Year 6 Maths: Multiplying a Mixed Number by a Fraction

Introduction to Mixed Numbers and Fractions

Hello Year 6! Today, we’re going to learn how to multiply a mixed number by a fraction.

What is a Mixed Number?

A mixed number is a whole number combined with a fraction. For example, (2 \frac{3}{4}) means 2 whole parts and 3 out of 4 parts of another whole.

What is a Fraction?

A fraction is a way to show a part of a whole. For example, (\frac{1}{2}) means one part out of two equal parts.

Steps to Multiply a Mixed Number by a Fraction

Let’s break it down into simple steps!

Step 1: Convert the Mixed Number to an Improper Fraction

An improper fraction has a numerator (the top number) that is larger than the denominator (the bottom number). To convert a mixed number:

1. Multiply the whole number by the denominator.
2. Add the numerator to that result.
3. Place that number over the original denominator.

For example, to convert (2 \frac{3}{4}) to an improper fraction:

• Multiply: (2 \times 4 = 8)
• Add: (8 + 3 = 11)
• So, (2 \frac{3}{4} = \frac{11}{4})

Step 2: Multiply the Improper Fraction by the Fraction

Now that we have our improper fraction, we can multiply it by another fraction.

For example, let’s say we want to multiply (\frac{11}{4}) by (\frac{1}{2}):

• Multiply the numerators: (11 \times 1 = 11)
• Multiply the denominators: (4 \times 2 = 8)
• So, (\frac{11}{4} \times \frac{1}{2} = \frac{11}{8})

Step 3: Convert Back to a Mixed Number (if needed)

If your answer is an improper fraction and you need to convert it back to a mixed number:

1. Divide the numerator by the denominator.
2. The quotient is your whole number, and the remainder is the numerator of your fraction.

For our previous example:

• Divide: (11 \div 8 = 1) remainder (3)
• So, (\frac{11}{8} = 1 \frac{3}{8})

Key Rules

1. Always convert mixed numbers to improper fractions before multiplying.
2. Multiply the numerators and denominators separately.
3. Always simplify your answer if possible.

Tips and Tricks

• Visual Aids: Drawing pictures can help you see what the fractions represent.
• Practice: The more you practice, the easier it will become.
• Check Your Work: After you finish, double-check your calculations.

Questions for Practice

Easy Level Questions

1. (1 \frac{1}{2} \times \frac{1}{3})
2. (2 \frac{1}{4} \times \frac{1}{2})
3. (3 \frac{1}{3} \times \frac{1}{4})
4. (4 \frac{1}{5} \times \frac{1}{2})
5. (1 \frac{2}{3} \times \frac{2}{3})
6. (2 \frac{3}{4} \times \frac{1}{4})
7. (3 \frac{1}{2} \times \frac{1}{5})
8. (1 \frac{3}{4} \times \frac{1}{2})
9. (2 \frac{1}{2} \times \frac{3}{4})
10. (3 \frac{1}{4} \times \frac{1}{6})
11. (2 \frac{2}{3} \times \frac{1}{2})
12. (1 \frac{1}{5} \times \frac{1}{3})
13. (4 \frac{1}{2} \times \frac{1}{2})
14. (3 \frac{2}{3} \times \frac{1}{4})
15. (1 \frac{1}{2} \times \frac{2}{5})
16. (2 \frac{3}{4} \times \frac{2}{3})
17. (4 \frac{1}{3} \times \frac{1}{3})
18. (1 \frac{2}{5} \times \frac{1}{2})
19. (3 \frac{1}{2} \times \frac{2}{3})
20. (2 \frac{1}{4} \times \frac{3}{5})

Medium Level Questions

1. (2 \frac{2}{3} \times \frac{3}{4})
2. (1 \frac{3}{5} \times \frac{4}{5})
3. (3 \frac{4}{6} \times \frac{2}{3})
4. (2 \frac{1}{2} \times \frac{5}{8})
5. (1 \frac{1}{3} \times \frac{3}{7})
6. (4 \frac{1}{2} \times \frac{5}{6})
7. (2 \frac{3}{4} \times \frac{3}{5})
8. (3 \frac{2}{5} \times \frac{4}{7})
9. (1 \frac{2}{3} \times \frac{5}{6})
10. (3 \frac{3}{8} \times \frac{1}{2})
11. (2 \frac{1}{4} \times \frac{7}{8})
12. (1 \frac{3}{7} \times \frac{2}{5})
13. (4 \frac{2}{3} \times \frac{2}{9})
14. (3 \frac{1}{4} \times \frac{5}{12})
15. (1 \frac{1}{2} \times \frac{8}{9})
16. (2 \frac{2}{5} \times \frac{3}{8})
17. (4 \frac{1}{5} \times \frac{4}{5})
18. (1 \frac{3}{8} \times \frac{5}{7})
19. (3 \frac{1}{2} \times \frac{2}{11})
20. (2 \frac{3}{4} \times \frac{3}{10})

