Year 5: Simplifying fractions

Key words. To simplify a fraction is to write it with smaller numbers. A common factor is a number that divides exactly into both the top and the bottom. The simplest form is when the only common factor is 1.

Method. Divide the top and the bottom by a common factor. The biggest common factor (the highest common factor, HCF) does it in one go.

1. List the factors of 2 and of 4. A factor divides exactly into the number. We need the factors both numbers share (the common factors).
   Factors of 2: 1, 2
   Factors of 4: 1, 2, 4
   Common factors: 1, 2
2. Pick the biggest common factor: 2. Divide the top and the bottom by 2. Dividing both numbers by the same number does not change the value of the fraction. It just writes it with smaller numbers.
   24 = 2 ÷ 24 ÷ 2 = 12
3. Check it is in its simplest form. If 1 and 2 still shared a factor, we could go on.
   The only common factor of 1 and 2 is 1, so 12 is the simplest form.

Check. Multiply back: 1 × 2 = 2 and 2 × 2 = 4. ✓

Watch out. Divide the top and the bottom. Subtracting the same number from both changes the fraction.

Key words. To simplify a fraction is to write it with smaller numbers. A common factor is a number that divides exactly into both the top and the bottom. The simplest form is when the only common factor is 1.

Method. Divide the top and the bottom by a common factor. The biggest common factor (the highest common factor, HCF) does it in one go.

1. List the factors of 4 and of 8. A factor divides exactly into the number. We need the factors both numbers share (the common factors).
   Factors of 4: 1, 2, 4
   Factors of 8: 1, 2, 4, 8
   Common factors: 1, 2, 4
2. Pick the biggest common factor: 4. Divide the top and the bottom by 4. Dividing both numbers by the same number does not change the value of the fraction. It just writes it with smaller numbers.
   48 = 4 ÷ 48 ÷ 4 = 12
3. Check it is in its simplest form. If 1 and 2 still shared a factor, we could go on.
   The only common factor of 1 and 2 is 1, so 12 is the simplest form.

Check. Multiply back: 1 × 4 = 4 and 2 × 4 = 8. ✓

Watch out. Divide the top and the bottom. Subtracting the same number from both changes the fraction.

Key words. To simplify a fraction is to write it with smaller numbers. A common factor is a number that divides exactly into both the top and the bottom. The simplest form is when the only common factor is 1.

Method. Divide the top and the bottom by a common factor. The biggest common factor (the highest common factor, HCF) does it in one go.

1. List the factors of 3 and of 12. A factor divides exactly into the number. We need the factors both numbers share (the common factors).
   Factors of 3: 1, 3
   Factors of 12: 1, 2, 3, 4, 6, 12
   Common factors: 1, 3
2. Pick the biggest common factor: 3. Divide the top and the bottom by 3. Dividing both numbers by the same number does not change the value of the fraction. It just writes it with smaller numbers.
   312 = 3 ÷ 312 ÷ 3 = 14
3. Check it is in its simplest form. If 1 and 4 still shared a factor, we could go on.
   The only common factor of 1 and 4 is 1, so 14 is the simplest form.

Check. Multiply back: 1 × 3 = 3 and 4 × 3 = 12. ✓

Watch out. Divide the top and the bottom. Subtracting the same number from both changes the fraction.

Key words. To simplify a fraction is to write it with smaller numbers. A common factor is a number that divides exactly into both the top and the bottom. The simplest form is when the only common factor is 1.

Method. Divide the top and the bottom by a common factor. The biggest common factor (the highest common factor, HCF) does it in one go.

1. List the factors of 2 and of 6. A factor divides exactly into the number. We need the factors both numbers share (the common factors).
   Factors of 2: 1, 2
   Factors of 6: 1, 2, 3, 6
   Common factors: 1, 2
2. Pick the biggest common factor: 2. Divide the top and the bottom by 2. Dividing both numbers by the same number does not change the value of the fraction. It just writes it with smaller numbers.
   26 = 2 ÷ 26 ÷ 2 = 13
3. Check it is in its simplest form. If 1 and 3 still shared a factor, we could go on.
   The only common factor of 1 and 3 is 1, so 13 is the simplest form.

Check. Multiply back: 1 × 2 = 2 and 3 × 2 = 6. ✓

Watch out. Divide the top and the bottom. Subtracting the same number from both changes the fraction.

Key words. To simplify a fraction is to write it with smaller numbers. A common factor is a number that divides exactly into both the top and the bottom. The simplest form is when the only common factor is 1.

Method. Divide the top and the bottom by a common factor. The biggest common factor (the highest common factor, HCF) does it in one go.

