Year 4 Maths: Counting in Fractions

Introduction to Counting in Fractions

Hello, Year 4! Today, we’re going to learn about counting in fractions. Fractions are parts of a whole, and counting in fractions helps us understand how to work with these parts. Let’s break it down step by step!

What is a Fraction?

A fraction has two parts:

• The numerator (the top number), which tells us how many parts we have.
• The denominator (the bottom number), which tells us how many equal parts the whole is divided into.

For example, in the fraction $$\frac{1}{2}$$:

• The 1 (numerator) means we have one part.
• The 2 (denominator) means the whole is divided into two equal parts.

Counting in Fractions

When we count in fractions, we can list fractions in a sequence. Let’s look at some examples:

Example 1: Counting in Halves

• Start with $$\frac{1}{2}$$
• Then, the next half is $$\frac{2}{2}$$ (which is the same as 1)
• After that, we can go to $$\frac{3}{2}$$ (which is 1 and a half)
• Then, $$\frac{4}{2}$$ (which is 2)

So, counting in halves looks like this:

$$\frac{1}{2}, 1, \frac{3}{2}, 2, \frac{5}{2}, 3, \ldots$$

Example 2: Counting in Quarters

• Start with $$\frac{1}{4}$$
• The next quarter is $$\frac{2}{4}$$ (which is the same as $$\frac{1}{2}$$)
• Then, $$\frac{3}{4}$$
• After that, $$\frac{4}{4}$$ (which is 1)

So, counting in quarters looks like this:

$$\frac{1}{4}, \frac{2}{4}, \frac{3}{4}, 1, \frac{5}{4}, \frac{6}{4}, \ldots$$

Key Rules for Counting in Fractions

1. Keep the Denominator the Same: When counting in fractions with the same denominator, only change the numerator.
   • Example: $$\frac{1}{3}, \frac{2}{3}, \frac{3}{3}, \frac{4}{3}, \ldots$$
2. Add the Same Amount: When counting, you’re adding the same fraction each time. For example, when counting in quarters, you add $$\frac{1}{4}$$ each time.
3. Understanding Improper Fractions: When the numerator is bigger than the denominator (like $$\frac{5}{4}$$), it means you have more than one whole.

Tips and Tricks

• Visuals: Draw circles or bars to represent fractions. This helps you see how fractions fit together.
• Use Number Lines: Draw a number line and mark where each fraction goes. This helps with understanding the size of each fraction.
• Practice with Real Objects: Use pizza slices or chocolate bars to create fractions that you can count.

Questions for Practice

Easy Level (20 Questions)

1. What is $$\frac{1}{2} + \frac{1}{2}$$?
2. Write the next fraction after $$\frac{1}{3}$$.
3. Count in halves from $$\frac{1}{2}$$ to $$2$$.
4. What is $$\frac{3}{4}$$ plus $$\frac{1}{4}$$?
5. How many quarters are in $$1$$?
6. Write the next two fractions after $$\frac{1}{4}$$.
7. What is $$\frac{2}{2}$$?
8. Count in thirds from $$\frac{1}{3}$$ to $$2$$.
9. What is $$\frac{1}{4}$$ plus $$\frac{2}{4}$$?
10. What is the numerator in $$\frac{2}{5}$$?
11. How many halves are in $$2$$?
12. Write the next fraction after $$\frac{2}{3}$$.
13. What is $$\frac{1}{3} + \frac{2}{3}$$?
14. Write the next two fractions after $$\frac{3}{4}$$.
15. What does $$\frac{4}{4}$$ equal?
16. How many quarters are in $$2$$?
17. Write the next fraction after $$\frac{1}{2}$$.
18. What is $$\frac{1}{5} + \frac{4}{5}$$?
19. How many halves are in $$1$$?
20. What is the next fraction after $$\frac{5}{5}$$?

Medium Level (20 Questions)

1. Count in quarters from $$\frac{1}{4}$$ to $$\frac{5}{4}$$.
2. What is $$\frac{3}{5} + \frac{1}{5}$$?
3. Write the next fraction after $$\frac{2}{6}$$.
4. How many eighths are in $$1$$?
5. Count in halves from $$1$$ to $$3$$.
6. What is $$\frac{1}{2} + \frac{1}{4}$$?
7. Write the next two fractions after $$\frac{5}{6}$$.
8. What is $$\frac{2}{3} + \frac{1}{3}$$?
9. How many quarters are in $$\frac{3}{2}$$?
10. Count in sixths starting from $$\frac{1}{6}$$.
11. What is $$\frac{1}{4} + \frac{3}{4}$$?
12. Write the next fraction after $$\frac{3}{3}$$.
13. What is $$\frac{5}{4} – 1$$?
14. How many halves are in $$\frac{7}{2}$$?
15. Count in thirds from $$\frac{2}{3}$$ to $$\frac{5}{3}$$.
16. What is $$\frac{2}{5} + \frac{3}{5}$$?
17. Write the next two fractions after $$\frac{4}{8}$$.
18. How many quarters are in $$\frac{5}{4}$$?
19. What is $$\frac{3}{4} + \frac{1}{2}$$?
20. Count in eighths from $$\frac{1}{8}$$ to $$2$$.

Hard Level (20 Questions)

1. Count in fifths from $$\frac{1}{5}$$ to $$\frac{6}{5}$$.
2. What is $$\frac{4}{6} + \frac{1}{3}$$?
3. Write the next two fractions after $$\frac{7}{8}$$.
4. How many thirds are in $$\frac{10}{3}$$?
5. Count in sixths from $$\frac{1}{6}$$ to $$\frac{5}{3}$$.
6. What is $$\frac{5}{8} + \frac{3}{8}$$?
7. Write the next fraction after $$\frac{9}{10}$$.
8. What does $$\frac{6}{4}$$ equal as a mixed number?
9. Count in quarters from $$\frac{5}{4}$$ to $$2$$.
10. How many eighths are in $$\frac{9}{4}$$?
11. What is $$\frac{2}{7} + \frac{3}{7}$$?
12. Write the next two fractions after $$\frac{5}{6}$$.
13. What is $$\frac{1}{2} + \frac{1}{3}$$?
14. Count in fifths starting from $$\frac{2}{5}$$.
15. How many halves are in $$\frac{11}{2}$$?
16. What is $$\frac{5}{3} – 1$$?
17. Count in eighths from $$\frac{3}{8}$$ to $$\frac{10}{8}$$.
18. What is $$\frac{2}{3} + \frac{5}{6}$$?
19. Write the next fraction after $$\frac{10}{11}$$.
20. Count in quarters from $$2$$ to $$\frac{9}{4}$$.

Answers and Explanations

Easy Level Answers

1. 1
2. $$\frac{2}{3}$$
3. $$\frac{1}{2}, 1, \frac{3}{2}, 2$$
4. 1
5. 4
6. $$\frac{2}{4}, \frac{3}{4}$$
7. 1
8. $$\frac{1}{3}, \frac{2}{3}, 1$$
9. 1
10. 2
11. 2
12. $$\frac{2}{3}, 1$$
13. 1
14. $$\frac{4}{4}, \frac{5}{4}$$
15. 1
16. 8
17. 1
18. $$\frac{5}{4}$$
19. 0
20. $$\frac{9}{4}$$

Medium Level Answers

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

Hard Level Answers

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

Feel free to practice these questions, and remember that counting in fractions can be fun! Keep working at it, and you’ll get even better!