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Year 6

Why 1/2 + 1/4 makes 3/4, not 2/6

Adding fractions: how do you add fractions with different denominators? Make the denominators (bottom numbers) match, then add the numerators (top numbers). Most Year 6 classes are working on fractions around now.

Why 1/2 + 1/4 makes 3/4, not 2/6. Text slide. Fractions only add when the denominators match. The fraction 1/4 with the top labelled numerator, how many parts you have, and the bottom labelled denominator, how many equal parts make 1 whole. A bar in halves with 1 shaded and a bar in quarters with 1 shaded: the half is bigger. 1/2 times 2 on the top and bottom makes 2/4. Then 2/4 + 1/4 = 3/4: add the numerators, keep the denominator. Wrong, in red: 1/2 + 1/4 = 2/6 adds the denominators. Right: 2/4 + 1/4 = 3/4 adds the numerators. Working on 1/3 + 1/4: 1/3 times 4 top and bottom makes 4/12; 1/4 times 3 makes 3/12; 4/12 + 3/12 = 7/12. Ruled bars: 1/2 and 1/4 shaded, and 3/4 shaded once the half bar is marked in quarters. Text slide asking to send to the Year 6 class group.

The method in words

The 2 steps for 1/2 + 1/4:

  1. Make the denominators match. Multiply the top and bottom of 1/2 by 2: 1/2 = 2/4
  2. Add the numerators and keep the denominator: 2/4 + 1/4 = 3/4

The common slip is adding the denominators too. 1/2 + 1/4 isn't 2/6: the denominator says how many equal parts make 1 whole, so it stays 4, and 2 quarters plus 1 quarter is 3 quarters.

For harder pairs, find a number both denominators go into. For 1/3 + 1/4 that's 12. Multiply 1/3 by 4, top and bottom, to get 4/12, and 1/4 by 3 to get 3/12. Then 4/12 + 3/12 = 7/12.

Try it with a ruler: draw 2 bars 16 cm long. Mark one every 8 cm and shade 1 part, the other every 4 cm and shade 1. Mark the first bar every 4 cm too, and count the shaded quarters: 3.

Sources: Oak National Academy, Year 6 lesson "Add and subtract non-related fractions with different denominators"; national curriculum for maths, Year 6. Contains public sector information licensed under the Open Government Licence v3.0.

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