1. List the factors of 5 and of 10. A factor divides exactly into the number. We need the factors both numbers share (the common factors).
   Factors of 5: 1, 5
   Factors of 10: 1, 2, 5, 10
   Common factors: 1, 5
2. Pick the biggest common factor: 5. Divide the top and the bottom by 5. Dividing both numbers by the same number does not change the value of the fraction. It just writes it with smaller numbers.
   510 = 5 ÷ 510 ÷ 5 = 12
3. Check it is in its simplest form. If 1 and 2 still shared a factor, we could go on.
   The only common factor of 1 and 2 is 1, so 12 is the simplest form.

Check. Multiply back: 1 × 5 = 5 and 2 × 5 = 10. ✓

Watch out. Divide the top and the bottom. Subtracting the same number from both changes the fraction.

Key words. To simplify a fraction is to write it with smaller numbers. A common factor is a number that divides exactly into both the top and the bottom. The simplest form is when the only common factor is 1.

Method. Divide the top and the bottom by a common factor. The biggest common factor (the highest common factor, HCF) does it in one go.

1. List the factors of 4 and of 10. A factor divides exactly into the number. We need the factors both numbers share (the common factors).
   Factors of 4: 1, 2, 4
   Factors of 10: 1, 2, 5, 10
   Common factors: 1, 2
2. Pick the biggest common factor: 2. Divide the top and the bottom by 2. Dividing both numbers by the same number does not change the value of the fraction. It just writes it with smaller numbers.
   410 = 4 ÷ 210 ÷ 2 = 25
3. Check it is in its simplest form. If 2 and 5 still shared a factor, we could go on.
   The only common factor of 2 and 5 is 1, so 25 is the simplest form.

Check. Multiply back: 2 × 2 = 4 and 5 × 2 = 10. ✓

Watch out. Divide the top and the bottom. Subtracting the same number from both changes the fraction.

Key words. To simplify a fraction is to write it with smaller numbers. A common factor is a number that divides exactly into both the top and the bottom. The simplest form is when the only common factor is 1.

Method. Divide the top and the bottom by a common factor. The biggest common factor (the highest common factor, HCF) does it in one go.

1. List the factors of 3 and of 9. A factor divides exactly into the number. We need the factors both numbers share (the common factors).
   Factors of 3: 1, 3
   Factors of 9: 1, 3, 9
   Common factors: 1, 3
2. Pick the biggest common factor: 3. Divide the top and the bottom by 3. Dividing both numbers by the same number does not change the value of the fraction. It just writes it with smaller numbers.
   39 = 3 ÷ 39 ÷ 3 = 13
3. Check it is in its simplest form. If 1 and 3 still shared a factor, we could go on.
   The only common factor of 1 and 3 is 1, so 13 is the simplest form.

Check. Multiply back: 1 × 3 = 3 and 3 × 3 = 9. ✓

Watch out. Divide the top and the bottom. Subtracting the same number from both changes the fraction.

Key words. To simplify a fraction is to write it with smaller numbers. A common factor is a number that divides exactly into both the top and the bottom. The simplest form is when the only common factor is 1.

Method. Divide the top and the bottom by a common factor. The biggest common factor (the highest common factor, HCF) does it in one go.

1. List the factors of 5 and of 15. A factor divides exactly into the number. We need the factors both numbers share (the common factors).
   Factors of 5: 1, 5
   Factors of 15: 1, 3, 5, 15
   Common factors: 1, 5
2. Pick the biggest common factor: 5. Divide the top and the bottom by 5. Dividing both numbers by the same number does not change the value of the fraction. It just writes it with smaller numbers.
   515 = 5 ÷ 515 ÷ 5 = 13
3. Check it is in its simplest form. If 1 and 3 still shared a factor, we could go on.
   The only common factor of 1 and 3 is 1, so 13 is the simplest form.

Check. Multiply back: 1 × 5 = 5 and 3 × 5 = 15. ✓

Watch out. Divide the top and the bottom. Subtracting the same number from both changes the fraction.

Key words. To simplify a fraction is to write it with smaller numbers. A common factor is a number that divides exactly into both the top and the bottom. The simplest form is when the only common factor is 1.

Method. Divide the top and the bottom by a common factor. The biggest common factor (the highest common factor, HCF) does it in one go.

1. List the factors of 10 and of 25. A factor divides exactly into the number. We need the factors both numbers share (the common factors).
   Factors of 10: 1, 2, 5, 10
   Factors of 25: 1, 5, 25
   Common factors: 1, 5
2. Pick the biggest common factor: 5. Divide the top and the bottom by 5. Dividing both numbers by the same number does not change the value of the fraction. It just writes it with smaller numbers.
   1025 = 10 ÷ 525 ÷ 5 = 25
3. Check it is in its simplest form. If 2 and 5 still shared a factor, we could go on.
   The only common factor of 2 and 5 is 1, so 25 is the simplest form.

