.2 = 6\frac{1}{5}) (Whole number: 6, Decimal: 0.2 = (\frac{1}{5})).
  8. (7.5 = 7\frac{1}{2}) (Whole number: 7, Decimal: 0.5 = (\frac{1}{2})).
  9. (8.8 = 8\frac{4}{5}) (Whole number: 8, Decimal: 0.8 = (\frac{4}{5})).
  10. (9.3 = 9\frac{3}{10}) (Whole number: 9, Decimal: 0.3 = (\frac{3}{10})).

Medium Level Answers

  1. (1.6 = 1\frac{3}{5}) (Whole number: 1, Decimal: 0.6 = (\frac{3}{5})).
  2. (2.33 = 2\frac{1}{3}) (Whole number: 2, Decimal: 0.33 ≈ (\frac{1}{3})).
  3. (3.75 = 3\frac{3}{4}) (Whole number: 3, Decimal: 0.75 = (\frac{3}{4})).
  4. (4.1 = 4\frac{1}{10}) (Whole number: 4, Decimal: 0.1 = (\frac{1}{10})).
  5. (5.5 = 5\frac{1}{2}) (Whole number: 5, Decimal: 0.5 = (\frac{1}{2})).
  6. (6.4 = 6\frac{2}{5}) (Whole number: 6, Decimal: 0.4 = (\frac{2}{5})).
  7. (7.25 = 7\frac{1}{4}) (Whole number: 7, Decimal: 0.25 = (\frac{1}{4})).
  8. (8.9 = 8\frac{9}{10}) (Whole number: 8, Decimal: 0.9 = (\frac{9}{10})).
  9. (9.75 = 9\frac{3}{4}) (Whole number: 9, Decimal: 0.75 = (\frac{3}{4})).
  10. (0.9 = 0\frac{9}{10}) (Whole number: 0, Decimal: 0.9 = (\frac{9}{10})).

Hard Level Answers

  1. (1.875 = 1\frac{7}{8}) (Whole number: 1, Decimal: 0.875 = (\frac{7}{8})).
  2. (2.666 = 2\frac{2}{3}) (Whole number: 2, Decimal: 0.666 ≈ (\frac{2}{3})).
  3. (3.125 = 3\frac{1}{8}) (Whole number: 3, Decimal: 0.125 = (\frac{1}{8})).
  4. (4.875 = 4\frac{7}{8}) (Whole number: 4, Decimal: 0.875 = (\frac{7}{8})).
  5. (5.5 = 5\frac{1}{2}) (Whole number: 5, Decimal: 0.5 = (\frac{1}{2})).
  6. (6.333 = 6\frac{1}{3}) (Whole number: 6, Decimal: 0.333 ≈ (\frac{1}{3})).
  7. (7.05 = 7\frac{1}{20}) (Whole number: 7, Decimal: 0.05 = (\frac{1}{20})).
  8. (8.2 = 8\frac{1}{5}) (Whole number: 8, Decimal: 0.2 = (\frac{1}{5})).
  9. (9.125 = 9\frac{1}{8}) (Whole number: 9, Decimal: 0.125 = (\frac{1}{8})).
  10. (0.875 = 0\frac{7}{8}) (Whole number: 0, Decimal: 0.875 = (\frac{7}{8})).