Hard Level Questions

1. (3 \frac{5}{6} \times \frac{7}{9})
2. (1 \frac{1}{2} \times \frac{11}{12})
3. (4 \frac{3}{4} \times \frac{6}{7})
4. (2 \frac{5}{8} \times \frac{9}{10})
5. (3 \frac{1}{3} \times \frac{8}{15})
6. (1 \frac{7}{8} \times \frac{5}{6})
7. (2 \frac{2}{3} \times \frac{7}{8})
8. (4 \frac{1}{2} \times \frac{3}{5})
9. (1 \frac{1}{4} \times \frac{13}{14})
10. (3 \frac{3}{5} \times \frac{5}{8})
11. (2 \frac{1}{2} \times \frac{4}{11})
12. (1 \frac{5}{6} \times \frac{2}{3})
13. (4 \frac{1}{3} \times \frac{5}{8})
14. (3 \frac{2}{5} \times \frac{3}{7})
15. (1 \frac{3}{4} \times \frac{11}{15})
16. (2 \frac{4}{5} \times \frac{9}{10})
17. (3 \frac{1}{6} \times \frac{4}{5})
18. (2 \frac{3}{4} \times \frac{5}{12})
19. (1 \frac{2}{3} \times \frac{3}{8})
20. (4 \frac{1}{2} \times \frac{7}{10})

Answers and Explanations

Easy Level Answers

1. (1 \frac{1}{6})
2. (1 \frac{1}{8})
3. (1 \frac{1}{3})
4. (2 \frac{1}{5})
5. (1)
6. ( \frac{11}{16})
7. ( \frac{7}{10})
8. ( \frac{3}{8})
9. (1 \frac{1}{2})
10. ( \frac{1}{8})
11. (1 \frac{1}{3})
12. ( \frac{1}{15})
13. (2)
14. ( \frac{1}{6})
15. ( \frac{3}{5})
16. (2)
17. (1 \frac{1}{9})
18. ( \frac{1}{5})
19. ( \frac{1}{3})
20. ( \frac{3}{5})

Medium Level Answers

1. (2)
2. (1 \frac{3}{5})
3. (2 \frac{1}{3})
4. (1 \frac{1}{4})
5. ( \frac{4}{21})
6. ( \frac{15}{12})
7. (1 \frac{1}{5})
8. (1 \frac{2}{5})
9. (1 \frac{1}{4})
10. ( \frac{1}{8})
11. ( \frac{14}{40})
12. ( \frac{2}{15})
13. (2 \frac{1}{3})
14. ( \frac{1}{8})
15. ( \frac{8}{9})
16. ( \frac{3}{10})
17. ( \frac{8}{15})
18. ( \frac{15}{56})
19. ( \frac{7}{22})
20. ( \frac{9}{20})

Hard Level Answers

1. ( \frac{35}{27}) or (1 \frac{8}{27})
2. ( \frac{5}{8})
3. ( \frac{18}{7}) or (2 \frac{4}{7})
4. ( \frac{9}{4}) or (2 \frac{1}{4})
5. ( \frac{22}{45})
6. ( \frac{5}{12})
7. ( \frac{21}{40})
8. ( \frac{6}{5}) or (1 \frac{1}{5})
9. ( \frac{13}{56})
10. ( \frac{15}{40}) or ( \frac{3}{8})
11. ( \frac{10}{11})
12. (1 \frac{1}{9})
13. ( \frac{27}{24}) or (1 \frac{1}{8})
14. ( \frac{9}{35})
15. ( \frac{13}{60})
16. ( \frac{4}{5})
17. ( \frac{24}{30}) or ( \frac{4}{5})
18. ( \frac{1}{5})
19. ( \frac{1}{4})
20. ( \frac{31}{20}) or (1 \frac{11}{20})

Feel free to ask any questions if you need help or clarification! Happy learning!