Check. Multiply back: 2 × 5 = 10 and 5 × 5 = 25. ✓

Watch out. Divide the top and the bottom. Subtracting the same number from both changes the fraction.

Key words. To simplify a fraction is to write it with smaller numbers. A common factor is a number that divides exactly into both the top and the bottom. The simplest form is when the only common factor is 1.

Method. Divide the top and the bottom by a common factor. The biggest common factor (the highest common factor, HCF) does it in one go.

1. List the factors of 6 and of 15. A factor divides exactly into the number. We need the factors both numbers share (the common factors).
   Factors of 6: 1, 2, 3, 6
   Factors of 15: 1, 3, 5, 15
   Common factors: 1, 3
2. Pick the biggest common factor: 3. Divide the top and the bottom by 3. Dividing both numbers by the same number does not change the value of the fraction. It just writes it with smaller numbers.
   615 = 6 ÷ 315 ÷ 3 = 25
3. Check it is in its simplest form. If 2 and 5 still shared a factor, we could go on.
   The only common factor of 2 and 5 is 1, so 25 is the simplest form.

Check. Multiply back: 2 × 3 = 6 and 5 × 3 = 15. ✓

Watch out. Divide the top and the bottom. Subtracting the same number from both changes the fraction.

Key words. To simplify a fraction is to write it with smaller numbers. A common factor is a number that divides exactly into both the top and the bottom. The simplest form is when the only common factor is 1.

Method. Divide the top and the bottom by a common factor. The biggest common factor (the highest common factor, HCF) does it in one go.

1. List the factors of 14 and of 21. A factor divides exactly into the number. We need the factors both numbers share (the common factors).
   Factors of 14: 1, 2, 7, 14
   Factors of 21: 1, 3, 7, 21
   Common factors: 1, 7
2. Pick the biggest common factor: 7. Divide the top and the bottom by 7. Dividing both numbers by the same number does not change the value of the fraction. It just writes it with smaller numbers.
   1421 = 14 ÷ 721 ÷ 7 = 23
3. Check it is in its simplest form. If 2 and 3 still shared a factor, we could go on.
   The only common factor of 2 and 3 is 1, so 23 is the simplest form.

Check. Multiply back: 2 × 7 = 14 and 3 × 7 = 21. ✓

Watch out. Divide the top and the bottom. Subtracting the same number from both changes the fraction.

Key words. To simplify a fraction is to write it with smaller numbers. A common factor is a number that divides exactly into both the top and the bottom. The simplest form is when the only common factor is 1.

Method. Divide the top and the bottom by a common factor. The biggest common factor (the highest common factor, HCF) does it in one go.

1. List the factors of 8 and of 20. A factor divides exactly into the number. We need the factors both numbers share (the common factors).
   Factors of 8: 1, 2, 4, 8
   Factors of 20: 1, 2, 4, 5, 10, 20
   Common factors: 1, 2, 4
2. Pick the biggest common factor: 4. Divide the top and the bottom by 4. Dividing both numbers by the same number does not change the value of the fraction. It just writes it with smaller numbers.
   820 = 8 ÷ 420 ÷ 4 = 25
3. Check it is in its simplest form. If 2 and 5 still shared a factor, we could go on.
   The only common factor of 2 and 5 is 1, so 25 is the simplest form.

Check. Multiply back: 2 × 4 = 8 and 5 × 4 = 20. ✓

Watch out. Divide the top and the bottom. Subtracting the same number from both changes the fraction.

Key words. To simplify a fraction is to write it with smaller numbers. A common factor is a number that divides exactly into both the top and the bottom. The simplest form is when the only common factor is 1.

Method. Divide the top and the bottom by a common factor. The biggest common factor (the highest common factor, HCF) does it in one go.

1. List the factors of 8 and of 12. A factor divides exactly into the number. We need the factors both numbers share (the common factors).
   Factors of 8: 1, 2, 4, 8
   Factors of 12: 1, 2, 3, 4, 6, 12
   Common factors: 1, 2, 4
2. Pick the biggest common factor: 4. Divide the top and the bottom by 4. Dividing both numbers by the same number does not change the value of the fraction. It just writes it with smaller numbers.
   812 = 8 ÷ 412 ÷ 4 = 23
3. Check it is in its simplest form. If 2 and 3 still shared a factor, we could go on.
   The only common factor of 2 and 3 is 1, so 23 is the simplest form.

