Add and subtract related fractions

The units must match

Half a strip and one quarter of an equal strip can be combined by working in quarters. One half is two quarters, so:

The denominator tells the size of the part. Adding one half and one quarter is not the same as adding one piece and one piece of an unspecified size.

Choose the smaller part as a common unit

For 5/6-1/3, thirds can be split into sixths: 1/3 = 2/6. Now remove two sixths from five sixths:

For these related fractions, one given denominator is a multiple of the other: six is a multiple of three. Here one given denominator works for both fractions. The given denominators do not exceed 12, and these examples remain within one whole.

Check your understanding 1 Rename before adding

Find 1/4 + 3/8. Draw one whole strip to check.

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One quarter is two eighths. So 1/4 + 3/8 = 2/8 + 3/8 = 5/8. In a strip split into eight equal parts, mark two parts and then three more.

Read what is left

A bottle is full. One third of its water is poured out, then another one sixth of the original full bottle is poured out. The poured amounts use the same whole.

The total poured out is 1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2. Half the original full bottle remains.

If the second fraction referred instead to the water remaining after the first pour, it would name a different amount. Identify the whole before calculating.

Check your understanding 2 Check a tempting answer

Ravi writes 3/4-1/8 = 2/2. Find the correct result and explain why his numerator and denominator subtractions do not measure what remains.

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Rename 3/4 as 6/8. Then 6/8-1/8 = 5/8. The whole is still split into eighths; subtracting denominator labels changes the size of the unit without justification.

Try without a drawn strip

Find 5/6-1/2. Check your answer by adding back the half you removed.