Check. Multiply back: 2 × 4 = 8 and 3 × 4 = 12. ✓

Watch out. Divide the top and the bottom. Subtracting the same number from both changes the fraction.

Key words. To simplify a fraction is to write it with smaller numbers. A common factor is a number that divides exactly into both the top and the bottom. The simplest form is when the only common factor is 1.

Method. Divide the top and the bottom by a common factor. The biggest common factor (the highest common factor, HCF) does it in one go.

1. List the factors of 9 and of 15. A factor divides exactly into the number. We need the factors both numbers share (the common factors).
   Factors of 9: 1, 3, 9
   Factors of 15: 1, 3, 5, 15
   Common factors: 1, 3
2. Pick the biggest common factor: 3. Divide the top and the bottom by 3. Dividing both numbers by the same number does not change the value of the fraction. It just writes it with smaller numbers.
   915 = 9 ÷ 315 ÷ 3 = 35
3. Check it is in its simplest form. If 3 and 5 still shared a factor, we could go on.
   The only common factor of 3 and 5 is 1, so 35 is the simplest form.

Check. Multiply back: 3 × 3 = 9 and 5 × 3 = 15. ✓

Watch out. Divide the top and the bottom. Subtracting the same number from both changes the fraction.

Key words. To simplify a fraction is to write it with smaller numbers. A common factor is a number that divides exactly into both the top and the bottom. The simplest form is when the only common factor is 1.

Method. Divide the top and the bottom by a common factor. The biggest common factor (the highest common factor, HCF) does it in one go.

1. List the factors of 16 and of 24. A factor divides exactly into the number. We need the factors both numbers share (the common factors).
   Factors of 16: 1, 2, 4, 8, 16
   Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
   Common factors: 1, 2, 4, 8
2. Pick the biggest common factor: 8. Divide the top and the bottom by 8. Dividing both numbers by the same number does not change the value of the fraction. It just writes it with smaller numbers.
   1624 = 16 ÷ 824 ÷ 8 = 23
3. Check it is in its simplest form. If 2 and 3 still shared a factor, we could go on.
   The only common factor of 2 and 3 is 1, so 23 is the simplest form.

Check. Multiply back: 2 × 8 = 16 and 3 × 8 = 24. ✓

Watch out. Divide the top and the bottom. Subtracting the same number from both changes the fraction.

Key words. To simplify a fraction is to write it with smaller numbers. A common factor is a number that divides exactly into both the top and the bottom. The simplest form is when the only common factor is 1.

Method. Divide the top and the bottom by a common factor. The biggest common factor (the highest common factor, HCF) does it in one go.

1. List the factors of 18 and of 30. A factor divides exactly into the number. We need the factors both numbers share (the common factors).
   Factors of 18: 1, 2, 3, 6, 9, 18
   Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
   Common factors: 1, 2, 3, 6
2. Pick the biggest common factor: 6. Divide the top and the bottom by 6. Dividing both numbers by the same number does not change the value of the fraction. It just writes it with smaller numbers.
   1830 = 18 ÷ 630 ÷ 6 = 35
3. Check it is in its simplest form. If 3 and 5 still shared a factor, we could go on.
   The only common factor of 3 and 5 is 1, so 35 is the simplest form.

Check. Multiply back: 3 × 6 = 18 and 5 × 6 = 30. ✓

Watch out. Divide the top and the bottom. Subtracting the same number from both changes the fraction.

Key words. To simplify a fraction is to write it with smaller numbers. A common factor is a number that divides exactly into both the top and the bottom. The simplest form is when the only common factor is 1.

Method. Divide the top and the bottom by a common factor. The biggest common factor (the highest common factor, HCF) does it in one go.

1. List the factors of 20 and of 32. A factor divides exactly into the number. We need the factors both numbers share (the common factors).
   Factors of 20: 1, 2, 4, 5, 10, 20
   Factors of 32: 1, 2, 4, 8, 16, 32
   Common factors: 1, 2, 4
2. Pick the biggest common factor: 4. Divide the top and the bottom by 4. Dividing both numbers by the same number does not change the value of the fraction. It just writes it with smaller numbers.
   2032 = 20 ÷ 432 ÷ 4 = 58
3. Check it is in its simplest form. If 5 and 8 still shared a factor, we could go on.
   The only common factor of 5 and 8 is 1, so 58 is the simplest form.

Check. Multiply back: 5 × 4 = 20 and 8 × 4 = 32. ✓

Watch out. Divide the top and the bottom. Subtracting the same number from both changes the fraction.

Key words. To simplify a fraction is to write it with smaller numbers. A common factor is a number that divides exactly into both the top and the bottom. The simplest form is when the only common factor is 1.

Method. Divide the top and the bottom by a common factor. The biggest common factor (the highest common factor, HCF) does it in one go.

1. List the factors of 24 and of 36. A factor divides exactly into the number. We need the factors both numbers share (the common factors).
   Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
   Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
   Common factors: 1, 2, 3, 4, 6, 12
2. Pick the biggest common factor: 12. Divide the top and the bottom by 12. Dividing both numbers by the same number does not change the value of the fraction. It just writes it with smaller numbers.
   2436 = 24 ÷ 1236 ÷ 12 = 23
3. Check it is in its simplest form. If 2 and 3 still shared a factor, we could go on.
   The only common factor of 2 and 3 is 1, so 23 is the simplest form.

Check. Multiply back: 2 × 12 = 24 and 3 × 12 = 36. ✓

Watch out. Divide the top and the bottom. Subtracting the same number from both changes the fraction.

Key words. To simplify a fraction is to write it with smaller numbers. A common factor is a number that divides exactly into both the top and the bottom. The simplest form is when the only common factor is 1.

Method. Divide the top and the bottom by a common factor. The biggest common factor (the highest common factor, HCF) does it in one go.

1. List the factors of 25 and of 100. A factor divides exactly into the number. We need the factors both numbers share (the common factors).
   Factors of 25: 1, 5, 25
   Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
   Common factors: 1, 5, 25
2. Pick the biggest common factor: 25. Divide the top and the bottom by 25. Dividing both numbers by the same number does not change the value of the fraction. It just writes it with smaller numbers.
   25100 = 25 ÷ 25100 ÷ 25 = 14
3. Check it is in its simplest form. If 1 and 4 still shared a factor, we could go on.
   The only common factor of 1 and 4 is 1, so 14 is the simplest form.

Check. Multiply back: 1 × 25 = 25 and 4 × 25 = 100. ✓

Watch out. Divide the top and the bottom. Subtracting the same number from both changes the fraction.

Key words. To simplify a fraction is to write it with smaller numbers. A common factor is a number that divides exactly into both the top and the bottom. The simplest form is when the only common factor is 1.

Method. Divide the top and the bottom by a common factor. The biggest common factor (the highest common factor, HCF) does it in one go.

1. List the factors of 60 and of 100. A factor divides exactly into the number. We need the factors both numbers share (the common factors).
   Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
   Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
   Common factors: 1, 2, 4, 5, 10, 20
2. Pick the biggest common factor: 20. Divide the top and the bottom by 20. Dividing both numbers by the same number does not change the value of the fraction. It just writes it with smaller numbers.
   60100 = 60 ÷ 20100 ÷ 20 = 35
3. Check it is in its simplest form. If 3 and 5 still shared a factor, we could go on.
   The only common factor of 3 and 5 is 1, so 35 is the simplest form.

Check. Multiply back: 3 × 20 = 60 and 5 × 20 = 100. ✓

Watch out. Divide the top and the bottom. Subtracting the same number from both changes the fraction.

Key words. To simplify a fraction is to write it with smaller numbers. A common factor is a number that divides exactly into both the top and the bottom. The simplest form is when the only common factor is 1.

Method. Divide the top and the bottom by a common factor. The biggest common factor (the highest common factor, HCF) does it in one go.

1. List the factors of 45 and of 100. A factor divides exactly into the number. We need the factors both numbers share (the common factors).
   Factors of 45: 1, 3, 5, 9, 15, 45
   Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
   Common factors: 1, 5
2. Pick the biggest common factor: 5. Divide the top and the bottom by 5. Dividing both numbers by the same number does not change the value of the fraction. It just writes it with smaller numbers.
   45100 = 45 ÷ 5100 ÷ 5 = 920
3. Check it is in its simplest form. If 9 and 20 still shared a factor, we could go on.
   The only common factor of 9 and 20 is 1, so 920 is the simplest form.

Check. Multiply back: 9 × 5 = 45 and 20 × 5 = 100. ✓

Watch out. Divide the top and the bottom. Subtracting the same number from both changes the fraction.

Key words. To simplify a fraction is to write it with smaller numbers. A common factor is a number that divides exactly into both the top and the bottom. The simplest form is when the only common factor is 1.

Method. Divide the top and the bottom by a common factor. The biggest common factor (the highest common factor, HCF) does it in one go.

1. List the factors of 75 and of 100. A factor divides exactly into the number. We need the factors both numbers share (the common factors).
   Factors of 75: 1, 3, 5, 15, 25, 75
   Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
   Common factors: 1, 5, 25
2. Pick the biggest common factor: 25. Divide the top and the bottom by 25. Dividing both numbers by the same number does not change the value of the fraction. It just writes it with smaller numbers.
   75100 = 75 ÷ 25100 ÷ 25 = 34
3. Check it is in its simplest form. If 3 and 4 still shared a factor, we could go on.
   The only common factor of 3 and 4 is 1, so 34 is the simplest form.

Check. Multiply back: 3 × 25 = 75 and 4 × 25 = 100. ✓

Watch out. Divide the top and the bottom. Subtracting the same number from both changes the fraction.

Key words. To simplify a fraction is to write it with smaller numbers. A common factor is a number that divides exactly into both the top and the bottom. The simplest form is when the only common factor is 1.

Method. Divide the top and the bottom by a common factor. The biggest common factor (the highest common factor, HCF) does it in one go.

1. List the factors of 8 and of 100. A factor divides exactly into the number. We need the factors both numbers share (the common factors).
   Factors of 8: 1, 2, 4, 8
   Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
   Common factors: 1, 2, 4
2. Pick the biggest common factor: 4. Divide the top and the bottom by 4. Dividing both numbers by the same number does not change the value of the fraction. It just writes it with smaller numbers.
   8100 = 8 ÷ 4100 ÷ 4 = 225
3. Check it is in its simplest form. If 2 and 25 still shared a factor, we could go on.
   The only common factor of 2 and 25 is 1, so 225 is the simplest form.

Check. Multiply back: 2 × 4 = 8 and 25 × 4 = 100. ✓

Watch out. Divide the top and the bottom. Subtracting the same number from both changes the fraction.

Key words. To simplify a fraction is to write it with smaller numbers. A common factor is a number that divides exactly into both the top and the bottom. The simplest form is when the only common factor is 1.

Method. Divide the top and the bottom by a common factor. The biggest common factor (the highest common factor, HCF) does it in one go.

1. List the factors of 36 and of 100. A factor divides exactly into the number. We need the factors both numbers share (the common factors).
   Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
   Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
   Common factors: 1, 2, 4
2. Pick the biggest common factor: 4. Divide the top and the bottom by 4. Dividing both numbers by the same number does not change the value of the fraction. It just writes it with smaller numbers.
   36100 = 36 ÷ 4100 ÷ 4 = 925
3. Check it is in its simplest form. If 9 and 25 still shared a factor, we could go on.
   The only common factor of 9 and 25 is 1, so 925 is the simplest form.

Check. Multiply back: 9 × 4 = 36 and 25 × 4 = 100. ✓

Watch out. Divide the top and the bottom. Subtracting the same number from both changes the fraction.

Key words. To simplify a fraction is to write it with smaller numbers. A common factor is a number that divides exactly into both the top and the bottom. The simplest form is when the only common factor is 1.

Method. A fraction is in its simplest form when the only number that divides into both the top and the bottom is 1.

1. List the factors of 4 and of 9. A factor divides exactly into the number. We need the factors both numbers share (the common factors).
   Factors of 4: 1, 2, 4
   Factors of 9: 1, 3, 9
   Common factors: 1
2. Look for a common factor bigger than 1. If the only common factor is 1, we cannot make the numbers smaller.
   The only common factor is 1, so 49 is already in its simplest form.
3. Write the answer.
   49

Check. There is no whole number bigger than 1 that goes into both numbers. ✓

Watch out. Do not simplify just because the numbers are odd or even. Always look for a common factor.

Key words. To simplify a fraction is to write it with smaller numbers. A common factor is a number that divides exactly into both the top and the bottom. The simplest form is when the only common factor is 1.

Method. Divide the top and the bottom by a common factor. The biggest common factor (the highest common factor, HCF) does it in one go.

1. List the factors of 6 and of 10. A factor divides exactly into the number. We need the factors both numbers share (the common factors).
   Factors of 6: 1, 2, 3, 6
   Factors of 10: 1, 2, 5, 10
   Common factors: 1, 2
2. Pick the biggest common factor: 2. Divide the top and the bottom by 2. Dividing both numbers by the same number does not change the value of the fraction. It just writes it with smaller numbers.
   610 = 6 ÷ 210 ÷ 2 = 35
3. Check it is in its simplest form. If 3 and 5 still shared a factor, we could go on.
   The only common factor of 3 and 5 is 1, so 35 is the simplest form.

Check. Multiply back: 3 × 2 = 6 and 5 × 2 = 10. ✓

Watch out. Divide the top and the bottom. Subtracting the same number from both changes the fraction.

Key words. To simplify a fraction is to write it with smaller numbers. A common factor is a number that divides exactly into both the top and the bottom. The simplest form is when the only common factor is 1.

Method. A fraction is in its simplest form when the only number that divides into both the top and the bottom is 1.

1. List the factors of 7 and of 15. A factor divides exactly into the number. We need the factors both numbers share (the common factors).
   Factors of 7: 1, 7
   Factors of 15: 1, 3, 5, 15
   Common factors: 1
2. Look for a common factor bigger than 1. If the only common factor is 1, we cannot make the numbers smaller.
   The only common factor is 1, so 715 is already in its simplest form.
3. Write the answer.
   715

Check. There is no whole number bigger than 1 that goes into both numbers. ✓

Watch out. Do not simplify just because the numbers are odd or even. Always look for a common factor.

Key words. To simplify a fraction is to write it with smaller numbers. A common factor is a number that divides exactly into both the top and the bottom. The simplest form is when the only common factor is 1.

Method. Divide the top and the bottom by a common factor. The biggest common factor (the highest common factor, HCF) does it in one go.

1. List the factors of 9 and of 12. A factor divides exactly into the number. We need the factors both numbers share (the common factors).
   Factors of 9: 1, 3, 9
   Factors of 12: 1, 2, 3, 4, 6, 12
   Common factors: 1, 3
2. Pick the biggest common factor: 3. Divide the top and the bottom by 3. Dividing both numbers by the same number does not change the value of the fraction. It just writes it with smaller numbers.
   912 = 9 ÷ 312 ÷ 3 = 34
3. Check it is in its simplest form. If 3 and 4 still shared a factor, we could go on.
   The only common factor of 3 and 4 is 1, so 34 is the simplest form.

Check. Multiply back: 3 × 3 = 9 and 4 × 3 = 12. ✓

Watch out. Divide the top and the bottom. Subtracting the same number from both changes the fraction.

Key words. To simplify a fraction is to write it with smaller numbers. A common factor is a number that divides exactly into both the top and the bottom. The simplest form is when the only common factor is 1.

Method. A fraction is in its simplest form when the only number that divides into both the top and the bottom is 1.

1. List the factors of 11 and of 20. A factor divides exactly into the number. We need the factors both numbers share (the common factors).
   Factors of 11: 1, 11
   Factors of 20: 1, 2, 4, 5, 10, 20
   Common factors: 1
2. Look for a common factor bigger than 1. If the only common factor is 1, we cannot make the numbers smaller.
   The only common factor is 1, so 1120 is already in its simplest form.
3. Write the answer.
   1120

Check. There is no whole number bigger than 1 that goes into both numbers. ✓

Watch out. Do not simplify just because the numbers are odd or even. Always look for a common factor.

Key words. To simplify a fraction is to write it with smaller numbers. A common factor is a number that divides exactly into both the top and the bottom. The simplest form is when the only common factor is 1.

Method. Divide the top and the bottom by a common factor. The biggest common factor (the highest common factor, HCF) does it in one go.

1. Write the fraction: the part over the whole. The part is 12 and the whole class is 30. The part goes on top and the whole goes on the bottom.
   1230
2. List the factors of 12 and of 30. A factor divides exactly into the number. We need the factors both numbers share (the common factors).
   Factors of 12: 1, 2, 3, 4, 6, 12
   Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
   Common factors: 1, 2, 3, 6
3. Pick the biggest common factor: 6. Divide the top and the bottom by 6. Dividing both numbers by the same number does not change the value of the fraction. It just writes it with smaller numbers.
   1230 = 12 ÷ 630 ÷ 6 = 25
4. Check it is in its simplest form. If 2 and 5 still shared a factor, we could go on.
   The only common factor of 2 and 5 is 1, so 25 is the simplest form.

Check. Multiply back: 2 × 6 = 12 and 5 × 6 = 30. ✓

Watch out. Divide the top and the bottom. Subtracting the same number from both changes the fraction.

Key words. To simplify a fraction is to write it with smaller numbers. A common factor is a number that divides exactly into both the top and the bottom. The simplest form is when the only common factor is 1.

Method. Divide the top and the bottom by a common factor. The biggest common factor (the highest common factor, HCF) does it in one go.

1. Write the fraction: the part over the whole. The part is 18 pages and the whole comic is 24 pages. The part goes on top and the whole goes on the bottom.
   1824
2. List the factors of 18 and of 24. A factor divides exactly into the number. We need the factors both numbers share (the common factors).
   Factors of 18: 1, 2, 3, 6, 9, 18
   Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
   Common factors: 1, 2, 3, 6
3. Pick the biggest common factor: 6. Divide the top and the bottom by 6. Dividing both numbers by the same number does not change the value of the fraction. It just writes it with smaller numbers.
   1824 = 18 ÷ 624 ÷ 6 = 34
4. Check it is in its simplest form. If 3 and 4 still shared a factor, we could go on.
   The only common factor of 3 and 4 is 1, so 34 is the simplest form.

Check. Multiply back: 3 × 6 = 18 and 4 × 6 = 24. ✓

Watch out. Divide the top and the bottom. Subtracting the same number from both changes the fraction.

Key words. To simplify a fraction is to write it with smaller numbers. A common factor is a number that divides exactly into both the top and the bottom. The simplest form is when the only common factor is 1.

Method. Divide the top and the bottom by a common factor. The biggest common factor (the highest common factor, HCF) does it in one go.

1. Write the fraction: the part over the whole. The part is 15 stickers and the whole pack is 45. The part goes on top and the whole goes on the bottom.
   1545
2. List the factors of 15 and of 45. A factor divides exactly into the number. We need the factors both numbers share (the common factors).
   Factors of 15: 1, 3, 5, 15
   Factors of 45: 1, 3, 5, 9, 15, 45
   Common factors: 1, 3, 5, 15
3. Pick the biggest common factor: 15. Divide the top and the bottom by 15. Dividing both numbers by the same number does not change the value of the fraction. It just writes it with smaller numbers.
   1545 = 15 ÷ 1545 ÷ 15 = 13
4. Check it is in its simplest form. If 1 and 3 still shared a factor, we could go on.
   The only common factor of 1 and 3 is 1, so 13 is the simplest form.

Check. Multiply back: 1 × 15 = 15 and 3 × 15 = 45. ✓

Watch out. Divide the top and the bottom. Subtracting the same number from both changes the fraction.

Key words. To simplify a fraction is to write it with smaller numbers. A common factor is a number that divides exactly into both the top and the bottom. The simplest form is when the only common factor is 1.

Method. Divide the top and the bottom by a common factor. The biggest common factor (the highest common factor, HCF) does it in one go.

1. Write the fraction: the part over the whole. The part is 20 cm and the whole ribbon is 50 cm. The part goes on top and the whole goes on the bottom.
   2050
2. List the factors of 20 and of 50. A factor divides exactly into the number. We need the factors both numbers share (the common factors).
   Factors of 20: 1, 2, 4, 5, 10, 20
   Factors of 50: 1, 2, 5, 10, 25, 50
   Common factors: 1, 2, 5, 10
3. Pick the biggest common factor: 10. Divide the top and the bottom by 10. Dividing both numbers by the same number does not change the value of the fraction. It just writes it with smaller numbers.
   2050 = 20 ÷ 1050 ÷ 10 = 25
4. Check it is in its simplest form. If 2 and 5 still shared a factor, we could go on.
   The only common factor of 2 and 5 is 1, so 25 is the simplest form.

Check. Multiply back: 2 × 10 = 20 and 5 × 10 = 50. ✓

Watch out. Divide the top and the bottom. Subtracting the same number from both changes the fraction.

Key words. Always means true every time. Never means false every time. Sometimes means true for some numbers and false for others.

Method. Test the statement with some numbers. If it is always true, never true, or true for some numbers only, that gives the answer.

1. Try some examples. Testing numbers helps us see if the statement is true every time.
   24 = 12 (divide by 2)
   610 = 35 (divide by 2)
   1416 = 78 (divide by 2)
2. Decide: always, sometimes or never? If the top and the bottom are both even, they are both in the 2 times table, so 2 is always a common factor.
   Always

Check. Each example was divided by 2. ✓

Watch out. To show a statement is “always” true you need a reason. A few examples are not enough to prove it, but one counter-example shows it is not always true.

Key words. Always means true every time. Never means false every time. Sometimes means true for some numbers and false for others.

Method. Test the statement with some numbers. If it is always true, never true, or true for some numbers only, that gives the answer.

1. Try some examples. Testing numbers helps us see if the statement is true every time.
   37: factors of 3 are 1, 3 and factors of 7 are 1, 7. Only 1 is common.
   511: only 1 is common.
   613: only 1 is common.
2. Decide: always, sometimes or never? A prime number only has factors 1 and itself. In a proper fraction the top is smaller than the bottom, so the only common factor is 1.
   Never

Check. We cannot find a proper fraction like this that simplifies. ✓

Watch out. To show a statement is “always” true you need a reason. A few examples are not enough to prove it, but one counter-example shows it is not always true.